| Title: | Estimation and Exogenous Covariate Selection for GARCH-X Models |
| Version: | 1.0 |
| Description: | Estimates the parameters of a GARCH-X model with exogenous covariates, performs hypothesis tests for the parameters returning the p-values, and uses False Discovery Rate p-value corrections to select the exogenous variables. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.2 |
| Imports: | GA, GenSA, pso, stats |
| NeedsCompilation: | no |
| Packaged: | 2025-06-13 23:07:41 UTC; azambom |
| Author: | Adriano Zambom [aut, cre], Elijah Sagaran [aut] |
| Maintainer: | Adriano Zambom <adriano.zambom@csun.edu> |
| Repository: | CRAN |
| Date/Publication: | 2025-06-17 06:00:06 UTC |
AIC for GARCHX model
Description
Calculates the Akaike Information Criterion for GARCHX model
Usage
AIC(model)
Arguments
model |
GARCHX object |
Value
AIC of GARCHX model
Examples
set.seed(123)
pi <- c(1, 0, 0, 4)
n <- 2000
d <- length(pi)
valinit <- 100
n2 <- n + d + 1
omega <- 0.1
alpha <- 0.2
beta <- 0.3
delta <- 2
e<-rnorm(n2+valinit)
Y<-e
for (t in 2:n2)
Y[t]<- 0.2*Y[t-1]+e[t]
x<-exp(Y)
X <- matrix(0, nrow = (n+valinit), ncol = length(pi))
for(j in 1:d)
X[, j] <- x[(d+2-j):(n+d+1-j+valinit)]
data <- GARCH.X::simulate(n, omega, alpha, beta, delta, X, pi, valinit = valinit)
model <- GARCHX_select(eps = data$eps, X = data$X)
AIC_value <- AIC(model)
BIC for GARCHX model
Description
Calculates the Bayesian Information Criterion of the GARCHX model
Usage
BIC(model)
Arguments
model |
GARCHX object |
Value
BIC of GARCHX model
Examples
set.seed(123)
pi <- c(1, 0, 0, 4)
n <- 2000
d <- length(pi)
valinit <- 100
n2 <- n + d + 1
omega <- 0.1
alpha <- 0.2
beta <- 0.3
delta <- 2
e<-rnorm(n2+valinit)
Y<-e
for (t in 2:n2)
Y[t]<- 0.2*Y[t-1]+e[t]
x<-exp(Y)
X <- matrix(0, nrow = (n+valinit), ncol = length(pi))
for(j in 1:d)
X[, j] <- x[(d+2-j):(n+d+1-j+valinit)]
data <- GARCH.X::simulate(n, omega, alpha, beta, delta, X, pi, valinit = valinit)
model <- GARCHX_select(eps = data$eps, X = data$X)
BIC_value <- BIC(model)
Fitting GARCHX model for variable selection
Description
Fits a GARCHX model with given data and estimates the coefficients for omega, alpha, beta, and pi
Usage
GARCHX(
eps,
X,
order = c(1, 1),
delta = 2,
optim.method = "NR"
)
Arguments
eps |
Time series |
X |
Matrix with exogenous covariates where the number of rows is equal to the length of eps |
order |
Order of the GARCH model. Value of p cannot be 0 |
delta |
Value of the power of the main time series to allow for Power GARCHX, default is 2 for GARCHX |
optim.method |
Optimization method for maximizing quasi-likelihood function. Options: "NR", "L-BFGS-B", "GA", "PS", "SA". Default value is "NR" |
Details
Uses the GARCHX model
\mathcal{E}_t = \sigma_tw_t
\sigma^2_t = \omega_0 + \sum^{p}_{i=1}\alpha_i\mathcal{E}_{t-i}^2 + \sum^q_{j=1}\beta_j\sigma^2_{t-j}+\mathbf{\pi}^T\mathbf{x}_{t-1}
To estimate the coefficients for
\omega, \alpha, \beta, \pi
. No variable selection is done in this function.
Value
An object of class GARCHX
Variable selection for exogenous covariates in GARCHX models
Description
Performs variable selection on the exogenous covariates through testing each covariate in X and correcting the p-values for multiple testing.
