VARXmdl function

Vector X autoregressive model

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

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

Arguments

• Y: a (T x q) 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.

Returns

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

• y: a (T-p x q) matrix of observations.
• X: a (T-p x p*q + 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*q) matrix of lagged observations.
• fitted: a (T-p x q) matrix of fitted values.
• resid: a (T-p x q) matrix of residuals.
• mu: a (1 x q) vector of estimated means of each process.
• beta: a ((1 + p + qz) x q) matrix of estimated coefficients.
• betaZ: a (qz x q) matrix of estimated exogenous regressor coefficients.
• intercept: estimate of intercepts.
• phi: a (q x p*q) matrix of estimated autoregressive coefficients.
• Fmat: Companion matrix containing autoregressive coefficients.
• stdev: a (q x 1) vector of estimated standard deviation of each process.
• sigma: a (q x q) estimated covariance matrix.
• theta: vector containing: mu, vech(sigma), and vec(t(phi)).
• theta_mu_ind: vector indicating location of mean with 1 and 0 otherwise.
• theta_sig_ind: vector indicating location of variance and covariances with 1 and 0 otherwise.
• theta_var_ind: vector indicating location of variances with 1 and 0 otherwise.
• 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.
• k: number of regimes. This is always 1 in VARmdl.
• Fmat: matrix from companion form. Used to determine is process is stationary.
• 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

# ----- Bivariate VAR(1) process ----- #
set.seed(1234)
# Define DGP of VAR process
mdl_var <- list(n     = 1000, 
                p     = 1,
                q     = 2,
                mu    = c(5,-2),
                sigma = rbind(c(5.0, 1.5),
                              c(1.5, 1.0)),
                phi   = rbind(c(0.50, 0.30),
                              c(0.20, 0.70)))

# Simulate process using simuVAR() function
y_simu <- simuVAR(mdl_var)

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

# Estimate model
y_var_mdl <- VARmdl(y_simu$y, p = 2, control = control)
summary(y_var_mdl)

See Also

MSVARmdl