ARXmdl: Autoregressive X Model
In roga11/MSTest: Hypothesis Testing for Markov Switching Models

ARXmdl

R Documentation

Autoregressive X Model

Description

This function estimates an ARX model with p lags. This can be used for the null hypothesis of a linear model against an alternative hypothesis of a Markov switching autoregressive model with k regimes.

Usage

ARXmdl(Y, p, Z, control = list())

Arguments

`Y`	A `(T x 1)` matrix of observations.
`p`	Integer determining the number of autoregressive lags.
`Z`	A `(T x qz)` matrix of exogenous regressors.
`control`	List with model options including: const: Boolean determining whether to estimate model with constant if `TRUE` or not if `FALSE`. Default is `TRUE`. getSE: Boolean determining whether to compute standard errors of parameters if `TRUE` or not if `FALSE`. Default is `TRUE`.

Value

List of class ARmdl (S3 object) with model attributes including:

y: a (T-p x 1) matrix of observations.
X: a (T-p x p + const) matrix of lagged observations with a leading column of 1s if const=TRUE or not if const=FALSE.
x: a (T-p x p) matrix of lagged observations.
fitted: a (T-p x 1) matrix of fitted values.
resid: a (T-p x 1) matrix of residuals.
mu: estimated mean of the process.
beta: a ((1 + p + qz) x 1) matrix of estimated coefficients.
betaZ: a (qz x q) matrix of estimated exogenous regressor coefficients.
intercept: estimate of intercept.
phi: estimates of autoregressive coefficients.
stdev: estimated standard deviation of the process.
sigma: estimated variance of the process.
theta: vector containing: mu, sigma, and phi.
theta_mu_ind: vector indicating location of mean with 1 and 0 otherwise.
theta_sig_ind: vector indicating location of variance with 1 and 0 otherwise.
theta_var_ind: vector indicating location of variance with 1 and 0 otherwise. This is the same as theta_sig_ind in ARmdl.
theta_phi_ind: vector indicating location of autoregressive coefficients with 1 and 0 otherwise.
stationary: Boolean indicating if process is stationary if TRUE or non-stationary if FALSE.
n: number of observations after lag transformation (i.e., n = T-p).
p: number of autoregressive lags.
q: number of series. This is always 1 in ARmdl.
k: number of regimes. This is always 1 in ARmdl.
control: List with model options used.
logLike: log-likelihood.
AIC: Akaike information criterion.
BIC: Bayesian (Schwarz) information criterion.
Hess: Hessian matrix. Approximated using hessian and only returned if getSE=TRUE.
info_mat: Information matrix. Computed as the inverse of -Hess. If matrix is not PD then nearest PD matrix is obtained using nearest_spd. Only returned if getSE=TRUE.
nearPD_used: Boolean determining whether nearPD function was used on info_mat if TRUE or not if FALSE. Only returned if getSE=TRUE.
theta_se: standard errors of parameters in theta. Only returned if getSE=TRUE.

Examples

set.seed(1234)
# Define DGP of AR process
mdl_ar <- list(n     = 500, 
               mu    = 5,
               sigma = 2,
               phi   = c(0.5,0.2))

# Simulate process using simuAR() function
y_simu <- simuAR(mdl_ar)

# Set options for model estimation
control <- list(const  = TRUE, 
                getSE  = TRUE)

# Estimate model
y_ar_mdl <- ARmdl(y_simu$y, p = 2, control)
y_ar_mdl

roga11/MSTest documentation built on Feb. 25, 2025, 6:10 p.m.