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,
  margin = 0,
  auto_ubound = 0,
  phi_lbound = NULL,
  phi_ubound = NULL,
  bound = FALSE,
  max_iter = 100000L
)

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

Numeric scalar specifying the stability threshold for the real part of the eigenvalues. The default 0.0 corresponds to the imaginary axis; values less than 0.0 enforce a stricter stability margin.

auto_ubound

Numeric scalar specifying the upper bound for the diagonal elements of \(\boldsymbol{\Phi}\). Default is 0.0, requiring all diagonal values to be \(\leq 0\).

phi_lbound

Optional numeric matrix of same dim as phi. Use NA for no lower bound.

phi_ubound

Optional numeric matrix of same dim as phi. Use NA for no upper bound.

bound

Logical; if TRUE, resample until all elements respect bounds (NA bounds ignored).

max_iter

Safety cap on resampling attempts per draw.

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(), SimBetaNCovariate(), SimCovDiagN(), SimCovN(), SimIotaN(), SimNuN(), 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
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,] -0.3644239 -0.00686005  0.009970126
#> [2,]  0.7239323 -0.52938142  0.003689034
#> [3,] -0.4719376  0.74081034 -0.754595776
#> 
#> [[2]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.4035570  0.03114586 -0.03271647
#> [2,]  0.8064403 -0.49974876  0.03096005
#> [3,] -0.4538086  0.71467118 -0.71241195
#> 
#> [[3]]
#>            [,1]          [,2]        [,3]
#> [1,] -0.3510828  0.0001627612 -0.06830001
#> [2,]  0.7582763 -0.4885667794 -0.01073329
#> [3,] -0.4247432  0.7258476066 -0.70662470
#> 
#> [[4]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.3735633 -0.04210809 -0.08426100
#> [2,]  0.7876941 -0.47384904  0.04763003
#> [3,] -0.4729038  0.71066065 -0.69490587
#> 
#> [[5]]
#>            [,1]        [,2]         [,3]
#> [1,] -0.3434258  0.02084666 -0.004789062
#> [2,]  0.8196683 -0.55031101  0.016136026
#> [3,] -0.4922228  0.72245455 -0.674902868
#> 
#> [[6]]
#>            [,1]       [,2]        [,3]
#> [1,] -0.3461487  0.0322910  0.01262215
#> [2,]  0.7449142 -0.5253309  0.03305843
#> [3,] -0.4975340  0.7853186 -0.73998345
#> 
#> [[7]]
#>            [,1]        [,2]          [,3]
#> [1,] -0.3615692 -0.03668001  0.0005504809
#> [2,]  0.7318196 -0.49750777 -0.0274337166
#> [3,] -0.4485742  0.69805598 -0.6928824748
#> 
#> [[8]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.3304681 -0.01838064 -0.04678486
#> [2,]  0.7534764 -0.50637754  0.03727028
#> [3,] -0.4956332  0.74469756 -0.68462958
#> 
#> [[9]]
#>            [,1]        [,2]         [,3]
#> [1,] -0.3975887 -0.05272651 -0.085302392
#> [2,]  0.7927197 -0.53432838 -0.004704189
#> [3,] -0.4492825  0.73642496 -0.716512771
#> 
#> [[10]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.3446627  0.02023395  0.03049497
#> [2,]  0.7672337 -0.52994584 -0.01360389
#> [3,] -0.4769160  0.71338521 -0.68765222
#>