Applied Statistical Time Series Analysis (more than just data)

Description

Contains data sets and scripts for analyzing time series in both the frequency and time domains including state space modeling as well as supporting the texts Time Series Analysis and Its Applications: With R Examples (5th ed, 2025) and Time Series: A Data Analysis Approach Using R, (1st ed, 2019).

Details

Warning

If loaded, the dplyr package corrupts the base scripts filter and lag among other things. In this case, whenever you analyze time series data, we suggest you either:

(1) Detach it:
⁠ detach(package:dplyr)⁠

(2) If you want to use dplyr, fix it: ⁠ library(dplyr, exclude = c("filter", "lag")) # load it but remove the culprits Lag <- dplyr::lag # and do what the dplyr ... Filter <- dplyr::filter # ... maintainer refuses to do⁠
then use Lag and Filter for dplyr scripts
and lag and filter can be use as originally intended

(3) Or just take back the commands:
⁠ filter = stats::filter⁠
⁠ lag = stats::lag ⁠

In this case you can still use
⁠ Lag <- dplyr::lag⁠
and
⁠ Filter <- dplyr::filter⁠
for dpylr.

Author(s)

David Stoffer <stoffer@pitt.edu>

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Convert ARMA Process to Infinite AR Process

Description

Gives the \pi-weights in the invertible representation of an ARMA model.

Usage

ARMAtoAR(ar = 0, ma = 0, lag.max=20)

Arguments

Value

A vector of coefficients.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

ARMAtoAR(ar=.9, ma=.5, 10)

Daily Returns of Three Banks

Description

Daily returns of three banks, 1. Bank of America [boa], 2. Citibank [citi], and 3. JP Morgan Chase [jpm], from 2005 to 2017.

Format

The format is: Time-Series [1:3243, 1:3] from 2005 to 2017: -0.01378 -0.01157 -0.00155 -0.01084 0.01252 ... with column names "boa" "citi" "jpm" .

Source

Gong & Stoffer (2021). A Note on Efficient Fitting of Stochastic Volatility Models. Journal of Time Series Analysis, 42(2), 186-200.

https://github.com/nickpoison/Stochastic-Volatility-Models

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

tsplot(BCJ, col=2:4)

Entire Epstein-Barr Virus (EBV) Nucleotide Sequence

Description

EBV nucleotide sequence - 172281 bp as a single string

Format

The format is: chr "AGAATTCGTCTT ..."

Note

EBV is not useful on its own, but using 'dna2vector', different regions can be explored. For example, ebv = dna2vector(EBV)

Source

https://www.ncbi.nlm.nih.gov/nuccore/V01555.2

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

dna2vector

EM Algorithm for State Space Models

Description

Estimation of the parameters in general linear state space models via the EM algorithm. Missing data may be entered as NA or as zero (0), however, use NAs if zero (0) can be an observation. Inputs in both the state and observation equations are allowed. This script replaces EM0 and EM1.

Usage

EM(y, A, mu0, Sigma0, Phi, Q, R, Ups = NULL, Gam = NULL, input = NULL, 
    max.iter = 100, tol = 1e-04)

Arguments

Details

This script replaces EM0 and EM1 by combining all cases and allowing inputs in the state and observation equations. It uses version 1 of the new Ksmooth script (hence correlated errors is not allowed).

The states x_t are p-dimensional, the data y_t are q-dimensional, and the inputs u_t are r-dimensional for t=1, \dots, n. The initial state is x_0 \sim N(\mu_0, \Sigma_0).

The general model is

x_t = \Phi x_{t-1} + \Upsilon u_{t} + w_t \quad w_t \sim iid\ N(0, Q)

y_t = A_t x_{t-1} + \Gamma u_{t} + v_t \quad v_t \sim iid\ N(0, R)

where w_t \perp v_t. The observation noise covariance matrix is assumed to be diagonal and it is forced to diagonal otherwise.

The measurement matrices A_t can be constant or time varying. If time varying, they should be entered as an array of dimension dim = c(q,p,n). Otherwise, just enter the constant value making sure it has the appropriate q \times p dimension.

Value

Note

The script does not allow for constrained estimation directly, however, constrained estimation is possible with some extra manipulations. There is an example of constrained estimation using EM at FUN WITH ASTSA, where the fun never stops.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

Kfilter, Ksmooth

Examples

# example used for ssm() 
# x[t] = Ups + Phi x[t-1] + w[t]
# y[t] = x[t] + v[t]
y = gtemp_land  
A = 1; Phi = 1; Ups = 0.01
Q = 0.001; R = 0.01
mu0 = -0.6; Sigma0 = 0.02
input = rep(1, length(y))
( em = EM(y, A, mu0, Sigma0, Phi, Q, R, Ups, Gam=NULL, input) ) 

El Nino - Southern Oscillation Index

Description

Southern Oscillation Index (SOI), 1/1951 to 10/2022; anomalies are departures from the 1981-2010 base period.

Format

The format is: Time-Series [1:862] from 1951 to 2022: 2.0 1.1 -0.3 -0.8 -1.1 -0.7 -1.5 -0.3 -0.7 -0.7 ...

Details

The \textrm{El Ni\~no - Southern Oscillation (ENSO)} is a recurring climate pattern involving changes in the temperature of waters in the central and eastern tropical Pacific Ocean. This data set is an update to soi.

Source

https://www.ncei.noaa.gov/access/monitoring/enso/soi

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

soi

Seismic Trace of Earthquake number 5

Description

Seismic trace of an earthquake [two phases or arrivals along the surface, the primary wave (t = 1,\dots,1024) and the shear wave (t = 1025,\dots,2048)] recorded at a seismic station.

Format

The format is: Time-Series [1:2048] from 1 to 2048: 0.01749 0.01139 0.01512 0.01477 0.00651 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

eqexp

Earthquake Counts

Description

Series of annual counts of major earthquakes (magnitude 7 and above) in the world between 1900 and 2006.

Format

The format is: Time-Series [1:107] from 1900 to 2006: 13 14 8 10 16 26 ...

Source

Zucchini and MacDonald (2009). Hidden Markov Models for Time Series: An Introduction using R. CRC Press.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Effective Sample Size (ESS)

Description

Estimates the ESS of a given vector of samples.

Usage

ESS(trace, tol = 1e-08, BIC = TRUE)

Arguments

Details

Uses spec.ic to estimate the spectrum of the input at frequency zero (spec0). Then, ESS is estimated as ESS = length(trace)*var(trace)/spec0.

Value

Returns the estimated ESS of the input.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

# Fit an AR(2) to the Recruitment series
u = ar.mcmc(rec, porder=2, n.iter=1000, plot=FALSE) 
# then calculate the ESSs 
apply(u, 2, ESS)

Seismic Trace of Explosion number 6

Description

Seismic trace of an explosion [two phases or arrivals along the surface, the primary wave (t = 1,\dots,1024) and the shear wave (t = 1025,\dots,2048)] recorded at a seismic station.

Format

The format is: Time-Series [1:2048] from 1 to 2048: -0.001837 -0.000554 -0.002284 -0.000303 -0.000721 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

eqexp

Basic False Discovery Rate

Description

Computes the basic false discovery rate given a vector of p-values and returns the index of the maximal p-value satisfying the FDR condition.

Usage

FDR(pvals, qlevel = 0.05)

Arguments

Value

Note

This is used primarily in Chapter 7.

Source

Built off of https://www.stat.berkeley.edu/~paciorek/code/fdr/fdr.R.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Quarterly U.S. GDP - updated to 2023

Description

Seasonally adjusted quarterly U.S. GDP from 1947(1) to 2023(1).

Format

The format is: Time-Series [1:305] from 1947 to 2023: 243.164 245.968 249.585 259.745 ...

Source

https://fred.stlouisfed.org/series/GDP

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

gdp, GNP, gnp

Quarterly U.S. GNP - updated to 2023

Description

Seasonally adjusted quarterly U.S. GNP from 1947(1) to 2003(1).

Format

The format is: Time-Series [1:305] from 1947 to 2023: 244.142 247.063 250.716 260.981 ...

Source

https://fred.stlouisfed.org/series/GNP

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

gnp, GDP, gdp

A Better Add Grid to a Plot

Description

Adds a grid to an existing plot with major and minor ticks. Works like R graphics grid() but the grid lines are solid and gray and minor ticks are produced by default.

Usage

Grid(nx = NULL, ny = nx, col = gray(0.9), lty = 1, lwd = par("lwd"), equilogs = TRUE,
    minor = TRUE, nxm = 2, nym = 2, tick.ratio = 0.5, xm.grid = TRUE, ym.grid = TRUE, ...)

Arguments

Author(s)

D.S. Stoffer

Source

The code for grid() in R graphics and minor.tick() from the Hmisc package were combined.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

grid

Hematocrit Levels

Description

HCT: Measurements made for 91 days on the three variables, log(white blood count) [WBC], log(platelet) [PLT] and hematocrit [HCT]. Missing data code is 0 (zero).

Format

The format is: Time-Series [1:91] from 1 to 91: 30 30 28.5 34.5 34 32 30.5 31 33 34 ...

Details

See Examples 6.1 and 6.9 for more details.

Source

Jones, R.H. (1984). Fitting multivariate models to unequally spaced data. In Time Series Analysis of Irregularly Observed Data, pp. 158-188. E. Parzen, ed. Lecture Notes in Statistics, 25, New York: Springer-Verlag.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

blood, PLT, WBC

Snowshoe Hare

Description

This is one of the classic studies of predator-prey interactions, the 90-year data set is the number, in thousands, of snowshoe hare pelts purchased by the Hudson's Bay Company of Canada. While this is an indirect measure of predation, the assumption is that there is a direct relationship between the number of pelts collected and the number of hare and lynx in the wild.

Usage

data("Hare")

Format

The format is: Time-Series [1:91] from 1845 to 1935: 19.6 19.6 19.6 12 28 ...

Note

This data set pairs with Lynx. The data are in units of one thousand.

Source

From Odum's "Fundamentals of Ecology", p. 191. Data listed at:
people.whitman.edu/~hundledr/courses/M250F03/LynxHare.txt.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

Lynx

Quick Kalman Filter

Description

Returns both the predicted and filtered values for various linear state space models; it also evaluates the likelihood at the given parameter values. This script replaces Kfilter0, Kfilter1, and Kfilter2

Usage

Kfilter(y, A, mu0, Sigma0, Phi, sQ, sR, Ups = NULL, Gam = NULL, 
         input = NULL, S = NULL, version = 1)

Arguments

Details

This script replaces Kfilter0, Kfilter1, and Kfilter2 by combining all cases. The major difference is how to specify the covariance matrices; in particular, sQ = t(cQ) and sR = t(cR) where cQ and cR were used in Kfilter0-1-2 scripts.

The states x_t are p-dimensional, the data y_t are q-dimensional, and the inputs u_t are r-dimensional for t=1, \dots, n. The initial state is x_0 \sim N(\mu_0, \Sigma_0).

The measurement matrices A_t can be constant or time varying. If time varying, they should be entered as an array of dimension dim = c(q,p,n). Otherwise, just enter the constant value making sure it has the appropriate q \times p dimension.

Version 1 (default): The general model is

x_t = \Phi x_{t-1} + \Upsilon u_{t} + sQ\, w_t \quad w_t \sim iid\ N(0,I)

y_t = A_t x_{t-1} + \Gamma u_{t} + sR\, v_t \quad v_t \sim iid\ N(0,I)

where w_t \perp v_t. Consequently the state noise covariance matrix is Q = sQ\, sQ' and the observation noise covariance matrix is R = sR\, sR' and sQ, sR do not have to be square as long as everything is conformable. Notice the specification of the state and observation covariances has changed from the original scripts.

NOTE: If it is easier to model in terms of Q and R, simply input the square root matrices sQ = Q %^% .5 and sR = R %^% .5.

Version 2 (correlated errors): The general model is

x_{t+1} = \Phi x_{t} + \Upsilon u_{t+1} + sQ\, w_t \quad w_t \sim iid\ N(0,I)

y_t = A_t x_{t-1} + \Gamma u_{t} + sR\, v_t \quad v_t \sim iid\ N(0,I)

where S = {\rm Cov}(w_t, v_t), and NOT {\rm Cov}(sQ\, w_t, sR\, v_t).

NOTE: If it is easier to model in terms of Q and R, simply input the square root matrices sQ = Q %^% .5 and sR = R %^% .5.

Note that in either version, sQ\, w_t has to be p-dimensional, but w_t does not, and sR\, v_t has to be q-dimensional, but v_t does not.

