bvhar (version 2.2.2)

sim_var: Generate Multivariate Time Series Process Following VAR(p)

Description

This function generates multivariate time series dataset that follows VAR(p).

Usage

sim_var(
  num_sim,
  num_burn,
  var_coef,
  var_lag,
  sig_error = diag(ncol(var_coef)),
  init = matrix(0L, nrow = var_lag, ncol = ncol(var_coef)),
  method = c("eigen", "chol"),
  process = c("gaussian", "student"),
  t_param = 5
)

Value

T x k matrix

Arguments

num_sim

Number to generated process

num_burn

Number of burn-in

var_coef

VAR coefficient. The format should be the same as the output of coef() from var_lm()

var_lag

Lag of VAR

sig_error

Variance matrix of the error term. By default, diag(dim).

init

Initial y1, ..., yp matrix to simulate VAR model. Try matrix(0L, nrow = var_lag, ncol = dim).

method

Method to compute ${\mathrm{\Sigma }}^{1/2}$. Choose between eigen (spectral decomposition) and chol (cholesky decomposition). By default, eigen.

process

Process to generate error term. gaussian: Normal distribution (default) or student: Multivariate t-distribution.

t_param

argument for MVT, e.g. DF: 5.

Details

1. Generate ${ϵ}_1,{ϵ}_n\sim N(0,\mathrm{\Sigma })$

2. For i = 1, ... n, $$y_{p+i}=(y_{p+i-1}^T,\dots ,y_i^T,1{)}^{T}B+{ϵ}_i$$

3. Then the output is $(y_{p+1},\dots ,y_{n+p}{)}^T$

Initial values might be set to be zero vector or $(I_m-A_1-\cdots -A_p{)}^{-1}c$.

References

Lütkepohl, H. (2007). New Introduction to Multiple Time Series Analysis. Springer Publishing.