Simulate Random Drift Matrices from the Multivariate Normal Distribution and Project to Hurwitz

This function simulates random dirft matrices from the multivariate normal distribution then projects each draw to the Hurwitz-stable region using ProjectToHurwitz().

Usage

SimPhiN2(n, phi, vcov_phi_vec_l, margin = 0.001)

Arguments

n: Positive integer. Number of replications.
phi: Numeric matrix. The drift matrix (\(\boldsymbol{\Phi}\)).
vcov_phi_vec_l: Numeric matrix. Cholesky factorization (t(chol(vcov_phi_vec))) of the sampling variance-covariance matrix of \(\mathrm{vec} \left( \boldsymbol{\Phi} \right)\).
margin: Positive numeric. Target buffer so that the spectral abscissa is \(\le -\text{margin}\) (default 1e-3).

Value

Returns a list of random drift 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(), SimCovN(), SimIotaN(), SimMVN(), SimMuN(), SimNuN(), SimPhiN(), SimPhiNCovariate(), SimSSMFixed(), SimSSMIVary(), SimSSMLinGrowth(), SimSSMLinGrowthIVary(), SimSSMLinSDEFixed(), SimSSMLinSDEIVary(), SimSSMOUFixed(), SimSSMOUIVary(), SimSSMVARFixed(), SimSSMVARIVary(), SpectralRadius(), TestPhi(), TestPhiHurwitz(), TestStability(), TestStationarity()

Author

Ivan Jacob Agaloos Pesigan

Examples

n <- 10
phi <- matrix(
  data = c(
    -0.357, 0.771, -0.450,
    0.0, -0.511, 0.729,
    0, 0, -0.693
  ),
  nrow = 3
)
vcov_phi_vec_l <- t(chol(0.001 * diag(9)))
SimPhiN2(n = n, phi = phi, vcov_phi_vec_l = vcov_phi_vec_l)
#> [[1]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.3898905 -0.00553865 -0.01778982
#> [2,]  0.7938146 -0.53407038  0.03052566
#> [3,] -0.5122352  0.74059043 -0.69089644
#> 
#> [[2]]
#>            [,1]       [,2]        [,3]
#> [1,] -0.3676836 -0.0039967 -0.06034504
#> [2,]  0.7744181 -0.4793175  0.03005414
#> [3,] -0.4750508  0.7039543 -0.65819457
#> 
#> [[3]]
#>            [,1]         [,2]         [,3]
#> [1,] -0.3648512  0.005999648  0.004565715
#> [2,]  0.7460663 -0.545095278  0.002514716
#> [3,] -0.4587547  0.718689032 -0.655266780
#> 
#> [[4]]
#>            [,1]         [,2]          [,3]
#> [1,] -0.3646226  0.002226638  0.0001713893
#> [2,]  0.7623997 -0.513546670 -0.0401962759
#> [3,] -0.4712947  0.759137005 -0.7331935022
#> 
#> [[5]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.3374115 -0.03631547 -0.03522833
#> [2,]  0.7829520 -0.51424701 -0.02122889
#> [3,] -0.4593276  0.71458045 -0.72769393
#> 
#> [[6]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.3639378 -0.02178019  0.03261244
#> [2,]  0.7968141 -0.51485211  0.00289716
#> [3,] -0.4635005  0.69815458 -0.66238104
#> 
#> [[7]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.3942297  0.02094066 -0.02158031
#> [2,]  0.7984825 -0.53096047  0.03250162
#> [3,] -0.4819357  0.74745080 -0.70935891
#> 
#> [[8]]
#>            [,1]       [,2]        [,3]
#> [1,] -0.3657105  0.0333104 -0.02528062
#> [2,]  0.8121938 -0.5232222 -0.04990546
#> [3,] -0.4275957  0.7362539 -0.64011685
#> 
#> [[9]]
#>            [,1]         [,2]        [,3]
#> [1,] -0.3276867  0.002224122  0.02757431
#> [2,]  0.7527464 -0.564012342 -0.02370732
#> [3,] -0.4262468  0.724154016 -0.70016594
#> 
#> [[10]]
#>            [,1]        [,2]         [,3]
#> [1,] -0.3434785 -0.03717281 -0.026153021
#> [2,]  0.8416886 -0.56042143  0.001184558
#> [3,] -0.4619536  0.76184134 -0.731455246
#>