Simulate Random Drift Matrices with a Covariate from the Multivariate Normal Distribution

This function simulates random drift matrices from the multivariate normal distribution, allowing the mean drift matrix to vary as a linear function of a covariate The function ensures that the generated drift matrices are stable using TestPhi().

Usage

SimPhiNCovariate(
  n,
  phi0,
  vcov_phi_vec_l,
  phi1,
  x,
  margin = 0,
  auto_ubound = 0,
  phi_lbound = NULL,
  phi_ubound = NULL,
  bound = FALSE,
  max_iter = 100000L
)

Arguments

n: Positive integer. Number of replications.
phi0: Numeric matrix. Baseline drift matrix (\(\boldsymbol{\Phi}_0\)).
vcov_phi_vec_l: Numeric matrix. Cholesky factorization (t(chol(vcov_phi_vec))) of the sampling variance-covariance matrix of \(\mathrm{vec} \left( \boldsymbol{\Phi} \right)\).
phi1: Numeric matrix. Matrix of covariate effects mapping \(\mathbf{x}\) to \(\mathrm{vec}(\boldsymbol{\Phi})\).
x: List of numeric vectors. Covariate values.
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.

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(), SimPhiN2(), SimSSMFixed(), SimSSMIVary(), SimSSMLinGrowth(), SimSSMLinGrowthIVary(), SimSSMLinSDEFixed(), SimSSMLinSDEIVary(), SimSSMOUFixed(), SimSSMOUIVary(), SimSSMVARFixed(), SimSSMVARIVary(), SpectralRadius(), TestPhi(), TestPhiHurwitz(), TestStability(), TestStationarity()

Author

Ivan Jacob Agaloos Pesigan

Examples

n <- 5
phi0 <- 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)))
# One scalar covariate per replication
phi1 <- matrix(data = 0, nrow = 9, ncol = 1)
phi1[1, 1] <- 0.10  # x shifts phi[1,1]
x <- list(c(0), c(1), c(-1), c(0.5), c(2))
SimPhiNCovariate(
  n = n,
  phi0 = phi0,
  vcov_phi_vec_l = vcov_phi_vec_l,
  phi1 = phi1,
  x = x
)
#> [[1]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.3765914 -0.01058848 -0.04617385
#> [2,]  0.8166669 -0.54811423 -0.01558777
#> [3,] -0.4811700  0.68307304 -0.66308147
#> 
#> [[2]]
#>            [,1]        [,2]        [,3]
#> [1,] -0.1827693 -0.04749673 -0.02039162
#> [2,]  0.7541351 -0.53188626  0.08655416
#> [3,] -0.4355784  0.71807782 -0.64235630
#> 
#> [[3]]
#>            [,1]         [,2]        [,3]
#> [1,] -0.4355311 -0.009941172 -0.02135158
#> [2,]  0.7472695 -0.540460856 -0.05944341
#> [3,] -0.4138522  0.734597964 -0.71644021
#> 
#> [[4]]
#>            [,1]        [,2]         [,3]
#> [1,] -0.3917425 -0.01756875  0.001208828
#> [2,]  0.7840805 -0.48789034  0.017578063
#> [3,] -0.4818337  0.74712907 -0.708353500
#> 
#> [[5]]
#>            [,1]         [,2]        [,3]
#> [1,] -0.1258044  0.005440268  0.05875903
#> [2,]  0.7839044 -0.521210732  0.00491790
#> [3,] -0.4534969  0.687419498 -0.64692547
#>