Value

Time varying values are returned as arrays.

Note

Note that Kfilter is similar to Kfilter-0-1-2 except that only the essential values need to be entered (and come first in the statement); the optional values such as input are set to NULL by default if they are not needed. This version is faster than the older versions. The biggest change was to how the covarainces are specified. For example, if you have code that used Kfilter1, just use sQ = t(cQ) and sR = t(cR) here.

NOTE: If it is easier to model in terms of Q and R, simply input the square root matrices sQ = Q%^%.5 and sR = R%^%.5.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

Ksmooth

Examples

# generate some data
 set.seed(1)
 sQ  = 1; sR = 3; n = 100  
 mu0 = 0; Sigma0 = 10; x0 = rnorm(1,mu0,Sigma0)
 w = rnorm(n); v = rnorm(n)
 x = c(x0 + sQ*w[1]);  y = c(x[1] + sR*v[1])   # initialize
for (t in 2:n){
  x[t] = x[t-1] + sQ*w[t]
  y[t] = x[t] + sR*v[t]   
  }
# run and plot the filter  
run = Kfilter(y, A=1, mu0, Sigma0, Phi=1, sQ, sR)
tsplot(cbind(y,run$Xf), spaghetti=TRUE, type='o', col=c(4,6), pch=c(1,NA), margins=1)
# CRAN tests need extra white space :( so margins=1 above is not necessary otherwise
legend('topleft', legend=c("y(t)","Xf(t)"), lty=1, col=c(4,6), bty="n", pch=c(1,NA))

Quick Kalman Smoother

Description

Returns the smoother values for various linear state space models. The predicted and filtered values and the likelihood at the given parameter values are also returned (via Kfilter). This script replaces Ksmooth0, Ksmooth1, and Ksmooth2.

Usage

Ksmooth(y, A, mu0, Sigma0, Phi, sQ, sR, Ups = NULL, Gam = NULL, 
         input = NULL, S = NULL, version = 1)

Arguments

Details

This script replaces Ksmooth0, Ksmooth1, and Ksmooth2 by combining all cases. The major difference is how to specify the covariance matrices; in particular, sQ = t(cQ) and sR = t(cR) where cQ and cR were used in Kfilter0-1-2 scripts.

The states x_t are p-dimensional, the data y_t are q-dimensional, and the inputs u_t are r-dimensional for t=1, \dots, n. The initial state is x_0 \sim N(\mu_0, \Sigma_0).

The measurement matrices A_t can be constant or time varying. If time varying, they should be entered as an array of dimension dim = c(q,p,n). Otherwise, just enter the constant value making sure it has the appropriate q \times p dimension.

Version 1 (default): The general model is

x_t = \Phi x_{t-1} + \Upsilon u_{t} + sQ\, w_t \quad w_t \sim iid\ N(0,I)

y_t = A_t x_{t-1} + \Gamma u_{t} + sR\, v_t \quad v_t \sim iid\ N(0,I)

where w_t \perp v_t. Consequently the state noise covariance matrix is Q = sQ\, sQ' and the observation noise covariance matrix is R = sR\, sR' and sQ, sR do not have to be square as long as everything is conformable. Notice the specification of the state and observation covariances has changed from the original scripts.

NOTE: If it is easier to model in terms of Q and R, simply input the square root matrices sQ = Q %^% .5 and sR = R %^% .5.

Version 2 (correlated errors): The general model is

x_{t+1} = \Phi x_{t} + \Upsilon u_{t+1} + sQ\, w_t \quad w_t \sim iid\ N(0,I)

y_t = A_t x_{t-1} + \Gamma u_{t} + sR\, v_t \quad v_t \sim iid\ N(0,I)

where S = {\rm Cov}(w_t, v_t), and NOT {\rm Cov}(sQ\, w_t, sR\, v_t).

NOTE: If it is easier to model in terms of Q and R, simply input the square root matrices sQ = Q %^% .5 and sR = R %^% .5.

Note that in either version, sQ\, w_t has to be p-dimensional, but w_t does not, and sR\, v_t has to be q-dimensional, but v_t does not.

Value

Time varying values are returned as arrays.

Note

Note that Ksmooth is similar to Ksmooth-0-1-2 except that only the essential values need to be entered (and come first in the statement); the optional values such as input are set to NULL by default if they are not needed. This version is faster than the older versions. The biggest change was to how the covarainces are specified. For example, if you have code that used Ksmooth1, just use sQ = t(cQ) and sR = t(cR) here.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

Kfilter

Examples

# generate some data
 set.seed(1)
 sQ  = 1; sR = 3; n = 100  
 mu0 = 0; Sigma0 = 10; x0 = rnorm(1,mu0,Sigma0)
 w = rnorm(n); v = rnorm(n)
 x = c(x0 + sQ*w[1]);  y = c(x[1] + sR*v[1])   # initialize
for (t in 2:n){
  x[t] = x[t-1] + sQ*w[t]
  y[t] = x[t] + sR*v[t]   
  }
# run and plot the smoother  
run = Ksmooth(y, A=1, mu0, Sigma0, Phi=1, sQ, sR)
tsplot(cbind(y,run$Xs), spaghetti=TRUE, type='o', col=c(4,6), pch=c(1,NA), margins=1)
# CRAN tests need extra white space :( so margins=1 above is not necessary otherwise
legend('topleft', legend=c("y(t)","Xs(t)"), lty=1, col=c(4,6), bty="n", pch=c(1,NA))

Lagged Regression

Description

Performs lagged regression as discussed in Chapter 4.

Usage

LagReg(input, output, L = c(3, 3), M = 40, threshold = 0, 
        inverse = FALSE)

Arguments

Details

For a bivariate series, input is the input series and output is the output series. The degree of smoothing for the spectral estimate is given by L; see spans in the help file for spec.pgram. The number of terms used in the lagged regression approximation is given by M, which must be even. The threshold value is the cut-off used to set small (in absolute value) regression coeffcients equal to zero (it is easiest to run LagReg twice, once with the default threshold of zero, and then again after inspecting the resulting coeffcients and the corresponding values of the CCF). Setting inverse=TRUE will fit a forward-lagged regression; the default is to run a backward-lagged regression. The script is based on code that was contributed by Professor Doug Wiens, Department of Mathematical and Statistical Sciences, University of Alberta.

Value

Graphs of the estimated impulse response function, the CCF, and the output with the predicted values superimposed.

Note

See Chapter 4 of the text for an example.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Canadian Lynx

Description

This is one of the classic studies of predator-prey interactions, the 90-year data set is the number, in thousands, of lynx pelts purchased by the Hudson's Bay Company of Canada. While this is an indirect measure of predation, the assumption is that there is a direct relationship between the number of pelts collected and the number of hare and lynx in the wild.

Usage

data("Lynx")

Format

The format is: Time-Series [1:91] from 1845 to 1935: 30.1 45.1 49.1 39.5 21.2 ...

Note

The data are in units of one thousand. This data set pairs with Hare and is NOT the same as lynx.

Source

From Odum's "Fundamentals of Ecology", p. 191. Additional information at
http://people.whitman.edu/~hundledr/courses/M250F03/M250.html

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

Hare

Multivariate El Nino/Southern Oscillation Index (version 1)

Description

Bimonthly MEI values, starting with Dec1949/Jan1950 through Oct/Nov2019. All values are normalized for each bimonthly season so that the 44 values from 1950 to 1993 have an average of zero and a standard deviation of 1. Larger values correspond to warmer temperatures (unlike soi and ENSO).

Format

The format is: Time-Series [1:827] from 1950 to 2019: -1.03 -1.13 -1.28 -1.07 -1.43 ...

Details

For full details, see https://psl.noaa.gov/enso/mei.old/mei.html. Multivariate ENSO Index (MEI) is a combined score on the six main observed variables over the tropical Pacific. These six variables are: sea-level pressure (P), zonal (U) and meridional (V) components of the surface wind, sea surface temperature (S), surface air temperature (A), and total cloudiness fraction of the sky (C). These observations have been collected and published in ICOADS for many years. The MEI is computed separately for each of twelve sliding bi-monthly seasons (Dec/Jan, Jan/Feb,..., Nov/Dec). After spatially filtering the individual fields into clusters, the MEI is calculated as the first unrotated Principal Component (PC) of all six observed fields combined. This is accomplished by normalizing the total variance of each field first, and then performing the extraction of the first PC on the co-variance matrix of the combined fields. In order to keep the MEI comparable, all seasonal values are standardized with respect to each season and to the 1950-93 reference period.

Source

https://psl.noaa.gov/enso/mei.old/table.html

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

soi, ENSO

Month Labels

Description

Provides labels for the (English) months of the year to be used in plotting monthly time series.

Format

The format is: chr [1:12] "J" "F" "M" "A" "M" "J" "J" "A" "S" "O" "N" "D"

Note

Hi Kids. The months of the year in English are:

January, February, March, April, May, June, July, August, September, October, November, December.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

sAR = sarima.sim(sar=.9, S=12, n=36)
tsplot(sAR, type='c')
points(sAR, pch=Months, cex=1.1, font=4, col=1:4)

Platelet Levels

Description

PLT: Measurements made for 91 days on the three variables, log(white blood count) [WBC], log(platelet) [PLT] and hematocrit [HCT]. Missing data code is 0 (zero).

Usage

data(PLT)

Format

The format is: Time-Series [1:91] from 1 to 91: 4.47 4.33 4.09 4.6 4.41 ...

Details

See Examples 6.1 and 6.9 for more details.

Source

Jones, R.H. (1984). Fitting multivariate models to unequally spaced data. In Time Series Analysis of Irregularly Observed Data, pp. 158-188. E. Parzen, ed. Lecture Notes in Statistics, 25, New York: Springer-Verlag.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

blood, HCT, WBC

Normal Quantile-Quantile Plot

Description

Produces a normal QQ plot with a line of equality and a confidence band (by default) of the input data. This is basically a prettier version of qqnorm from the stats package.

Usage

QQnorm(xdata, col = c(4, 6), ylab = "Sample Quantiles", xlab = "Theoretical Quantiles", 
        main = "Normal Q-Q Plot", ylim = NULL, ci = TRUE, width.ci = 99.995, 
        qqlwd = 1, ...)

Arguments

Details

If you want a graphic to check normality of your data in xdata, just enter QQnorm(xdata) and sit back and enjoy the beauty of this script (you may want to wear sunglasses).

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

QQnorm(log(varve))

Fit Bayesian Stochastic Volatility Model

Description

Fits a stochastic volatility model to a univariate time series of returns.

Usage

SV.mcmc(y, nmcmc = 1000, burnin = 100, init = NULL, hyper = NULL, tuning = NULL, 
         sigma_MH = NULL, npart = NULL, mcmseed = NULL)

Arguments

Details

The log-volatility process is x_t and the returns are y_t. The SV model is

x_t = \phi x_{t-1} + \sigma w_t \qquad y_t = \beta \exp\{\frac{1}{2} x_t\}\epsilon_t

where w_t and \epsilon_t are independent standard normal white noise.

The model is fit using a technique described in the paper listed below (in the Source section) where the state parameters (\phi, \sigma) are sampled simultaneously with a bivariate normal prior specified in the arguments init and hyper.

Two graphics are returned: (1) the three parameter traces with the posterior mean highlighted, their ACFs [with effective sample sizes (ESS)], and their histograms with the .025, .5, and .975 quantiles displayed, and (2) the log-volatility posterior mean along with corresponding .95 credible intervals.

Value

Returned invisibly:

Note

Except for the data, all the other inputs have defaults. The time to run and the acceptance rate are returned at the end of the analysis. The acceptance rate should be around 30% and this is easily adjusted using the tuning parameter.

Author(s)

D.S. Stoffer

Source

Gong & Stoffer (2021). A note on efficient fitting of stochastic volatility models. Journal of Time Series Analysis, 42(2), 186-200. https://github.com/nickpoison/Stochastic-Volatility-Models

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

SV.mle

Examples

## Not run: 
#--   A minimal example  --##
myrun <- SV.mcmc(sp500w)   # results in object myrun - don't forget it 

str(myrun)                 # an easy way to see the default input options

## End(Not run)

Stochastic Volatility Model with Feedback via MLE

Description

Fits a stochastic volatility model with feedback (optional) to a univariate time series of returns via quasi-MLE.

Usage

SV.mle(returns, gamma = 0, phi = 0.95, sQ = 0.1, alpha = NULL, sR0 = 1, mu1 = -3, sR1 = 2, 
        rho = NULL, feedback = FALSE)

Arguments

Details

The returns are r_t (input this). The log-volatility process is x_t and y_t = \log r_t^2.

