sim_vhar {bvhar}

Generate Multivariate Time Series Process Following VAR(p)

Description

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.varlse() 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.

Details

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

1. Generate \epsilon_1, \epsilon_n \sim N(0, \Sigma)

2. For i = 1, ... n,

   y_{M + i} = (y_{M + i - 1}^T, \ldots, y_i^T, 1)^T C_{HAR}^T \Phi + \epsilon_i

3. Then the output is (y_{M + 1}, \ldots, y_{n + M})^T

4. For i = 1, ... n,

   y_{p + i} = (y_{p + i - 1}^T, \ldots, y_i^T, 1)^T B + \epsilon_i

5. 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.

Value

T x k matrix

References

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