Simulate Diagonal Covariance Matrices from the Multivariate Normal Distribution

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

Usage

SimCovDiagN(n, sigma_diag, vcov_sigma_diag_l)

Arguments

n: Positive integer. Number of replications.
sigma_diag: Numeric matrix. The covariance matrix (\(\boldsymbol{\Sigma}\)).
vcov_sigma_diag_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 diagonal covariance matrices.

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

Author

Ivan Jacob Agaloos Pesigan

Examples

n <- 10
sigma_diag <- c(1, 1, 1)
vcov_sigma_diag_l <- t(chol(0.001 * diag(3)))
SimCovDiagN(
  n = n,
  sigma_diag = sigma_diag,
  vcov_sigma_diag_l = vcov_sigma_diag_l
)
#> [[1]]
#>          [,1]    [,2]     [,3]
#> [1,] 1.037143 0.00000 0.000000
#> [2,] 0.000000 1.01046 0.000000
#> [3,] 0.000000 0.00000 1.042843
#> 
#> [[2]]
#>          [,1]     [,2]      [,3]
#> [1,] 1.020923 0.000000 0.0000000
#> [2,] 0.000000 1.014463 0.0000000
#> [3,] 0.000000 0.000000 0.9894816
#> 
#> [[3]]
#>           [,1]     [,2]      [,3]
#> [1,] 0.9979561 0.000000 0.0000000
#> [2,] 0.0000000 1.001538 0.0000000
#> [3,] 0.0000000 0.000000 0.9954625
#> 
#> [[4]]
#>          [,1]     [,2]      [,3]
#> [1,] 1.004346 0.000000 0.0000000
#> [2,] 0.000000 1.000931 0.0000000
#> [3,] 0.000000 0.000000 0.9629609
#> 
#> [[5]]
#>          [,1]     [,2]      [,3]
#> [1,] 1.010956 0.000000 0.0000000
#> [2,] 0.000000 1.020065 0.0000000
#> [3,] 0.000000 0.000000 0.9734267
#> 
#> [[6]]
#>          [,1]     [,2]    [,3]
#> [1,] 1.036298 0.000000 0.00000
#> [2,] 0.000000 1.004114 0.00000
#> [3,] 0.000000 0.000000 1.03409
#> 
#> [[7]]
#>          [,1]     [,2]     [,3]
#> [1,] 0.988666 0.000000 0.000000
#> [2,] 0.000000 1.019745 0.000000
#> [3,] 0.000000 0.000000 1.008761
#> 
#> [[8]]
#>         [,1]     [,2]     [,3]
#> [1,] 1.02682 0.000000 0.000000
#> [2,] 0.00000 1.041622 0.000000
#> [3,] 0.00000 0.000000 1.029924
#> 
#> [[9]]
#>           [,1]     [,2]      [,3]
#> [1,] 0.9748926 0.000000 0.0000000
#> [2,] 0.0000000 1.037662 0.0000000
#> [3,] 0.0000000 0.000000 0.9818589
#> 
#> [[10]]
#>           [,1]      [,2]     [,3]
#> [1,] 0.9839876 0.0000000 0.000000
#> [2,] 0.0000000 0.9579473 0.000000
#> [3,] 0.0000000 0.0000000 1.002912
#>