If feedback=TRUE, the model is

x_{t+1} = \gamma r_t + \phi x_t + \sigma w_t \qquad y_t = \alpha + x_t + \eta_t

where w_t is standard normal noise. The observation error \eta_t is a mixture of two normals, N(0, \sigma_0^2) and N(\mu_1, \sigma_1^2). The state and observation noise can be correlated if \rho is given a value between -1 and 1.

If feedback=FALSE, \gamma and \rho are not included in the model.

Value

Returned invisibly:

In addition to the one step ahead predicted log-volatility, corresponding root MSPE, and table of estimates returned invisibly, the estimates and SEs are printed and a graph of (1) the data with the predicted log-volatility, and (2) the normal mixture are displayed in one graphic.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

SV.mcmc

Examples

## Not run: 

SV.mle(sp500.gr, feedback=TRUE)

SV.mle(nyse)

## End(Not run)

Signal Extraction And Optimal Filtering

Description

Performs signal extraction and optimal filtering as discussed in Chapter 4.

Usage

SigExtract(series, L = c(3, 3), M = 50, max.freq = 0.05, col = 4)

Arguments

Details

The basic function of the script, and the default setting, is to remove frequencies above 1/20 (and, in particular, the seasonal frequency of 1 cycle every 12 time points). The sampling frequency of the time series is set to unity prior to the analysis.

Value

Returns plots of (1) the original and filtered series, (2) the estiamted spectra of each series, (3) the filter coefficients and the desired and attained frequency response function. The filtered series is returned invisibly.

Note

The script is based on code that was contributed by Professor Doug Wiens, Department of Mathematical and Statistical Sciences, University of Alberta.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

U.S. Population - 1900 to 2010

Description

U.S. Population by official census, every ten years from 1900 to 2010.

Format

The format is: Time-Series [1:12] from 1900 to 2010: 76 92 106 123 132 ...

Details

The census from 2020 is not included in this data set because, by many accounts, it was a nightmare (https://www.npr.org/2022/01/15/1073338121/2020-census-interference-trump) due to the COVID-19 pandemic coupled with the fact that the Census Bureau is in the Department of Commerce, and its head is appointed by and reports directly to the POTUS, who at the time was DJ tRump: "Historians rank Trump among worst presidents in US history ... " (https://www.businessinsider.com/historians-rank-trump-among-worst-presidents-us-history-c-span-2021-6).

Source

https://www.census.gov/

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

U.S. Unemployment Rate

Description

Monthly U.S. unemployment rate in percent unemployed (Jan, 1948 - Nov, 2016, n = 827)

Format

The format is: Time-Series [1:827] from 1948 to 2017: 4 4.7 4.5 4 3.4 3.9 3.9 3.6 3.4 2.9 ...

Source

https://data.bls.gov/timeseries/LNU04000000/

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

unemp

White Blood Cell Levels

Description

WBC: Measurements made for 91 days on the three variables, log(white blood count) [WBC], log(platelet) [PLT] and hematocrit [HCT]. Missing data code is 0 (zero).

Format

The format is: Time-Series [1:91] from 1 to 91: 2.33 1.89 2.08 1.82 1.82 ...

Details

See Examples 6.1 amd 6.9 for more details.

Source

Jones, R.H. (1984). Fitting multivariate models to unequally spaced data. In Time Series Analysis of Irregularly Observed Data, pp. 158-188. E. Parzen, ed. Lecture Notes in Statistics, 25, New York: Springer-Verlag.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

blood, HCT, PLT

Plot and print ACF or PACF of a time series

Description

Produces a plot (and a printout) of the sample ACF or PACF. The zero lag value of the ACF is removed.

Usage

acf1(series, max.lag = NULL, plot = TRUE, main = NULL, ylim = NULL, pacf = FALSE,
      ylab = NULL, xlab = NULL, na.action = na.pass, ...)

Arguments

Details

Will print and/or plot the sample ACF or PACF (if pacf=TRUE). The zero lag of the ACF (which is always 1) has been removed. If plot=TRUE, a graph is produced and the values are rounded and listed. If FALSE, no graph is produced and the values are listed but not rounded by the script. The error bounds are approximate white noise bounds, -1/n \pm 2/\sqrt{n}; no other option is given.

Value

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

acf2, acfm, ccf2

Examples

acf1(rnorm(100))

acf1(sarima.sim(ar=.9), pacf=TRUE)

# show it to your mom:
acf1(soi, col=2:7, lwd=4, gg=TRUE)

Plot and print ACF and PACF of a time series

Description

Produces a simultaneous plot (and a printout) of the sample ACF and PACF on the same scale. The zero lag value of the ACF is removed.

Usage

acf2(series, max.lag = NULL, plot = TRUE, main = NULL, ylim = NULL, 
      na.action = na.pass, ...)

Arguments

Details

Will print and/or plot the sample ACF and PACF on the same scale. The zero lag of the ACF (which is always 1) has been removed. If plot=TRUE, a graph is produced and the values are rounded and listed. If FALSE, no graph is produced and the values are listed but not rounded by the script. The error bounds are approximate white noise bounds, -1/n \pm 2/\sqrt{n}; no other option is given.

Value

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

acf1, acfm, ccf2

Examples

acf2(rnorm(100))

acf2(rnorm(100), 25, main='')  # no title

acf2(rnorm(100), plot=FALSE)[,'ACF']  # print only ACF

acf2(soi, col=2:7, lwd=4, gg=TRUE)  # mother's day present

ACF and CCF for Multiple Time Series

Description

Produces a grid of plots of the sample ACF (diagonal) and CCF (off-diagonal). The values are returned invisibly.

Usage

acfm(series, max.lag = NULL,  na.action = na.pass, ylim = NULL,
      acf.highlight = TRUE, plot = TRUE, ...)

Arguments

Details

Produces a grid of plots of the sample ACF (diagonal) and CCF (off-diagonal). The plots in the grid are estimates of corr{x(t+LAG), y(t)}. Thus x leads y if LAG is positive and x lags y if LAG is negative. If plot is FALSE, then there is no graphic.

Value

The correlations are returned invisibly.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

acf1, acf2, ccf2

Examples

acfm(diff(log(econ5)), gg=TRUE, acf.highlight=FALSE)

( acfm(diff(log(econ5)), 2, plot=FALSE) )

Bootstrap Distribution of AR Model Parameters

Description

Performs a nonparametric bootstrap to obtain the distribution of the AR model parameters.

Usage

ar.boot(series, order.ar, nboot = 500, seed = NULL, plot = TRUE, col = 5)

Arguments

Details

For a specified series, finds the bootstrap distribution of the Yule-Walker estimates of \phi_1,\dots,\phi_p in the AR model specified by order.ar,

x_t = \mu + \phi_1 (x_{t-1}-\mu) + \dots + \phi_p (x_{t-p}-\mu) + w_t ,

where w_t is white noise. The data are centered by the estimate of \mu prior to the bootstrap simulations.

The script displays a number of quantiles of the bootstrapped estimates, the means, the biases, and the root mean squared errors.

Value

Returned invisibly:

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

## Not run: 

u = ar.boot(rec, 2)
head(u[[1]])       # some booted AR parameters
head(u[[2]][,1:5]) # some booted data

## End(Not run)

Fit Bayesian AR Model

Description

Uses Gibbs sampling to fit an AR model to time series data.

Usage

ar.mcmc(xdata, porder, n.iter = 1000, n.warmup = 100, plot = TRUE, col = 4, 
        prior_var_phi = 50, prior_sig_a = 1, prior_sig_b = 2, ...)

Arguments

Details

Assumes a normal-inverse gamma model,

x_t = \phi_0 + \phi_1 x_{t-1} + \dots + \phi_p x_{t-p} + \sigma z_t ,

where z_t is standard Gaussian noise. With \Phi being the (p+1)-dimensional vector of the \phis, the priors are \Phi \mid \sigma \sim N(0, \sigma^2 V_0) and \sigma^2 \sim IG(a,b), where V_0 = \gamma^2 I. Defaults are given for the hyperparameters, but the user may choose (a,b) as (prior_sig_a, prior_sig_b) and \gamma^2 as prior_var_phi.

The algorithm is efficient and converges quickly. Further details can be found in Chapter 6 of the 5th edition of the Springer text.

Value

In addition to the graphics (if plot is TRUE), the draws of each parameter (phi0, phi1, ..., sigma) are returned invisibly and various quantiles are displayed.

Author(s)

D.S. Stoffer

Source

Based on the script arp.mcmc used in Douc, Moulines, & Stoffer, D. (2014). Nonlinear Time Series: Theory, Methods and Applications with R Examples. CRC press. ISBN 9781466502253.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

## Not run: 

u = ar.mcmc(rec, 2)

tsplot(u, ncolm=2, col=4)  # plot the traces

apply(u, 2, ESS)    # effective sample sizes

## End(Not run)

AR with Missing Values

Description

Data used in Chapter 6

Format

The format is: Time-Series [1:100] with NA for missing values.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Simulated ARFIMA

Description

1000 simulated observations from an ARFIMA(1, 1, 0) model with \phi = .75 and d = .4.

Format

The format is: Time-Series [1:1000] from 1 to 1000: -0.0294 0.7487 -0.3386 -1.0332 -0.2627 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Spectral Density of an ARMA Model

Description

Gives the ARMA spectrum, tests for causality, invertibility, and common zeros.

Usage

arma.spec(ar = 0, ma = 0, var.noise = 1, n.freq = 500, main = NULL, 
           frequency = 1, ylim = NULL, plot = TRUE, ...)

Arguments

Details

The basic call is arma.spec(ar, ma) where ar and ma are vectors containing the model parameters. Use log='y' if you want the plot on a log scale. If the model is not causal or invertible an error message is given. If there are approximate common zeros, a spectrum will be displayed and a warning will be given; e.g., arma.spec(ar= .9, ma= -.9) will yield a warning and the plot will be the spectrum of white noise.

Value

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

arma.spec(ar = c(1, -.9), ma = .8)

arma.spec(ar = c(1, -.9), log='y')

arma.spec(ar = c(1, -.9), main='AR(2)', gg=TRUE, col=5, lwd=2)

arma.spec(ar=c(rep(0,11),.4), ma=.5, col=5, lwd=3, frequency=12)

astsa color palette with transparency

Description

Modifies the opacity level of the astsa color palette.

Usage

astsa.col(col = 1, alpha = 1)

Arguments

Value

a color vector using the astsa color palette at the chosen transparency level

Note

The astsa color palette is attached when the package is attached. The colors follow the R pattern of shades of: (1) black, (2) red, (3) green, (4) blue, (5) cyan, (6) magenta, (7) gold, (8) gray. The opacity of these colors can be changed easily using this script. Values are recycled, e.g., col=9 is the same as col=1.

The astsa palette was developed from two basic ideas. The first is the general idea that time series should be plotted using dark colors. The second is personal in that we prefer to anchor plots with the best blue, dodgerblue3. From there, we used the website https://www.color-hex.com/ to pick colors of type 2 to 7 that complement dodgerblue3.

Author(s)

D.S.Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

# plotting 2 series that touch (but in a nice way)
tsplot(cbind(gtemp_land, gtemp_ocean), col=astsa.col(c(4,2), .5), lwd=2, spaghetti=TRUE, 
       type='o', pch=20, ylab="Temperature Deviations", addLegend=TRUE, location='topleft',
       legend=c("Land Only", "Ocean Only"), gg=TRUE)  

# View the astsa palette
pie(rep(1,8), col=1:8, main='astsa palette', labels=1:8)
legend('topright', legend=astsa.col(1:8), fill=1:8, title='Hex Color Code')

autoParm - Structural Break Estimation Using AR Models

Description

Uses minimum description length (MDL) to fit piecewise AR processes with the goal of detecting changepoints in time series. Optimization is accomplished via a genetic algorithm (GA).

Usage

autoParm(xdata, Pi.B = NULL, Pi.C = NULL, PopSize = 70, generation = 70, P0 = 20, 
         Pi.P = 0.3, Pi.N = 0.3, NI = 7)

Arguments

Details

Details my be found in Davis, Lee, & Rodriguez-Yam (2006). Structural break estimation for nonstationary time series models. JASA, 101, 223-239. doi:10.1198/016214505000000745

Value

Returns three values, (1) the breakpoints including the endpoints, (2) the number of segments, and (3) the segment AR orders. See the examples.

Note

The GA is a stochastic optimization procedure and consequently will give different results at each run. It is a good idea to run the algorithm a few times before coming to a final decision.

