| Type: | Package |
| Title: | Testing Large VARs for the Presence of Cointegration |
| Version: | 1.0.3 |
| Maintainer: | Eszter Kiss <ekiss2803@gmail.com> |
| Description: | Conducts a cointegration test for high-dimensional vector autoregressions (VARs) of order k based on the large N,T asymptotics of Bykhovskaya and Gorin, 2022 (<doi:10.48550/arXiv.2202.07150>). The implemented test is a modification of the Johansen likelihood ratio test. In the absence of cointegration the test converges to the partial sum of the Airy-1 point process. This package contains simulated quantiles of the first ten partial sums of the Airy-1 point process that are precise up to the first three digits. |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 7.3.2 |
| Depends: | R (≥ 3.5.0) |
| Imports: | methods, graphics, stats, utils |
| Suggests: | testthat (≥ 3.0.0), tibble (≥ 3.0.0), data.table (≥ 1.14.0), readr (≥ 2.1.0) |
| Config/testthat/edition: | 3 |
| License: | MIT + file LICENSE |
| URL: | https://github.com/eszter-kiss/Largevars |
| NeedsCompilation: | no |
| Packaged: | 2025-05-18 23:53:25 UTC; ekiss |
| Author: | Anna Bykhovskaya [aut], Vadim Gorin [aut], Eszter Kiss [cre, aut] |
| Repository: | CRAN |
| Date/Publication: | 2025-05-19 02:10:02 UTC |
Input checker for largevar function
Description
This is an internal function that checks the validity of the inputs of the largevar function.
Usage
check_input_largevar(
data,
k,
r,
fin_sample_corr,
plot_output,
significance_level
)
Arguments
data |
a numeric matrix where columns contain the individual time series that will be examined for presence of cointegrating relationships |
k |
The number of lags we wish to employ in the VECM form (default: k=1) |
r |
The number of cointegrating relationships we impose on the H1 hypothesis (default: r=1) |
fin_sample_corr |
A boolean variable indicating whether we wish to employ finite sample correction on our test statistic. Default is false |
plot_output |
A boolean variable indicating whether we wish to generate the distribution of the eigenvalues (default: TRUE) |
significance_level |
Specify the significance level at which the decision about the H0 should be made. For r=1 this can be any level of significance. For r=2 and r=3, the significance level input will be rounded up to the nearest of the following: 0.1, 0.05, 0.025, 0.01. If the significance level is larger than 0.1, the decision will be made at the 10% level. For r>3 only the test statistic is returned. For an empirical p-value for r>3 use the sim_function fun. in the package. |
Value
Nothing (or warning message) if all inputs are correct, and an error message otherwise.
Input checker for simfun function
Description
This is an internal function that checks the validity of the inputs of the sim function function.
Usage
check_input_simfun(N, tau, stat_value, k, r, fin_sample_corr, sim_num, seed)
Arguments
N |
a number representing the number of time series we want to simulate in the system |
tau |
a number representing the length of the time series we want to simulate in the system |
stat_value |
the test statistic value we want to calculate p-value based on |
k |
The number of lags we wish to employ in the VECM form (default: k=1) |
r |
The number of cointegrating relationships we impose on the H1 hypothesis (default: r=1) |
sim_num |
The number of simulation we wish to run. |
Value
Nothing (or warning message) if all inputs are correct, and an error message otherwise.
