ARmdl function

Autoregressive Model

This function estimates an 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 autoregressive model with k regimes.

ARmdl(Y, p, control = list())

Arguments

• Y: A (T x 1) matrix of observations.

• p: Integer determining the number of autoregressive lags.

• 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 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) x 1) matrix of estimated 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

See Also

MSARmdl