Author(s)

D.S. Stoffer

Source

The code is adapted from R code provided to us by Rex Cheung (https://www.linkedin.com/in/rexcheung).

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

autoSpec

Examples

## Not run: 

##-- simulation
x1 = sarima.sim(ar=c(1.69, -.81), n=500)
x2 = sarima.sim(ar=c(1.32, -.81), n=500) 
x = c(x1, x2)

##-- look at the data
tsplot(x)

##-- run procedure
autoParm(x)

##-- output (yours will be slightly different - 
##--         the nature of GA) 
# returned breakpoints include the endpoints 
# $breakpoints
# [1]    1  514 1000
# 
# $number_of_segments
# [1] 2
# 
# $segment_AR_orders
# [1] 2 2

## End(Not run)

autoSpec - Changepoint Detection of Narrowband Frequency Changes

Description

Uses changepoint detection to discover if there have been slight changes in frequency in a time series. The autoSpec procedure uses minimum description length (MDL) to do nonparametric spectral estimation with the goal of detecting changepoints. Optimization is accomplished via a genetic algorithm (GA).

Usage

autoSpec(xdata, Pi.B = NULL, Pi.C = NULL, PopSize = 70, generation = 70, m0 = 10, 
         Pi.P = 0.3, Pi.N = 0.3, NI = 7, taper = .5, min.freq = 0, max.freq = .5)

Arguments

Details

Details my be found in Stoffer, D. S. (2023). AutoSpec: Detection of narrowband frequency changes in time series. Statistics and Its Interface, 16(1), 97-108. doi:10.4310/21-SII703

Value

Returns three values, (1) the breakpoints including the endpoints, (2) the number of segments, and (3) the segment kernel orders. See the examples.

Note

The GA is a stochastic optimization procedure and consequently will give different results at each run. It is a good idea to run the algorithm a few times before coming to a final decision.

Author(s)

D.S. Stoffer

Source

The genetic algorithm code is adapted from R code provided to us by Rex Cheung (https://www.linkedin.com/in/rexcheung). The code originally supported Aue, Cheung, Lee, & Zhong (2014). Segmented model selection in quantile regression using the minimum description length principle. JASA, 109, 1241-1256. A similar version also supported Davis, Lee, & Rodriguez-Yam (2006). Structural break estimation for nonstationary time series models. JASA, 101, 223-239.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

autoParm

Examples

## Not run: 

##-- simulation
set.seed(1)
num = 500
t   = 1:num
w   = 2*pi/25
d   = 2*pi/150
x1  = 2*cos(w*t)*cos(d*t) + rnorm(num)
x2  = cos(w*t) + rnorm(num)
x   = c(x1,x2)

##-- plot and periodogram (all action below 0.1)
tsplot(x, main='not easy to see the change')
mvspec(x) 

##-- run procedure
autoSpec(x, max.freq=.1)

##-- output (yours will be slightly different - 
##--         the nature of GA) 
# returned breakpoints include the endpoints 
# $breakpoints
# [1]    1  503 1000
# 
# $number_of_segments
# [1] 2
# 
# $segment_kernel_orders_m
# [1] 2 4


##-- plot everything
par(mfrow=c(3,1))
tsplot(x, col=4)
 abline(v=503, col=6, lty=2, lwd=2)
mvspec(x[1:502],    kernel=bart(2), taper=.5, main='segment 1', col=4, xlim=c(0,.25))
mvspec(x[503:1000], kernel=bart(4), taper=.5, main='segment 2', col=4, xlim=c(0,.25))   

## End(Not run)

Bartlett Kernel

Description

Smoothing (triangular) kernel that decreases one unit from the center.

Usage

bart(m)

Arguments

Details

Uses kernel from the stats package to construct a Bartlett (triangular) kernel of width 2m + 1; see help(kernel) for further details.

Value

Returns an object of class tskernel with the coefficients, the kernel dimension, and attribute "Bartlett".

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

bart(4)                         # for a list
plot(bart(4), ylim=c(.01,.21))  # for a graph

Infrasonic Signal from a Nuclear Explosion

Description

Infrasonic signal from a nuclear explosion.

Usage

data(beamd)

Format

A data frame with 2048 observations (rows) on 3 numeric variables (columns): sensor1, sensor2, sensor3.

Details

This is a data frame consisting of three columns (that are not time series objects). The data are an infrasonic signal from a nuclear explosion observed at sensors on a triangular array.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

U.S. Monthly Live Births

Description

Monthly live births (adjusted) in thousands for the United States, 1948-1979.

Format

The format is: Time-Series [1:373] from 1948 to 1979: 295 286 300 278 272 268 308 321 313 308 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Daily Blood Work with Missing Values

Description

Multiple time series of measurements made for 91 days on the three variables, log(white blood count) [WBC], log(platelet) [PLT] and hematocrit [HCT]. Missing data code is NA.

Format

Time-Series [1:91, 1:3] from 1 to 91: 2.33 1.89 2.08 1.82 1.82 ...

..$ : NULL ..$ : chr [1:3] "WBC" "PLT" "HCT"

Details

This data set is used in Chapter 6 for a missing data example.

Source

Jones, R.H. (1984). Fitting multivariate models to unequally spaced data. In Time Series Analysis of Irregularly Observed Data, pp. 158-188. E. Parzen, ed. Lecture Notes in Statistics, 25, New York: Springer-Verlag.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

HCT, PLT, WBC

Examples

tsplot(blood, type='o', pch=19, cex=1.1, col=2:4, gg=TRUE, xlab='day')

Nucleotide sequence - BNRF1 Epstein-Barr

Description

Nucleotide sequence of the BNRF1 gene of the Epstein-Barr virus (EBV): 1=A, 2=C, 3=G, 4=T. The data are used in Chapter 7.

Format

The format is: Time-Series [1:3954] from 1 to 3954: 1 4 3 3 1 1 3 1 3 1 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Nucleotide sequence - BNRF1 of Herpesvirus saimiri

Description

Nucleotide sequence of the BNRF1 gene of the herpesvirus saimiri (HVS): 1=A, 2=C, 3=G, 4=T. The data are used in Chapter 7.

Format

The format is: Time-Series [1:3741] from 1 to 3741: 1 4 3 2 4 4 3 4 4 4 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Monthly Carbon Dioxide Levels at Mauna Loa

Description

Monthly mean carbon dioxide (in ppm) measured at Mauna Loa Observatory, Hawaii. This is an update to co2 in the datasets package.

Format

The format is: Time-Series [1:781] from 1958 to 2023: 316 317 318 317 316 ...

Details

The carbon dioxide data measured as the mole fraction in dry air, on Mauna Loa constitute the longest record of direct measurements of CO2 in the atmosphere. They were started by C. David Keeling of the Scripps Institution of Oceanography in March of 1958 at a facility of the National Oceanic and Atmospheric Administration. NOAA started its own CO2 measurements in May of 1974, and they have run in parallel with those made by Scripps since then. Data are reported as a dry mole fraction defined as the number of molecules of carbon dioxide divided by the number of molecules of dry air multiplied by one million (ppm).

Due to the eruption of the Mauna Loa Volcano, measurements from Mauna Loa Observatory were suspended as of Nov. 29, 2022. Observations starting in December 2022 are from a site at the Maunakea Observatories, approximately 21 miles north of the Mauna Loa Observatory.

Source

https://gml.noaa.gov/ccgg/trends/

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Cross Correlation

Description

Calculates and plots the sample CCF of two time series.

Usage

ccf2(x, y, max.lag = NULL, main = NULL, ylab = "CCF", plot = TRUE,
         na.action = na.pass, type = c("correlation", "covariance"), ...)

Arguments

Details

This will produce a graphic of the sample corr[x(t+lag), y(t)] from -max.lag to max.lag. Also, the (rounded) values of the CCF are returned invisibly unless plot=FALSE. Similar details apply to the cross-covariance.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

acf1, acf2, acfm

Examples

ccf2(soi, rec, plot=FALSE)  # now you see it
ccf2(soi, rec)              # now you don't

# happy birthday mom
ccf2(soi, rec, col=rainbow(36, v=.8), lwd=4, gg=TRUE)

Monthly price of a pound of chicken

Description

Poultry (chicken), Whole bird spot price, Georgia docks, US cents per pound

Format

The format is: Time-Series [1:180] from August 2001 to July 2016: 65.6 66.5 65.7 64.3 63.2 ...

Source

https://www.indexmundi.com/commodities/

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Lake Shasta inflow data

Description

Lake Shasta inflow data. This is a data frame.

Format

A data frame with 454 observations (rows) on the following 6 numeric variables (columns): Temp, DewPt, CldCvr, WndSpd, Precip, Inflow.

Details

The data are 454 months of measured values for the climatic variables: air temperature, dew point, cloud cover, wind speed, precipitation, and inflow, at Lake Shasta, California. The man-made lake is famous for the placard stating, "We don't swim in your toilet, so don't pee in our lake."

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Cardiovascular Mortality from the LA Pollution study

Description

Average weekly cardiovascular mortality in Los Angeles County; 508 six-day smoothed averages obtained by filtering daily values over the 10 year period 1970-1979.

Format

The format is: Time-Series [1:508] from 1970 to 1980: 97.8 104.6 94.4 98 95.8 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

lap, lap.xts

Hard Drive Cost per GB

Description

Median annual cost per gigabyte (GB) of storage.

Format

The format is: Time-Series [1:29] from 1980 to 2008: 213000.00 295000.00 260000.00 175000.00 160000.00 ...

Details

The median annual cost of hard drives used in computers. The data are retail prices per GB taken from a sample of manufacturers.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Detrend a Time Series

Description

Returns a time series with the trend removed. The trend can be estimated using polynomial regression or using a lowess fit.

Usage

detrend(series, order = 1, lowess = FALSE, lowspan = 2/3)

Arguments

Value

The detrended series is returned.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

trend

Examples

tsplot( cbind(salmon, detrend(salmon)), gg=TRUE, main='Norwegian Salmon USD/KG' ) 

Dow Jones Industrial Average

Description

Daily DJIA values from April 2006 - April 2016

Format

The format is: xts [1:2518, 1:5] 11279 11343 11347 11337 11283 ...
- attr(*, "class")= chr [1:2] "xts" "zoo"
..$ : chr [1:5] "Open" "High" "Low" "Close" "Volume"

Source

The data were obtained via the TTR package and Yahoo financial data. Unfortunately, this does not work now. It seems like the R package quantmod is a good bet and Yahoo still has financial data.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Convert DNA Sequence to Indicator Vectors

Description

Takes a string (e.g., a DNA sequence) of general form (e.g., FASTA) and converts it to a sequence of indicator vectors for use with the Spectral Envelope (specenv).

Usage

dna2vector(data, alphabet = NULL)

Arguments

Details

Takes a string of categories and converts it to a matrix of indicators. The data can then be used by the script specenv, which calculates the Spectral Envelope of the sequence (or subsequence). Many different type of sequences can be used, including FASTA and GenBank, as long as the data is a string of categories.

The indicator vectors (as a matrix) are returned invisibly in case the user forgets to put the results in an object wherein the screen would scroll displaying the entire sequence. In other words, the user should do something like xdata = dna2vector(data) where data is the original sequence.

If the DNA sequence is in a FASTA file, say sequence.fasta, the following code can be used to read the data into the session, create the indicator sequence and save it as a compressed R data file:

  fileName <- 'sequence.fasta'      # name of FASTA file
  data     <- readChar(fileName, file.info(fileName)$size)  # input the sequence
  myseq    <- dna2vector(data)      # convert it to indicators

  ##== to compress and save the data ==##
  save(myseq, file='myseq.rda')
  ##== and then load it when needed ==##
  load('myseq.rda')

Value

matrix of indicator vectors; returned invisibly

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

specenv

Examples

# Epstein-Barr virus (entire sequence included in astsa)
xdata = dna2vector(EBV)
head(xdata)

# part of EBV with  1, 2, 3, 4 for "A", "C", "G", "T"
xdata = dna2vector(bnrf1ebv)
head(xdata)

# raw GenBank sequence
data <-
c("1 agaattcgtc ttgctctatt cacccttact tttcttcttg cccgttctct ttcttagtat
  61 gaatccagta tgcctgcctg taattgttgc gccctacctc ttttggctgg cggctattgc")
xdata = dna2vector(data, alphabet=c('a', 'c', 'g', 't'))
head(xdata)

# raw FASTA sequence
data <-
 c("AGAATTCGTCTTGCTCTATTCACCCTTACTTTTCTTCTTGCCCGTTCTCTTTCTTAGTATGAATCCAGTA
    TGCCTGCCTGTAATTGTTGCGCCCTACCTCTTTTGGCTGGCGGCTATTGCCGCCTCGTGTTTCACGGCCT")
xdata = dna2vector(data)
head(xdata)

Five Quarterly Economic Series

Description

Multiple time series of quarterly U.S. unemployment, GNP, consumption, and government and private investment, from 1948-III to 1988-II.

