Simulate Random Drift Matrices from the Multivariate Normal Distribution

This function simulates random drift matrices from the multivariate normal distribution. The function ensures that the generated drift matrices are stable using TestPhi().

Usage

SimPhiN(n, phi, vcov_phi_vec_l)

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 \(\mathrm{vec} \left( \boldsymbol{\Phi} \right)\).

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(), SimPhiN2(), 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)))
SimPhiN(n = n, phi = phi, vcov_phi_vec_l = vcov_phi_vec_l)
#> [[1]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.3190641  0.03503587  0.02114061
#> [2,]  0.7662336 -0.48145138 -0.01244207
#> [3,] -0.4364891  0.77205909 -0.68438869
#> 
#> [[2]]
#>            [,1]        [,2]         [,3]
#> [1,] -0.3394220  0.05248648  0.062837536
#> [2,]  0.7783253 -0.58011157  0.004901415
#> [3,] -0.4661241  0.76906195 -0.650828177
#> 
#> [[3]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.3162300 -0.00156391 -0.02669320
#> [2,]  0.7447820 -0.55108987  0.01353968
#> [3,] -0.4417182  0.77294645 -0.68782445
#> 
#> [[4]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.3425154  0.02838189  0.01433782
#> [2,]  0.7610361 -0.53387189  0.02186514
#> [3,] -0.4443914  0.76735112 -0.68585070
#> 
#> [[5]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.3786049  0.02613982  0.04793082
#> [2,]  0.7696926 -0.53921143  0.02534600
#> [3,] -0.4986717  0.73863608 -0.69941142
#> 
#> [[6]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.2926671  0.06408923 -0.06179864
#> [2,]  0.7507533 -0.49265442 -0.04235275
#> [3,] -0.4439021  0.74013590 -0.72922121
#> 
#> [[7]]
#>            [,1]        [,2]         [,3]
#> [1,] -0.3528044  0.01056376  0.018110223
#> [2,]  0.7481218 -0.49991164  0.006361179
#> [3,] -0.3979919  0.69905303 -0.687941615
#> 
#> [[8]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.3312080 -0.03685342  0.01274581
#> [2,]  0.7317721 -0.49631504  0.01093565
#> [3,] -0.4326465  0.74995482 -0.66396122
#> 
#> [[9]]
#>            [,1]        [,2]         [,3]
#> [1,] -0.3610083 -0.03531067 -0.033914896
#> [2,]  0.7960642 -0.50036814  0.003523242
#> [3,] -0.3862721  0.73619880 -0.727511046
#> 
#> [[10]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.3484965  0.01285986 -0.02193760
#> [2,]  0.7208592 -0.51842387 -0.00686005
#> [3,] -0.5307973  0.68193233 -0.71138142
#>