Generate Multivariate Time Series Process Following VAR(p)

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

Usage

sim_vhar(
  num_sim,
  num_burn,
  vhar_coef,
  week = 5L,
  month = 22L,
  sig_error = diag(ncol(vhar_coef)),
  init = matrix(0L, nrow = month, ncol = ncol(vhar_coef)),
  method = c("eigen", "chol"),
  process = c("gaussian", "student"),
  t_param = 5
)

Arguments

num_sim: Number to generated process
num_burn: Number of burn-in
vhar_coef: VAR coefficient. The format should be the same as the output of coef() from var_lm()
week: Weekly order of VHAR. By default, 5.
month: Weekly order of VHAR. By default, 22.
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 = month, ncol = dim).
method: Method to compute $\Sigma^{1/2}$. 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.

Value

T x k matrix

Details

Let $M$ be the month order, e.g. $M = 22$.

Generate $\epsilon_1, \epsilon_n \sim N(0, \Sigma)$
For i = 1, ... n, $$y_{M + i} = (y_{M + i - 1}^T, \ldots, y_i^T, 1)^T C_{HAR}^T \Phi + \epsilon_i$$
Then the output is $(y_{M + 1}, \ldots, y_{n + M})^T$
For i = 1, ... n, $$y_{p + i} = (y_{p + i - 1}^T, \ldots, y_i^T, 1)^T B + \epsilon_i$$
Then the output is $(y_{p + 1}, \ldots, y_{n + p})^T$

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.