Format

Multiple time series with 161 observations (rows) on the following 5 numeric variables (columns): unemp, gnp, consum, govinv, prinv.

Source

Young, P.C. and Pedregal, D.J. (1999). Macro-economic relativity: government spending, private investment and unemployment in the USA 1948-1998. Structural Change and Economic Dynamics, 10, 359-380.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Earthquake and Explosion Seismic Series

Description

This is a data frame of the earthquake and explosion seismic series used throughout the text.

Format

A data frame with 2048 observations (rows) on 17 variables (columns). Each column is a numeric vector.

Details

The matrix has 17 columns, the first eight are earthquakes, the second eight are explosions, and the last column is the Novaya Zemlya event of unknown origin.

The column names are: EQ1, EQ2,...,EQ8; EX1, EX2,...,EX8; NZ. The first 1024 observations correspond to the P wave, the second 1024 observations correspond to the S wave.

All events in the data set were on or near land and were distributed uniformly over Scandinavia so as to minimize the possibility that discriminators might be keying on location or land-sea differences. The events are earthquakes ranging in magnitude from 2.74 to 4.40 and explosions in the range 2.13 to 2.19. Also added is an event of uncertain origin that was located in the Novaya Zemlya region of Russia. All events except the Russian event occurred in the Scandinavian peninsula and were recorded by seismic arrays located in Norway by Norwegian and Arctic experimental seismic stations (NORESS, ARCESS) and in Finland by Finnish experimental seismic stations (FINESS).

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

## Not run: 

# view all series 
# first 2 rows EQs - second 2 rows EXs
# 5th row NZ event 

tsplot(eqexp, ncol=4, col=1:8)

## End(Not run)

Forward Filtering Backward Sampling

Description

FFBS algorithm for state space models

Usage

ffbs(y, A, mu0, Sigma0, Phi, sQ, sR, Ups = NULL, Gam = NULL, input = NULL)

Arguments

Details

For a linear state space model, the FFBS algorithm provides a way to sample a state sequence x_{0:n} from the posterior \pi(x_{0:n} \mid \Theta, y_{1:n}) with parameters \Theta and data y_{1:n}.

The general model is

x_t = \Phi x_{t-1} + \Upsilon u_{t} + sQ\, w_t \quad w_t \sim iid\ N(0,I)

y_t = A_t x_{t-1} + \Gamma u_{t} + sR\, v_t \quad v_t \sim iid\ N(0,I)

where w_t \perp v_t. Consequently the state noise covariance matrix is Q = sQ\, sQ' and the observation noise covariance matrix is R = sR\, sR' and sQ, sR do not have to be square as long as everything is conformable.

x_t is p-dimensional, y_t is q-dimensional, and u_t is r-dimensional. Note that sQ\, w_t has to be p-dimensional, but w_t does not, and sR\, v_t has to be q-dimensional, but v_t does not.

Value

Note

The script uses Kfilter. If A_t is constant wrt time, it is not necessary to input an array; see the example. The example below is just one pass of the algorithm; see the example at FUN WITH ASTSA for the real fun.

Author(s)

D.S. Stoffer

Source

Chapter 6 of the Shumway and Stoffer Springer text.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

## Not run: 

## -- this is just one pass --##
# generate some data
 set.seed(1)
 sQ  = 1; sR = 3; n = 100  
 mu0 = 0; Sigma0 = 10; x0 = rnorm(1,mu0,Sigma0)
 w = rnorm(n); v = rnorm(n)
 x = c(x0 + sQ*w[1]);  y = c(x[1] + sR*v[1])   # initialize
for (t in 2:n){
  x[t] = x[t-1] + sQ*w[t]
  y[t] = x[t] + sR*v[t]   
  }

## run one pass of FFBS, plot data, states and sampled states  
run = ffbs(y, A=1, mu0=0, Sigma0=10, Phi=1, sQ=1, sR=3)
tsplot(cbind(y,run$Xs), spaghetti=TRUE, type='o', col=c(8,4), pch=c(1,NA))
legend('topleft', legend=c("y(t)","xs(t)"), lty=1, col=c(8,4), bty="n", pch=c(1,NA))

## End(Not run)

Monthly pneumonia and influenza deaths in the U.S., 1968 to 1978.

Description

Monthly pneumonia and influenza deaths per 10,000 people in the United States for 11 years, 1968 to 1978.

Usage

data(flu)

Format

The format is: Time-Series [1:132] from 1968 to 1979: 0.811 0.446 0.342 0.277 0.248 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

fMRI - complete data set

Description

Data (as a vector list) from an fMRI experiment in pain, listed by location and stimulus. The data are BOLD signals when a stimulus was applied for 32 seconds and then stopped for 32 seconds. The signal period is 64 seconds and the sampling rate was one observation every 2 seconds for 256 seconds (n = 128). The number of subjects under each condition varies.

Details

The LOCATIONS of the brain where the signal was measured were [1] Cortex 1: Primary Somatosensory, Contralateral, [2] Cortex 2: Primary Somatosensory, Ipsilateral, [3] Cortex 3: Secondary Somatosensory, Contralateral, [4] Cortex 4: Secondary Somatosensory, Ipsilateral, [5] Caudate, [6] Thalamus 1: Contralateral, [7] Thalamus 2: Ipsilateral, [8] Cerebellum 1: Contralateral and [9] Cerebellum 2: Ipsilateral.

The TREATMENTS or stimuli (and number of subjects in each condition) are [1] Awake-Brush (5 subjects), [2] Awake-Heat (4 subjects), [3] Awake-Shock (5 subjects), [4] Low-Brush (3 subjects), [5] Low-Heat (5 subjects), and [6] Low-Shock (4 subjects). Issue the command summary(fmri) for further details. In particular, awake (Awake) or mildly anesthetized (Low) subjects were subjected levels of periodic brushing (Brush), application of heat (Heat), and mild shock (Shock) effects.

As an example, fmri$L1T6 (Location 1, Treatment 6) will show the data for the four subjects receiving the Low-Shock treatment at the Cortex 1 location; note that fmri[[6]] will display the same data.

Source

Joseph F. Antognini, Michael H. Buonocore, Elizabeth A. Disbrow, Earl Carstens, Isoflurane anesthesia blunts cerebral responses to noxious and innocuous stimuli: a fMRI study, Life Sciences, Volume 61, Issue 24, 1997, Pages PL349-PL354, ISSN 0024-3205,
https://doi.org/10.1016/S0024-3205(97)00960-0.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

fMRI Data Used in Chapter 1

Description

A data frame that consists of average fMRI BOLD signals at eight locations.

Usage

data(fmri1)

Format

The format is: mts [1:128, 1:9]

Details

Multiple time series consisting of fMRI BOLD signals at eight locations (in columns 2-9, column 1 is time period), when a stimulus was applied for 32 seconds and then stopped for 32 seconds. The signal period is 64 seconds and the sampling rate was one observation every 2 seconds for 256 seconds (n = 128). The columns are labeled: "time" "cort1" "cort2" "cort3" "cort4" "thal1" "thal2" "cere1" "cere2".

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

fmri

Gas Prices

Description

New York Harbor conventional regular gasoline weekly spot price FOB (in cents per gallon) from 2000 to mid-2010.

Format

The format is: Time-Series [1:545] from 2000 to 2010: 70.6 71 68.5 65.1 67.9 ...

Details

Pairs with series oil

Source

Data were obtained from: https://www.eia.gov/dnav/pet/pet_pri_spt_s1_w.htm

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

oil

Quarterly U.S. GDP

Description

Seasonally adjusted quarterly U.S. GDP from 1947(1) to 2018(3).

Format

The format is: Time-Series [1:287] from 1947 to 2018: 2033 2028 2023 2055 2086 ...

Source

https://tradingeconomics.com/united-states/gdp

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

GDP, GNP, gnp

Quarterly U.S. GNP

Description

Seasonally adjusted quarterly U.S. GNP from 1947(1) to 2002(3).

Format

The format is: Time-Series [1:223] from 1947 to 2002: 1489 1497 1500 1524 1547 ...

Source

https://fred.stlouisfed.org/series/GNP

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

GNP, GDP, gdp

Monthly global average surface temperatures by year

Description

Monthly global average surface temperatures by year. The temperature of the air measured 2 meters above the ground, encompassing land, sea, and in-land water surfaces.

Format

A data frame with 12 monthly observations (as rows) for the years 1975-2023 (as columns in reverse order).

Details

Temperature of air at 2m above the surface of land, sea or in-land waters. 2m temperature is calculated by interpolating between the lowest model level and the Earth's surface, taking account of the atmospheric conditions. Technical details at https://cds.climate.copernicus.eu/datasets/reanalysis-era5-pressure-levels-monthly-means?tab=overview.

Source

https://ourworldindata.org/grapher/monthly-average-surface-temperatures-by-year

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

## Not run: 

# functional data plot showing warming trend
tsplot(gtemp.month, spaghetti=TRUE, col=rainbow(49, start=.2, v=.8, rev=TRUE), ylab='\u00b0C', 
        xlab='Month', xaxt='n', main='Mean Monthly Global Temperature', lwd=c(3,rep(1,47),3))
axis(1, labels=Months, at=1:12)
text(10, 13, '1975')
text(10.3, 15.5, '2023')


## End(Not run)

Global mean land and open ocean temperature deviations, 1850-2023

Description

Annual temperature anomalies (in degress centigrade) averaged over the Earth's land and ocean area from 1850 to 2023. Anomalies are with respect to the 1991-2020 average.

Format

The format is: Time-Series [1:174] from 1850 to 2023: -0.24 -0.25 -0.27 -0.15 -0.05 -0.16 -0.29 -0.32 -0.19 -0.04 ...

Source

https://www.ncei.noaa.gov/access/monitoring/climate-at-a-glance/global/time-series/

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

gtemp_land, gtemp_ocean

Global mean land temperature deviations, 1850-2023

Description

Annual temperature anomalies (in degress centigrade) averaged over the Earth's land area from 1850 to 2023. Anomalies are with respect to the 1991-2020 average.

Format

The format is: Time-Series [1:174] from 1850 to 2023: -0.50 -0.60 -0.50 -0.50 -0.20 -0.50 -0.80 -0.40 -0.40 -0.10 ...

Source

https://www.ncei.noaa.gov/access/monitoring/climate-at-a-glance/global/time-series/

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

gtemp_ocean, gtemp_both

Global mean ocean temperature deviations, 1850-2023

Description

Annual sea surface temperature anomalies averaged over the part of the ocean that is free of ice at all times (open ocean) from 1850 to 2023. Anomalies are with respect to the 1991-2020 average.

Format

The format is: Time-Series [1:174] from 1850 to 2023: -0.12 -0.08 -0.14 0.04 0.04 0.00 -0.05 -0.27 -0.09 0.01 ...

Source

https://www.ncei.noaa.gov/access/monitoring/climate-at-a-glance/global/time-series/

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

gtemp_land, gtemp_both

Hawaiian occupancy rates

Description

Quarterly Hawaiian hotel occupancy rate (percent of rooms occupied) from 1982-I to 2015-IV

Format

The format is: Time-Series [1:136] from 1982 to 2015: 79 65.9 70.9 66.7 ...

Source

https://dbedt.hawaii.gov/economic/qser/tourism/

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

tsplot(hor, type='c')                           # plot data and
text(hor, labels=1:4, col=c(1,4,2,6), cex=.9)   # add quarter labels

Johnson and Johnson Quarterly Earnings Per Share

Description

Johnson and Johnson quarterly earnings per share, 84 quarters (21 years) measured from the first quarter of 1960 to the last quarter of 1980.

Format

The format is: Time-Series [1:84] from 1960 to 1981: 0.71 0.63 0.85 0.44 0.61 0.69 0.92 0.55 0.72 0.77 ...

Details

The data were provided (personal communication) by Professor Paul Griffin, https://gsm.ucdavis.edu/profile/paul-griffin, of the Graduate School of Management, University of California, Davis. This data set is also included with the R distribution as JohnsonJohnson.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Lag Plot - one time series

Description

Produces a grid of scatterplots of a series versus lagged values of the series.

