Simulate Covariance Matrices from the Multivariate Normal Distribution

This function simulates random covariance matrices from the multivariate normal distribution. The function ensures that the generated covariance matrices are positive semi-definite.

Usage

SimCovN(n, sigma, vcov_sigma_vech_l)

Arguments

n: Positive integer. Number of replications.
sigma: Numeric matrix. The covariance matrix (\(\boldsymbol{\Sigma}\)).
vcov_sigma_vech_l: Numeric matrix. Cholesky factorization (t(chol(vcov_sigma_vech))) of the sampling variance-covariance matrix of \(\mathrm{vech} \left( \boldsymbol{\Sigma} \right)\).

Value

Returns a list of random covariance matrices.

Other Simulation of State Space Models Data Functions: LinSDE2SSM(), LinSDECovEta(), LinSDECovY(), LinSDEInterceptEta(), LinSDEInterceptY(), LinSDEMeanEta(), LinSDEMeanY(), ProjectToHurwitz(), ProjectToStability(), SSMCovEta(), SSMCovY(), SSMInterceptEta(), SSMInterceptY(), SSMMeanEta(), SSMMeanY(), SimAlphaN(), SimBetaN(), SimBetaN2(), SimBetaNCovariate(), SimCovDiagN(), SimIotaN(), SimMVN(), SimMuN(), SimNuN(), SimPhiN(), SimPhiN2(), SimPhiNCovariate(), SimSSMFixed(), SimSSMIVary(), SimSSMLinGrowth(), SimSSMLinGrowthIVary(), SimSSMLinSDEFixed(), SimSSMLinSDEIVary(), SimSSMOUFixed(), SimSSMOUIVary(), SimSSMVARFixed(), SimSSMVARIVary(), SpectralRadius(), TestPhi(), TestPhiHurwitz(), TestStability(), TestStationarity()

Author

Ivan Jacob Agaloos Pesigan

Examples

n <- 10
sigma <- matrix(
  data = c(
    1.0, 0.5, 0.3,
    0.5, 1.0, 0.4,
    0.3, 0.4, 1.0
  ),
  nrow = 3
)
vcov_sigma_vech_l <- t(
  chol(
    0.001 * diag(3 * (3 + 1) / 2)
  )
)
SimCovN(
  n = n,
  sigma = sigma,
  vcov_sigma_vech_l = vcov_sigma_vech_l
)
#> [[1]]
#>           [,1]      [,2]      [,3]
#> [1,] 0.9742215 0.4844067 0.3289707
#> [2,] 0.4844067 1.0065213 0.4237028
#> [3,] 0.3289707 0.4237028 0.9572151
#> 
#> [[2]]
#>           [,1]      [,2]      [,3]
#> [1,] 0.9597157 0.4643785 0.2954098
#> [2,] 0.4643785 0.9975186 0.4238913
#> [3,] 0.2954098 0.4238913 0.9484577
#> 
#> [[3]]
#>           [,1]      [,2]      [,3]
#> [1,] 0.9898989 0.5065099 0.3439838
#> [2,] 0.5065099 0.9841791 0.4070641
#> [3,] 0.3439838 0.4070641 0.9440822
#> 
#> [[4]]
#>           [,1]      [,2]      [,3]
#> [1,] 0.9471224 0.5097071 0.2638273
#> [2,] 0.5097071 1.0174320 0.4290599
#> [3,] 0.2638273 0.4290599 0.9734041
#> 
#> [[5]]
#>           [,1]      [,2]      [,3]
#> [1,] 0.9846425 0.4959778 0.3286602
#> [2,] 0.4959778 0.9919400 0.3803007
#> [3,] 0.3286602 0.3803007 1.0068224
#> 
#> [[6]]
#>           [,1]      [,2]      [,3]
#> [1,] 1.0009730 0.5796971 0.2974445
#> [2,] 0.5796971 1.0318089 0.4512592
#> [3,] 0.2974445 0.4512592 0.9680744
#> 
#> [[7]]
#>           [,1]      [,2]      [,3]
#> [1,] 1.0099154 0.4502194 0.2802876
#> [2,] 0.4502194 1.0110675 0.3887407
#> [3,] 0.2802876 0.3887407 0.9849274
#> 
#> [[8]]
#>           [,1]      [,2]      [,3]
#> [1,] 0.9747801 0.4793178 0.3656572
#> [2,] 0.4793178 0.9663087 0.3904455
#> [3,] 0.3656572 0.3904455 0.9793431
#> 
#> [[9]]
#>           [,1]      [,2]      [,3]
#> [1,] 0.9594177 0.5274351 0.3060267
#> [2,] 0.5274351 1.0358792 0.3990601
#> [3,] 0.3060267 0.3990601 0.9455439
#> 
#> [[10]]
#>           [,1]      [,2]      [,3]
#> [1,] 0.9357604 0.4534859 0.3150958
#> [2,] 0.4534859 1.0011291 0.3767855
#> [3,] 0.3150958 0.3767855 1.0697661
#>