Usage
GARCHX_select(
eps,
X,
order = c(1, 1),
delta = 2,
alpha.level = 0.05,
adjust.method = "fdr",
optim.method = "NR"
)
Arguments
eps |
Time series data |
X |
Matrix with exogenous covariates where the number of rows is equal to the length of eps |
order |
Order of the GARCH model. Value of p cannot be 0. |
delta |
Value of the power of the main time series to allow for Power GARCHX, default is 2 for GARCHX |
alpha.level |
Alpha level for p-value cut-off in variable selection |
adjust.method |
Multiple testing p-value adjustment, see p.adjust. Possible values are "holm", "hochberg", "hommel", "bonferonni", "BH", "BY", "fdr", "none" |
optim.method |
Optimization method for maximizing quasi-likelihood function. Options: "NR", "L-BFGS-B", "GA", "PS", "SA". Default value is "NR" |
Details
Using the GARCHX model
\mathcal{E}_t = \sigma_tw_t
\sigma^2_t = \omega_0 + \sum^{p}_{i=1}\alpha_i\mathcal{E}_{t-i}^2 + \sum^q_{j=1}\beta_j\sigma^2_{t-j}+\mathbf{\pi}^T\mathbf{x}_{t-1}
performs variable selection by testing
H_0: \pi_j = 0, \forall j
and compares the p-values to the adjusted alpha level according to adjust.method. If alpha.level = 1, then no variable selection is performed and the function only estimates the parameters
Value
An object of class GARCHX
References
Francq, C. and Thieu, L.Q.(2018). QML Inference for Volatility Models with Covariates. Econometric Theory, Cambridge University Press
Examples
set.seed(123)
pi <- c(1, 0, 0, 4)
n <- 2000
d <- length(pi)
valinit <- 100
n2 <- n + d + 1
omega <- 0.1
alpha <- 0.2
beta <- 0.3
delta <- 2
e<-rnorm(n2+valinit)
Y<-e
for (t in 2:n2)
Y[t]<- 0.2*Y[t-1]+e[t]
x<-exp(Y)
X <- matrix(0, nrow = (n+valinit), ncol = length(pi))
for(j in 1:d)
X[, j] <- x[(d+2-j):(n+d+1-j+valinit)]
data <- GARCH.X::simulate(n, omega, alpha, beta, delta, X, pi, valinit = valinit)
model <- GARCHX_select(eps = data$eps, X = data$X)
Predict GARCHX future time series values
Description
Predicts values for GARCHX model
Usage
predict(model, X, n_pred)
Arguments
model |
GARCHX object |
X |
Exogenous covariates for predictions |
n_pred |
Number of predictions into the future |
Value
Vector of predicted time series data
References
Francq, C. and Thieu, L.Q.(2018). QML Inference for Volatility Models with Covariates. Econometric Theory, Cambridge University Press
Examples
set.seed(123)
pi <- c(1, 0, 0, 4)
n <- 2000
d <- length(pi)
valinit <- 100
n2 <- n + d + 1
omega <- 0.1
alpha <- 0.2
beta <- 0.3
delta <- 2
e<-rnorm(n2+valinit)
Y<-e
for (t in 2:n2)
Y[t]<- 0.2*Y[t-1]+e[t]
x<-exp(Y)
X <- matrix(0, nrow = (n+valinit), ncol = length(pi))
for(j in 1:d)
X[, j] <- x[(d+2-j):(n+d+1-j+valinit)]
data <- GARCH.X::simulate(n, omega, alpha, beta, delta, X, pi, valinit = valinit)
model <- GARCHX_select(eps = data$eps, X = data$X)
n_pred = 10
test.X <- data$X[(n-n_pred+1):n, ]
predictions <- predict(model = model, X = test.X, n_pred = n_pred)
Simulate GARCHX model
Description
Simulates Time series data from GARCH model with exogenous covariates
Usage
simulate(n, omega, alpha, beta, delta = 2, X, pi, shock.distr = "Normal", valinit = 200)
Arguments
n |
Desired length of simulated time series data |
omega |
Coefficient value for omega, required to be
|
alpha |
ARCH Coefficient value, required to be
|
beta |
GARCH Coefficient value, required to be
|
delta |
Value of the power of the time series to allow for Power GARCHX, default is 2 for GARCHX |
X |
Matrix with exogenous covariates where the number of rows is equal to the length of n + valinit |
pi |
Vector containing coefficients for exogenous covariates. |
shock.distr |
Distribution of the shock eta_t that multiply w_t in the GARCH-X model eps_ = w_t*eta_t. |
valinit |
Initialization value, default value is 200 |
Value
A named list containing vector of Time Series data and X covariates used
Examples
n <- 200
d <- 4
valinit <- 100
n2 <- n + d + 1
omega <- 0.05
alpha <- 0.05
beta <- 0.05
delta <- 2
pi <- rep(0.05, d)
e<-rnorm(n2+valinit)
Y<-e
for (t in 2:n2)
Y[t]<- 0.2*Y[t-1]+e[t]
x<-exp(Y)
X <- matrix(0, nrow = (n+valinit), ncol = length(pi))
for(j in 1:d)
X[, j] <- x[(d+2-j):(n+d+1-j+valinit)]
data <- simulate(n, omega, alpha, beta, delta, X, pi, valinit = valinit)