Usage

lag1.plot(series, max.lag = 1, corr = TRUE, smooth = TRUE, col = gray(.1), 
           bg = NA, lwl = 1, lwc = 2, bgl = NULL, ltcol = 1, box.col = NULL, 
           cex = .9, gg = FALSE, ...)

Arguments

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

lag2.plot

Examples

lag1.plot(log(varve), max.lag=9)
lag1.plot(soi, 12, cex=1, pch=19, col=astsa.col(4, .3), gg=TRUE)

Lag Plot - two time series

Description

Produces a grid of scatterplots of one series versus another lagged. The first named series is the one that gets lagged.

Usage

lag2.plot(series1, series2, max.lag = 0, corr = TRUE, smooth = TRUE, col = gray(.1), 
          bg = NA, lwl = 1, lwc = 2, bgl = NULL, ltcol = 1, box.col = NULL, cex = .9, 
          gg = FALSE, ...)

Arguments

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

lag1.plot

Examples

lag2.plot(Hare, Lynx, max.lag=5, lwl=2, lwc=3, cex=1.5, pch=24, bg='orange')
lag2.plot(soi, rec, 8, cex=1.1, pch=19, col=5, lwl=2)

LA Pollution-Mortality Study

Description

LA Pollution-Mortality Study (1970-1979), weekly data.

Format

The format is: mts [1:508, 1:11]

Details

Note

Details may be found in http://www.sungpark.net/ShumwayAzariPawitan88.pdf

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

lap.xts

LA Pollution-Mortality Study: Sampled Daily

Description

Original data from a study of the effects of pollution and weather on mortality, LA, 1970-1979. These are 3652 daily observations for the 10 year period. The data set is an xts object indexed by Date.

Format

The format is: An xts object on 1970-01-01 / 1979-12-31 containing:
Data: double [3652, 11]
Columns: Tmort, Rmort, Cmort, Temp, Rhumid, CO, SO2, NO2, HC, Ozone, Part
Index: Date [3652] (TZ: "UTC")

Details

Note

These are the original data from https://github.com/DSStoffer/dsstoffer.github.io/blob/main/files/LAP.pdf.

The weekly data in lap were taken from this data set last century. The details, however, were never entirely made clear and it's too late to get them now. It is easy to pull out the weekly averages from this data set, and how to do so is given in the Examples section below; the resulting data set will be slightly different than lap. The names for this data set are different from lap, the main difference is these names have capitals.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

lap

Examples

## Not run: 

library(xts)   # assumes package has been installed

plot(lap.xts$Cmort, col=4)   

lapw = apply.weekly(lap.xts, FUN=colMeans)  # get weekly averages

plot(lapw[,c('Cmort', 'Temp', 'Part')], col=astsa.col(2:4, .7), main=NA) 
addLegend(col=2:4, lty=1, lwd=2, ncol=3, bty="white")

sarima(lapw$Cmort, 0,1,1, no.constant=TRUE)  # fit ARIMA(0,1,1) to weekly Cmort

## End(Not run)

Leading Indicator

Description

Leading indicator, 150 months; taken from Box and Jenkins (1970).

Usage

data(lead)

Format

The format is: Time-Series [1:150] from 1 to 150: 10.01 10.07 10.32 9.75 10.33 ...

Details

This is also the R time series BJsales.lead: The sales time series BJsales and leading indicator BJsales.lead each contain 150 observations. The objects are of class "ts".

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

sales

Powers of a Square Matrix

Description

matrixpwr computes powers of a square matrix including negative powers for nonsingular matrices.

%^% is a more intuitive interface as an operator.

Usage

matrixpwr(A, power)

A %^% power

Arguments

Details

Raises matrix to the specified power. The matrix must be square and if power < 0, the matrix must be nonsingular.

Note that %^% is defined as "%^%" <- function(A, power) matrixpwr(A, power)

If power = 0, the identity matrix is returned.

Value

Returns matrix raised to the given power.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

# 2-state Markov transition matrix to steady state
( P = matrix(c(.7,.4,.3,.6), 2) )
P %^% 50

# surround with parentheses if used in an expression
c(.2, .8) %*% (P %^% 50)

# Inverse square root
var(econ5) %^% -.5

Univariate and Multivariate Spectral Estimation

Description

This is spec.pgram with a few changes in the defaults and written so you can easily extract the estimate of the multivariate spectral matrix as fxx. The bandwidth calculation has been changed to the more practical definition given in the text and this can be used to replace spec.pgram.

Usage

mvspec(x, spans = NULL, kernel = NULL, taper = 0, pad = 0, fast = TRUE, 
        demean = FALSE, detrend = TRUE, lowess = FALSE, log = 'n', plot = TRUE, 
        gg = FALSE, type = NULL, na.action = na.fail, nxm = 2, nym = 1, 
        main = NULL, xlab=NULL, cex.main=NULL, ci.col=4, ...) 

Arguments

Details

This is built off of spec.pgram from the stats package with a few changes in the defaults and written so you can easily extract the estimate of the multivariate spectral matrix as fxx.

The default for the plot is NOT to plot on a log scale and the graphic will have a grid.

The bandwidth calculation has been changed to the more practical definition given in the text, (L_h/n.used)*frequency(x). Also, the bandwidth is not displayed in the graphic, but is returned.

Although initially meant to be used to easily obtain multivariate (mv) spectral (spec) estimates, this script can be used for univariate time series as a replacement for spec.pgram.

Note that the script does not taper by default (taper=0); this forces the user to do "conscious tapering".

Value

All results are returned invisibly.

If plot is TRUE and smoothing is used, the bandwidth, degrees of freedom, and taper amount are printed.

An object of class "spec", which is a list containing at least the following components:

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

# real raw periodogram
mvspec(soi)
mvspec(soi, log='y')  # on a log scale

# smooth and some details printed
mvspec(soi, spans=c(7,7), taper=.5)$details[1:45,]

# multivariate example
deth = cbind(mdeaths, fdeaths)    # two R data sets, male/female monthly deaths ...
tsplot(deth, type='b', col=c(4,6), spaghetti=TRUE, pch=c('M','F'))
dog = mvspec(deth, spans=c(3,3), taper=.1)
dog$fxx[,,1:5]  # look at a few spectral matrix estimates
dog$bandwidth   # bandwidth with time unit = year
dog$df          # degrees of freedom
mvspec(deth, spans=c(3,3), taper=.1, plot.type='coh')  # coherence

Returns of the New York Stock Exchange

Description

Returns of the New York Stock Exchange (NYSE) from February 2, 1984 to December 31, 1991.

Format

The format is: Time-Series [1:2000] from 1 to 2000: 0.00335 -0.01418 -0.01673 0.00229 -0.01692 ...

Note

Various packages have data sets called nyse. Consequently, it may be best to specify this data set as nyse = astsa::nyse to avoid conflicts.

Source

S+GARCH module - Version 1.1 Release 2: 1998

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Crude oil, WTI spot price FOB

Description

Crude oil, WTI spot price FOB (in dollars per barrel), weekly data from 2000 to mid-2010.

Format

The format is: Time-Series [1:545] from 2000 to 2010: 26.2 26.1 26.3 24.9 26.3 ...

Details

pairs with the series gas

Source

Data were obtained from the URL: www.eia.doe.gov/dnav/pet/pet_pri_spt_s1_w.htm

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

gas

Particulate levels from the LA pollution study

Description

Particulate series corresponding to cmort from the LA pollution study.

Format

The format is: Time-Series [1:508] from 1970 to 1980: 72.7 49.6 55.7 55.2 66 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

lap, lap.xts

Poliomyelitis cases in US

Description

Monthly time series of poliomyelitis cases reported to the U.S. Centers for Disease Control for the years 1970 to 1983, 168 observations.

Format

The format is: Time-Series [1:168] from 1970 to 1984: 0 1 0 0 1 3 9 2 3 5 ...

Details

The data were originally modelled by Zeger (1988) “A Regression Model for Time Series of Counts,” Biometrika, 75, 822-835.

Source

Data taken from the gamlss.data package; see https://www.gamlss.com/.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

tsplot(polio, type='s')

Multiplication of Two Polynomials

Description

Multiplication of two polynomials.

Usage

polyMul(p, q)

Arguments

Details

inputs are vectors of coefficients a, b, c, ..., in order of power ax^0 + bx^1 + cx^2 + ...

Value

coefficients of the product in order of power

Author(s)

D.S. Stoffer

Source

based on code from the polynom package https://CRAN.R-project.org/package=polynom

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

a = 1:3  # 1 + 2x + 3x^2
b = 1:2  # 1 + 2x
polyMul(a, b)
# [1] 1 4 7 6
# 1 + 4x + 7x^2 + 6x^3

Cross-Correlation Analysis With Automatic Prewhitening

Description

Performs a cross-correlation analysis on two series after prewhitening the first series and filtering the second series accordingly.

Usage

pre.white(series1, series2, diff = FALSE, max.lag = NULL, main = NULL, 
           order.max = NULL, plot = TRUE, ...)

Arguments

Details

The first series is prewhitened by fitting a long AR based on AIC and the second series is filtered appropriately. Then a cross-correlation analysis is performed via ccf2. If differencing is specified, both series are differenced the same way prior to the prewhitening. The resulting series are returned invisibly.

The default is no differencing. Differences of order 1 can be set be entering diff = TRUE or diff = 1. If it is necessary to use higher orders, then enter a positive integer (this is rare).

The maximum lag (max.lag) in the CCF graphic defaults (if NULL) to the smaller of 50 and 20% of the sample size.

The maximum order (order.max) for fitting the AR via AIC defaults (if NULL) to the minimum of 30 and 15% of the number of observations.

Value

Returns the sample CCF graphic using the prewhitened series unless plot = FALSE. The prewhitened series are returned invisibly.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

pre.white(cmort, part, diff=TRUE, col=4)

Monthly Federal Reserve Board Production Index

Description

Monthly Federal Reserve Board Production Index (1948-1978, n = 372 months).

Usage

data(prodn)

Format

The format is: Time-Series [1:372] from 1948 to 1979: 40.6 41.1 40.5 40.1 40.4 41.2 39.3 41.6 42.3 43.2 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Quarterly Inflation

Description

Quarterly inflation rate in the Consumer Price Index from 1953-Ito 1980-II, n = 110 observations.

Format

The format is: Time-Series [1:110] from 1953 to 1980: 1.673 3.173 0.492 -0.327 -0.333 ...

Details

pairs with qintr (interest rate)

Source

Newbold, P. and T. Bos (1985). Stochastic Parameter Regression Models. Beverly Hills: Sage.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

qintr

Quarterly Interest Rate

Description

Quarterly interest rate recorded for Treasury bills from 1953-Ito 1980-II, n = 110 observations.

Format

The format is: Time-Series [1:110] from 1953 to 1980: 1.98 2.15 1.96 1.47 1.06 ...

Details

pairs with qinfl (inflation)

Source

Newbold, P. and T. Bos (1985). Stochastic Parameter Regression Models. Beverly Hills: Sage.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

qinfl

Recruitment (number of new fish index)

Description

Recruitment (index of the number of new fish) for a period of 453 months ranging over the years 1950-1987. Recruitment is loosely defined as an indicator of new members of a population to the first life stage at which natural mortality stabilizes near adult levels.

Usage

data(rec)

Format

The format is: Time-Series [1:453] from 1950 to 1988: 68.6 68.6 68.6 68.6 68.6 ...

Details

can pair with soi (Southern Oscillation Index)

Source

Data furnished by Dr. Roy Mendelssohn of the Pacific Fisheries Environmental Laboratory, NOAA (personal communication). Further discussion of the concept of Recruitment may be found here: derekogle.com/fishR/examples/oldFishRVignettes/StockRecruit.pdf

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

soi

Sales

Description

Sales, 150 months; taken from Box and Jenkins (1970).

Format

The format is: Time-Series [1:150] from 1 to 150: 200 200 199 199 199 ...

Details

This is also the R data set BJsales: The sales time series BJsales and leading indicator BJsales.lead each contain 150 observations. The objects are of class "ts".

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

lead

Monthly export price of salmon

Description

Farm Bred Norwegian Salmon, export price, US Dollars per Kilogram

Format

The format is: Time-Series [1:166] from September 2003 to June 2017: 2.88 3.16 2.96 3.12 3.23 3.32 3.45 3.61 3.48 3.21 ...

Source

https://www.indexmundi.com/commodities/

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Salt Profiles

Description

Salt profiles taken over a spatial grid set out on an agricultural field, 64 rows at 17-ft spacing.

