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.

See also

Other Simulation of State Space Models Data Functions: LinSDE2SSM(), LinSDECovEta(), LinSDECovY(), LinSDEMeanEta(), LinSDEMeanY(), ProjectToHurwitz(), ProjectToStability(), SSMCovEta(), SSMCovY(), SSMMeanEta(), SSMMeanY(), SimAlphaN(), SimBetaN(), SimBetaN2(), SimCovDiagN(), SimCovN(), SimIotaN(), SimNuN(), SimPhiN(), 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,] -0.3461487  0.0322910  0.01262215
#> [2,]  0.7449142 -0.5253309  0.03305843
#> [3,] -0.4975340  0.7853186 -0.73998345
#> 
#> [[2]]
#>            [,1]        [,2]          [,3]
#> [1,] -0.3615692 -0.03668001  0.0005504809
#> [2,]  0.7318196 -0.49750777 -0.0274337166
#> [3,] -0.4485742  0.69805598 -0.6928824748
#> 
#> [[3]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.3304681 -0.01838064 -0.04678486
#> [2,]  0.7534764 -0.50637754  0.03727028
#> [3,] -0.4956332  0.74469756 -0.68462958
#> 
#> [[4]]
#>            [,1]        [,2]         [,3]
#> [1,] -0.3975887 -0.05272651 -0.085302392
#> [2,]  0.7927197 -0.53432838 -0.004704189
#> [3,] -0.4492825  0.73642496 -0.716512771
#> 
#> [[5]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.3446627  0.02023395  0.03049497
#> [2,]  0.7672337 -0.52994584 -0.01360389
#> [3,] -0.4769160  0.71338521 -0.68765222
#> 
#> [[6]]
#>            [,1]         [,2]        [,3]
#> [1,] -0.3488294 -0.002825644 -0.05151846
#> [2,]  0.7693948 -0.511840568  0.01103531
#> [3,] -0.5055667  0.677296735 -0.73582263
#> 
#> [[7]]
#>            [,1]        [,2]         [,3]
#> [1,] -0.3640059  0.01491232 -0.016820119
#> [2,]  0.7871740 -0.47741060 -0.002503593
#> [3,] -0.3991533  0.76332088 -0.651841743
#> 
#> [[8]]
#>            [,1]         [,2]        [,3]
#> [1,] -0.3498894  0.008644179  0.04224443
#> [2,]  0.8016439 -0.528705326  0.01818416
#> [3,] -0.4456561  0.675355254 -0.72861089
#> 
#> [[9]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.3365547  0.02514259  0.03446106
#> [2,]  0.7938113 -0.52518519 -0.07951748
#> [3,] -0.4749720  0.72711246 -0.68422099
#> 
#> [[10]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.4015380  0.01008559 -0.03289046
#> [2,]  0.7673999 -0.48921153  0.02281463
#> [3,] -0.3932220  0.71701902 -0.75523524
#>