Cointegration test for settings of large N and T
Description
Runs the Bykhovskaya-Gorin test for cointegration. Paper can be found at: https://doi.org/10.48550/arXiv.2202.07150
Usage
largevar(
data = NULL,
k = 1,
r = 1,
fin_sample_corr = FALSE,
plot_output = TRUE,
significance_level = 0.05
)
Arguments
data |
A numeric matrix where the columns contain individual time series that will be examined for the presence of cointegrating relationships. |
k |
The number of lags that we wish to employ in the vector autoregression. The default value is k = 1. |
r |
The number of largest eigenvalues used in the test. The default value is r = 1. |
fin_sample_corr |
A boolean variable indicating whether we wish to employ finite sample correction on our test statistic. The default value is fin_sample_corr = FALSE. |
plot_output |
A boolean variable indicating whether we wish to generate a plot of the empirical distribution of eigenvalues. The default value plot_output = TRUE. |
significance_level |
Specify the significance level at which the decision about H0 should be made. The default value is significance_level = 0.05. |
Value
A list that contains the test statistic, a table with theoretical quantiles presented for r=1 to r=10, and the decision about H0 at the significance level specified by the user.
Examples
largevar(
data = matrix(rnorm(60, mean = 0.05, sd = 0.01), 20, 3),
k = 1,
r = 1,
fin_sample_corr = FALSE,
plot_output = FALSE,
significance_level = 0.05
)
Internal skeleton function of cointegration test for simfun function
Description
This is the "skeleton" version of the largevar function in the package. It is called within the sim_function function to make runtime faster. For the actual cointegration test, use the largevar function.
Usage
largevar_scel(data, k, r, fin_sample_corr)
Arguments
data |
a numeric matrix where columns contain the individual time series that will be examined for presence of cointegrating relationships |
k |
The number of lags we wish to employ in the VECM form (default: k=1) |
r |
The number of cointegrating relationships we impose on the H1 hypothesis (default: r=1) |
fin_sample_corr |
A boolean variable indicating whether we wish to employ finite sample correction on our test statistic. Default is false. |
Value
The test statistic.
Quantiles for the limiting distribution of the test
Description
A data frame containing the simulated quantiles for the test statistic used in the largevar function. More details about how these simulations were conducted can be found in Section 4 of the vignette.
Format
A data frame with 99 rows and 11 variables:
Source
Calculated through own simulations (see details in vignette).
Creates the quantile table output for largevar function
Description
Outputs the quantile tables from the package's corresponding vignette.
Usage
quantile_tables(r = 1)
Arguments
r |
Which partial sum the quantile table should be returned for. (Only r<=10 is available.) Default is r=1. |
Value
A numeric matrix.
Examples
quantile_tables(r=3)
Stock price data for example in vignette
Description
A data frame containing weekly S&P100 prices over ten years: 01.01.2010 - 01.01.2020, The S&P100 includes 101 leading U.S. stocks of which 92 were collected here.
Format
A data frame with 522 rows and 93 variables:
Source
Refer to the data source used in: A. Bykhovskaya and V. Gorin. Cointegration in large vars. Annals of Statistics, 2022.
Empirical p-value for cointegration test
Description
Runs a simulation on the H0 for the Bykhovskaya-Gorin test for cointegration and returns an empirical p-value. Paper can be found at: https://doi.org/10.48550/arXiv.2202.07150
Usage
sim_function(
N = NULL,
tau = NULL,
stat_value = NULL,
k = 1,
r = 1,
fin_sample_corr = FALSE,
sim_num = 1000,
seed = NULL
)
Arguments
N |
The number of time series used in simulations. |
tau |
The length of the time series used in simulations. |
stat_value |
The test statistic value for which the p-value is calculated. |
k |
The number of lags that we wish to employ in the vector autoregression. The default value is k = 1. |
r |
The number of largest eigenvalues used in the test. The default value is r = 1. |
fin_sample_corr |
A boolean variable indicating whether we wish to employ finite sample correction on our test statistics. The default value is fin_sample_corr = FALSE. |
sim_num |
The number of simulations that the function conducts for H0. The default value is sim_num = 1000. |
seed |
The random seed that a user can set for replicable simulation results. The default value is seed = NULL. |
Value
A list that contains the simulation values, the empirical percentage (realizations larger than the test statistic provided by the user) and a histogram.
Examples
sim_function(N=90, tau=501, stat_value=-0.27,k=1,r=1,sim_num=30, seed = 0)