Usage

data(salt)

Format

The format is: Time-Series [1:64] from 1 to 64: 6 6 6 3 3 3 4 4 4 1.5 ...

Details

pairs with saltemp, temperature profiles on the same grid

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

saltemp

Temperature Profiles

Description

Temperature profiles over a spatial grid set out on an agricultural field, 64 rows at 17-ft spacing.

Usage

data(saltemp)

Format

The format is: Time-Series [1:64] from 1 to 64: 5.98 6.54 6.78 6.34 6.96 6.51 6.72 7.44 7.74 6.85 ...

Details

pairs with salt, salt profiles on the same grid

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

salt

Fit ARIMA Models

Description

Fits ARIMA models (with diagnostics) in a short command. It can also be used to perform regression with autocorrelated errors.

Usage

sarima(xdata, p, d, q, P = 0, D = 0, Q = 0, S = -1, 
       details = TRUE, xreg = NULL, Model = TRUE,
       fixed = NULL, tol = sqrt(.Machine$double.eps), 
       no.constant = FALSE, col, ...)

Arguments

Details

If your time series is in x and you want to fit an ARIMA(p,d,q) model to the data, the basic call is sarima(x,p,d,q). The values p,d,q, must be specified as there is no default. The results are the parameter estimates, standard errors, AIC, AICc, BIC (as defined in Chapter 2) and diagnostics. To fit a seasonal ARIMA model, the basic call is sarima(x,p,d,q,P,D,Q,S). For example, sarima(x,2,1,0) will fit an ARIMA(2,1,0) model to the series in x, and sarima(x,2,1,0,0,1,1,12) will fit a seasonal ARIMA(2,1,0)*(0,1,1)_{12} model to the series in x. The difference between the information criteria given by sarima() and arima() is that they differ by a scaling factor of the effective sample size.

Value

A t-table, the estimated noise variance, and AIC, AICc, BIC are printed. The following are returned invisibly:

Source

This is an enhancement of arima from the stats package.

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

sarima.for, sarima.sim

Examples

# easy to use 
sarima(rec, 2,0,0)  # data, p, d, and q
sarima(rec, 2,0,0, details=FALSE)  # minimal output

dog <- sarima(log(AirPassengers), 0,1,1, 0,1,1,12)
str(dog, vec.len=1) # dog has all the returned values
tsplot(resid(dog$fit))  # plot the innovations (residuals) 
dog$ICs # view the 3 ICs

# fixed parameters
x = sarima.sim( ar=c(0,-.9), n=200 ) + 50 
sarima(x, 2,0,0, fixed=c(0,NA,NA))  # phi1 fixed, phi2 and mean free

# fun with diagnostics
sarima(log(AirPassengers), 0,1,1, 0,1,1,12, gg=TRUE, col=4)

# regression with autocorrelated errors 
pp = ts.intersect(L = Lynx, L1 = lag(Lynx,-1), H1 = lag(Hare,-1), dframe=TRUE)
sarima(pp$L, 2,0,0, xreg = cbind(L1=pp$L1, LH1=pp$L1*pp$H1))

ARIMA Forecasting

Description

ARIMA forecasting.

Usage

sarima.for(xdata, n.ahead, p, d, q, P=0, D=0, Q=0, S=-1, tol = sqrt(.Machine$double.eps),
         no.constant = FALSE, plot = TRUE, plot.all = FALSE,  ylab = NULL,
         xreg = NULL, newxreg = NULL, fixed = NULL, ...)

Arguments

Details

For example, sarima.for(x,5,1,0,1) will forecast five time points ahead for an ARMA(1,1) fit to x. The output prints the forecasts and the standard errors of the forecasts, and supplies a graphic of the forecast with +/- 1 and 2 prediction error bounds.

Value

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

sarima

Examples

sarima.for(log(AirPassengers),12,0,1,1,0,1,1,12) 

# fun with the graphic 
sarima.for(log(AirPassengers),12,0,1,1,0,1,1,12, gg=TRUE, col=4, main='arf') 

# with regressors 
nummy   = length(soi)
n.ahead = 24 
nureg   = time(soi)[nummy] + seq(1,n.ahead)/12
sarima.for(soi,n.ahead,2,0,0,2,0,0,12, xreg=time(soi), newxreg=nureg) 

ARIMA Simulation

Description

Simulate data from (seasonal) ARIMA models.

Usage

sarima.sim(ar = NULL, d = 0, ma = NULL, sar = NULL, D = 0, sma = NULL, S = NULL, 
            n = 500, rand.gen = rnorm, innov = NULL, burnin = NA, t0 = 0, ...)

Arguments

Details

Will generate a time series of length n from the specified SARIMA model using simplified input.

The use of the term mean in ... refers to the generation of normal innovations. For example, sarima.sim(ar=.9, mean=5) will generate data using N(5,1) or 5+N(0,1) innovations, so that the constant in the model is 5 and the mean of the AR model is 5/(1-.9) = 50. In sarima.sim(ma=.9, mean=5), however, the model mean is 5 (the constant). Also, a random walk with drift = .1 can be generated by sarima.sim(d=1, mean=.1, burnin=0), which is equivalent to cumsum(rnorm(500, mean=.1)). The same story goes if sd is specified; i.e., it's applied to the innovations. Because anything specified in ... refers to the innovations, a simpler way to generate a non-zero mean is to add the value outside the call; see the examples.

If innov is used to input the innovations and override rand.gen, be sure that length(innov) is at least n + burnin. If the criterion is not met, the script will return less than the desired number of values and a warning will be given.

Value

A time series of length n from the specified SARIMA model with the specified frequency if the model is seasonal and start time t0.

Note

The model autoregressive polynomial ('AR side' = AR x SAR) is checked for causality and the model moving average polynomial ('MA side' = MA x SMA) is checked invertibility. The script stops and reports an error at the first violation of causality or invertibility; i.e., it will not report multiple errors.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

## AR(2) with mean 50 [n = 500 is default]
y = sarima.sim(ar=c(1.5,-.75)) + 50
tsplot(y)

## ARIMA(0,1,1) with drift ['mean' refers to the innovations] 
tsplot(sarima.sim(ma=-.8, d=1, mean=.1))

## SAR(1) example from text
set.seed(666)   # not that 666
sAR = sarima.sim(sar=.9, S=12, n=36)
tsplot(sAR, type='c')
points(sAR, pch=Months, cex=1.1, font=4, col=1:4)

## SARIMA(0,1,1)x(0,1,1)_12 - B&J's favorite
set.seed(101010)
tsplot(sarima.sim(d=1, ma=-.4, D=1, sma=-.6, S=12, n=120))  

## infinite variance t-errors 
tsplot(sarima.sim(ar=.9, rand.gen=function(n, ...) rt(n, df=2) ))

## use your own innovations
dog = rexp(150, rate=.5)*sign(runif(150,-1,1))
tsplot(sarima.sim(n=100, ar=.99, innov=dog, burnin=50))

## generate seasonal data but no P, D or Q - you will receive 
## a message to make sure that you wanted to do this on purpose: 
tsplot(sarima.sim(ar=c(1.5,-.75), n=144, S=12), ylab='doggy', xaxt='n')
mtext(seq(0,144,12), side=1, line=.5, at=0:12)

Scatterplot with Marginal Histograms

Description

Draws a scatterplot with histograms in the margins.

Usage

scatter.hist(x, y, xlab = NULL, ylab = NULL, title = NULL, pt.size = 1, 
              hist.col = gray(0.82), pt.col = gray(0.1, 0.25), pch = 19, 
              reset.par = TRUE, ...)

Arguments

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

scatter.hist(tempr, cmort, hist.col=astsa.col(5,.4), pt.col=5, pt.size=1.5, reset=FALSE)
lines(lowess(tempr, cmort), col=6)

Sleep State and Movement Data - Group 1

Description

Sleep-state and number of movements of infants taken from a study on the effects of prenatal exposure to alcohol. This is Group 1 where the mothers did not drink alcohol during pregnancy.

Format

List of 12 (by subjects) :'data.frame': 120 obs. of 3 variables: .. min : int [1:120] minute (1 to 120) .. state: int [1:120] sleep state 1 to 6 with NA missing (see details) .. mvmnt: int [1:120] number of movements

Details

Per minute sleep state, for approximately 120 minutes, is categorized into one of six possible states, non-REM: NR1 [1] to NR4 [4], and REM [5], or AWAKE [6]. NA means no state is recorded for that minute (if there, it occurs at end of the session). Group 1 (this group) is from mothers who abstained from drinking during pregnancy. In addition, the number of movements per minute are listed.

Source

Stoffer, D. S., Scher, M. S., Richardson, G. A., Day, N. L., Coble, P. A. (1988). A Walsh-Fourier Analysis of the Effects of Moderate Maternal Alcohol Consumption on Neonatal Sleep-State Cycling. Journal of the American Statistical Association, 83(404), 954-963. https://doi.org/10.2307/2290119

Stoffer, D. S. (1990). Multivariate Walsh-Fourier Analysis. Journal of Time Series Analysis, 11(1), 57-73. https://doi.org/10.1111/j.1467-9892.1990.tb00042.x

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

sleep2

Examples

## Not run: 

# plot data 
par(xpd = NA, oma=c(0,0,0,8) )
tsplot(sleep1[[1]][2:3], type='s', col=2:3, spag=TRUE, gg=TRUE)
legend('topright', inset=c(-0.3,0), bty='n', lty=1, col=2:3, legend=c('sleep state',
        'number of \nmovements'))
## you may have to change the first value of 'inset' in the legend to get it to fit        

# spectral analysis
x = dna2vector(sleep1[[1]]$state[1:115], alphabet=c('1','2','3','4','5'))  # never awake
specenv(x, spans=c(3,3))
abline(v=1/60, lty=2, col=8)

## End(Not run)

Sleep State and Movement Data - Group 2

Description

Sleep-state and number of movements of infants taken from a study on the effects of prenatal exposure to alcohol. This is Group 2 where the mothers drank alcohol in moderation during pregnancy.

Format

List of 12 (by subjects) :'data.frame': 120 obs. of 3 variables: .. min : int [1:120] minute (1 to 120) .. state: int [1:120] sleep state 1 to 6 with NA missing (see details) .. mvmnt: int [1:120] number of movements

Details

Per minute sleep state, for approximately 120 minutes, is categorized into one of six possible states, non-REM: NR1 [1] to NR4 [4], and REM [5], or AWAKE [6]. NA means no state is recorded for that minute (if there, it occurs at end of the session). Group 2 (this group) is from mothers who drank alcohol in moderation during pregnancy. In addition, the number of movements per minute are listed.

Source

Stoffer, D. S., Scher, M. S., Richardson, G. A., Day, N. L., Coble, P. A. (1988). A Walsh-Fourier Analysis of the Effects of Moderate Maternal Alcohol Consumption on Neonatal Sleep-State Cycling. Journal of the American Statistical Association, 83(404), 954-963. https://doi.org/10.2307/2290119

Stoffer, D. S. (1990). Multivariate Walsh-Fourier Analysis. Journal of Time Series Analysis, 11(1), 57-73. https://doi.org/10.1111/j.1467-9892.1990.tb00042.x

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

sleep1

Examples

## Not run: 

# plot data 
par(xpd = NA, oma=c(0,0,0,8) )
tsplot(sleep2[[3]][2:3], type='s', col=2:3, spag=TRUE, gg=TRUE)
legend('topright', inset=c(-0.3,0), bty='n', lty=1, col=2:3, legend=c('sleep state',
        'number of \nmovements'))
## you may have to change the first value of 'inset' in the legend to get it to fit        

# spectral analysis
x = dna2vector(sleep1[[1]]$state[1:115], alphabet=c('1','2','3','4','5'))  # never awake
specenv(x, spans=c(3,3))
abline(v=1/60, lty=2, col=8)

## End(Not run)

SO2 levels from the LA pollution study

Description

Sulfur dioxide levels from the LA pollution study

Format

The format is: Time-Series [1:508] from 1970 to 1980: 3.37 2.59 3.29 3.04 3.39 2.57 2.35 3.38 1.5 2.56 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

lap

Southern Oscillation Index

Description

Southern Oscillation Index (SOI) for a period of 453 months ranging over the years 1950-1987.

Format

The format is: Time-Series [1:453] from 1950 to 1988: 0.377 0.246 0.311 0.104 -0.016 0.235 0.137 0.191 -0.016 0.29 ...

