bvhar (version 2.1.0)

sim_mnormal: Generate Multivariate Normal Random Vector

Description

This function samples n x muti-dimensional normal random matrix.

Usage

sim_mnormal(
  num_sim,
  mu = rep(0, 5),
  sig = diag(5),
  method = c("eigen", "chol")
)

Value

T x k matrix

Arguments

num_sim

Number to generate process

mu

Mean vector

sig

Variance matrix

method

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

Details

Consider $x_1,\dots ,x_n\sim N_m(\mu ,\mathrm{\Sigma })$.

1. Lower triangular Cholesky decomposition: $\mathrm{\Sigma }=L{L}^T$

2. Standard normal generation: $Z_{i1},Z_{in}\stackrel{iid}{\sim }N(0,1)$

3. $Z_i=(Z_{i1},\dots ,Z_{in}{)}^T$

4. $X_i=L{Z}_i+\mu$