Details

pairs with rec (Recruitment)

Source

Data furnished by Dr. Roy Mendelssohn of the Pacific Fisheries Environmental Laboratory, NOAA (personal communication).

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

rec, ENSO

Spatial Grid of Surface Soil Temperatures

Description

A 64 by 36 matrix of surface soil temperatures.

Format

The format is: num [1:64, 1:36] 6.7 8.9 5 6.6 6.1 7 6.5 8.2 6.7 6.6 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Returns of the S&P 500

Description

Daily growth rate of the S&P 500 from 2001 though 2011.

Format

The format is: Time Series; Start = c(2001, 2); End = c(2011, 209); Frequency = 252

Source

Douc, Moulines, & Stoffer (2014). Nonlinear Time Series: Theory, Methods and Applications with R Examples. CRC Press. ISBN: <9781466502253>

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Weekly Growth Rate of the Standard and Poor's 500

Description

Weekly closing returns of the SP 500 from 2003 to September, 2012.

Format

An 'xts' object on 2003-01-03 to 2012-09-28; Indexed by objects of class: [Date] TZ: UTC

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Estimate Spectral Density of a Time Series from AR Fit

Description

Fits an AR model to data and computes (and by default plots) the spectral density of the fitted model based on AIC (default) or BIC.

Usage

spec.ic(xdata, BIC=FALSE, order.max=NULL, main=NULL, plot=TRUE, detrend=TRUE, 
         lowess=FALSE, method=NULL, cex.main=NULL, xlab=NULL, ...)

Arguments

Details

Uses ar to fit the best AR model based on pseudo AIC or BIC. Using method='mle' will be slow. The minimum centered AIC and BIC values and the spectral and frequency ordinates are returned silently.

Value

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

ar, spec.ar

Examples

## Not run: 
# AIC
spec.ic(soi)  
spec.ic(sunspotz, method='burg', col=4)   

# BIC after detrending on log scale
spec.ic(soi, BIC=TRUE, detrend=TRUE, log='y')  

# plot AIC and BIC without spectral estimate
tsplot(0:30, spec.ic(soi, plot=FALSE)[[1]][,2:3], type='o', xlab='order', nxm=5)  

## End(Not run)

Spectral Envelope

Description

Computes the spectral envelope of categorical-valued or real-valued time series.

Usage

specenv(xdata, section = NULL, spans = NULL, kernel = NULL, taper = 0,
         significance = 1e-04, plot = TRUE, ylim = NULL, real = FALSE, ...)

Arguments

Details

Calculates the spectral envelope for categorical-valued series as discussed in
https://www.stat.pitt.edu/stoffer/dss_files/spenv.pdf
and summarized in
https://doi.org/10.1214/ss/1009212816.
Alternately, calculates the spectral envelope for real-valued series as discussed in
https://doi.org/10.1016/S0378-3758(96)00044-4.

These concepts are also presented (with examples) in Section 7.9 (Chapter 7) of Time Series Analysis and Its Applications: With R Examples: https://www.stat.pitt.edu/stoffer/tsa4/.

For categorical-valued series, the input xdata must be a matrix of indicators which is perhaps a sequence preprocessed using dna2vector.

For real-valued series, the input xdata should be a matrix whose columns are various transformations of the univariate series.

The script does not detrend the data prior to estimating spectra. If this is an issue, then detrend the data prior to using this script.

Value

By default, will produce a graph of the spectral envelope and an approximate significance threshold. A matrix containing: frequency, spectral envelope ordinates, and (1) the scalings of the categories in the order of the categories in the alphabet or (2) the coefficients of the transformations, is returned invisibly.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

dna2vector

Examples

## Not run: 
# a DNA sequence
data  = bnrf1ebv
xdata = dna2vector(data)
u = specenv(xdata, section=1:1000, spans=c(7,7))
head(u)  # scalings are for A, C, G, and last one T=0 always

# a real-valued series (nyse returns)
x = astsa::nyse
xdata = cbind(x, abs(x), x^2)
u = specenv(xdata, real=TRUE,  spans=c(3,3))
# plot optimal transform at freq = .001
beta = u[2, 3:5]
b = beta/beta[2]  # makes abs(x) coef=1
gopt = function(x) { b[1]*x+b[2]*abs(x)+b[3]*x^2 }
curve(gopt, -.2, .2, col=4, lwd=2, panel.first=Grid())
g2 = function(x) { b[2]*abs(x) } # corresponding to |x|
curve(g2, -.2,.2, add=TRUE, col=6)

## End(Not run)

Speech Recording

Description

A small .1 second (1000 points) sample of recorded speech for the phrase "aaa...hhh".

Format

The format is: Time-Series [1:1020] from 1 to 1020: 1814 1556 1442 1416 1352 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

State Space Model

Description

Fits a simple univariate state space model to data. The parameters are estimated (the state regression parameter may be fixed). State predictions, filters, and smoothers and corresponding error variances are evaluated at the estimates. The sample size must be at least 20.

Usage

ssm(y, A, phi, alpha, sigw, sigv, fixphi = FALSE)

Arguments

Details

The script works for a specific univariate state space model,

x_t = \alpha + \phi x_{t-1} + w_t \quad {\rm and} \quad y_t = A x_t + v_t.

The initial state conditions use a default calculation and cannot be specified. The parameter estimates are printed and the script returns the state predictors and smoothers. The regression parameter \phi may be fixed.

Value

At the MLEs, these are returned invisibly:

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

## Not run: 

u = ssm(gtemp_land, A=1, alpha=.01, phi=1, sigw=.05, sigv=.15, fixphi=TRUE)
tsplot(gtemp_land, type='o', col=4)
lines(u$Xs, col=6, lwd=2)

## End(Not run)

Variable Star

Description

The magnitude of a star taken at midnight for 600 consecutive days. The data are taken from the classic text, The Calculus of Observations, a Treatise on Numerical Mathematics, by E.T. Whittaker and G. Robinson, (1923, Blackie and Son, Ltd.).

Format

The format is: Time-Series [1:600] from 1 to 600: 25 28 31 32 33 33 32 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Frequency Domain Stochastic Regression

Description

Performs frequency domain stochastic regression discussed in Chapter 7.

Usage

stoch.reg(xdata, cols.full, cols.red=NULL, alpha, L, M, plot.which, col.resp=NULL, ...)

Arguments

Details

This function computes the spectral matrix, F statistics and coherences, and plots them. Returned as well are the coefficients in the impulse response function.

Enter, as the argument to this function, the full data matrix, and then the labels of the columns of input series in the "full" and "reduced" regression models - enter NULL if there are no inputs under the reduced model.

If the response variable is the LAST column of the data matrix, it need not be specified. Otherwise specify which column holds the responses as col.resp.

Other inputs are alpha (test size), L (smoothing), M (number of points in the discretization of the integral) and plot.which = "coh" or "F", to plot either the coherences or the F statistics.

Value

Note

See Example 7.1 of the text. The script is based on code that was contributed by Professor Doug Wiens, Department of Mathematical and Statistical Sciences, University of Alberta.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Biannual Sunspot Numbers

Description

Biannual smoothed (12-month moving average) number of sunspots from June 1749 to December 1978; n = 459. The "z" on the end is to distinguish this series from the one included with R (called sunspots).

Format

The format is: Time Series: Start = c(1749, 1) End = c(1978, 1) Frequency = 2

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Temperatures from the LA pollution study

Description

Temperature series corresponding to cmort from the LA pollution study.

Format

The format is: Time-Series [1:508] from 1970 to 1980: 72.4 67.2 62.9 72.5 74.2 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

lap, lap.xts

Test Linearity of a Time Series via Normalized Bispectrum

Description

Produces a plot of the tail probabilities of a normalized bispectrum of a series under the assumption the model is a linear process with iid innovations.

Usage

test.linear(series, color = TRUE, detrend = FALSE, main = NULL)

Arguments

Value

Note

The null hypothesis is that the data are from a linear process with i.i.d. innovations. Under the null hypothesis, the bispectrum is constant over all frequencies. Chi-squared test statistics are formed in blocks to measure departures from the null hypothesis and the corresponding p-values are displayed in a graphic and returned invisibly. Details are in Hinich, M. and Wolinsky, M. (2005). Normalizing bispectra. Journal of Statistical Planning and Inference, 130, 405–411.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

## Not run: 
test.linear(nyse)  # :(
test.linear(soi)   # :)

## End(Not run)

Estimate Trend

Description

Estimates the trend (polynomial or lowess) of a time series and returns a graphic of the series with the trend and error bounds superimposed.

Usage

trend(series, order = 1, lowess = FALSE, lowspan = .75, robust = TRUE,
         col = c(4, 6), ylab = NULL, ci = TRUE, results = FALSE, ...)

Arguments

Details

Produces a graphic of the time series with the trend and a .95 pointwise confidence interval superimposed. The trend estimate and the error bounds are returned invisibly.

Value

Produces a graphic and returns the trend estimate fit and error bounds lwr and upr invisibly (see details) and with the same time series attributes as the input series.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

detrend

Examples

## Not run: 

par(mfrow=2:1)
trend(soi)
trend(soi, lowess=TRUE)

## End(Not run)

Time Series Plot

Description

Produces a nice plot of univariate or multiple time series in one easy line.

Usage

tsplot(x, y=NULL, main=NULL, ylab=NULL, xlab='Time', type=NULL,  margins=.25, 
        ncolm=1, byrow=TRUE, nx=NULL, ny=nx, minor=TRUE, nxm=2, nym=1, 
        xm.grid=TRUE, ym.grid=TRUE, col=1, gg=FALSE, spaghetti=FALSE, pch=NULL, 
        lty=1, lwd=1, mgpp=0, topper=NULL, addLegend=FALSE, location='topright', 
        boxit=TRUE, horiz=FALSE, legend=NULL, llwd=NULL, scale=1, ...)

Arguments

Value

Produces a graphic and returns it invisibly so it can be saved in an R variable with the ability to replay it; see recordPlot.

Note

A legend can be added using addLegend=TRUE for spaghetti plots only. Spaghetti plots work if spaghetti=TRUE and there is more than one series being plotted.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Examples

## Not run: 

# minimal
tsplot(soi)
# prettified
tsplot(soi, col=4, main="Southern Oscillation Index")

# gris-gris multiple plot 
tsplot(climhyd, ncolm=2, gg=TRUE, col=2:7, lwd=2)  

# spaghetti (and store it in an object - ?recordPlot for details)
x <- replicate(100, cumsum(rcauchy(1000))/1:1000)
u <- tsplot(x, col=1:8, main='No LLN For You', spaghetti=TRUE)
u   #  plot on demand

# quick legend with spaghetti
tsplot(cbind(Mortality=cmort, Pollution=part), col=5:6, gg=TRUE, spaghetti=TRUE, addLegend=TRUE)
# ... and a little more control
tsplot(cbind(gtemp_land, gtemp_ocean), spaghetti=TRUE, lwd=2, col=astsa.col(c(4,2),.7), 
  ylab="\u00B0C", main="Global Temperature Anomalies", addLegend=TRUE, location='topleft', 
  horiz=TRUE, legend=c("Land Surface","Sea Surface"))


# compare these
par(mfrow=2:1)
tsplot(1:453, soi, ylab='SOI', xlab='Month')
# now recklessly add to the margins and add to mgp to get to the default
tsplot(1:453, soi, ylab='SOI', xlab='Month', margins=c(2,3,4,5), las=1, mgpp=c(1.4,.4,0))


# cex (and scale)
par(mfrow=c(3,1))  # cex gets small with mf plots 
  tsplot(cmort); tsplot(tempr); tsplot(part)
par(mfrow=c(3,1), cex=.9)  # so fix it 
  tsplot(cmort); tsplot(tempr); tsplot(part)

# it's rescaled here for your pleasure
tsplot(cbind(big=rnorm(100), bad=rnorm(100), john=rnorm(100)))  # default scale=1
tsplot(cbind(big=rnorm(100), bad=rnorm(100), john=rnorm(100)), scale=1.5)  # big

## End(Not run)

U.S. Unemployment

Description

Monthly U.S. Unemployment series (1948-1978, n = 372)

Usage

data(unemp)

Format

The format is: Time-Series [1:372] from 1948 to 1979: 235 281 265 241 201 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

See Also

UnempRate

Annual Varve Series

Description

Sedimentary deposits from one location in Massachusetts for 634 years, beginning nearly 12,000 years ago.

Format

The format is: Time-Series [1:634] from 1 to 634: 26.3 27.4 42.3 58.3 20.6 ...

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts and some help on using R for time series analysis can be found at https://nickpoison.github.io/.