Simulate Transition Matrices with a Covariate from the Multivariate Normal Distribution

This function simulates random transition matrices from a multivariate normal distribution, allowing the mean transition matrix to vary as a linear function of a covariate. The function ensures that the generated transition matrices are stationary using TestStationarity() with a rejection sampling approach.

Usage

SimBetaNCovariate(
  n,
  beta0,
  vcov_beta_vec_l,
  beta1,
  x,
  margin = 1,
  beta_lbound = NULL,
  beta_ubound = NULL,
  bound = FALSE,
  max_iter = 100000L
)

Arguments

n

Positive integer. Number of replications.

beta0

Numeric matrix. Baseline transition matrix \(\boldsymbol{\beta}_0\) corresponding to \(\mathbf{x} = \mathbf{0}\).

vcov_beta_vec_l

Numeric matrix. Cholesky factorization (t(chol(vcov_beta_vec))) of the sampling variance-covariance matrix of \(\mathrm{vec} \left( \boldsymbol{\beta} \right)\).

beta1

Numeric matrix. Matrix of covariate effects mapping \(\mathbf{x}\) to \(\mathrm{vec}(\boldsymbol{\beta})\).

x

List of numeric vectors. Covariate values.

margin

Numeric scalar specifying the stationarity threshold. Values less than 1 indicate stricter stationarity criteria.

beta_lbound

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

beta_ubound

Optional numeric matrix of same dim as beta. 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 transition 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(), SimPhiN2(), SimPhiNCovariate(), SimSSMFixed(), SimSSMIVary(), SimSSMLinGrowth(), SimSSMLinGrowthIVary(), SimSSMLinSDEFixed(), SimSSMLinSDEIVary(), SimSSMOUFixed(), SimSSMOUIVary(), SimSSMVARFixed(), SimSSMVARIVary(), SpectralRadius(), TestPhi(), TestPhiHurwitz(), TestStability(), TestStationarity()

Author

Ivan Jacob Agaloos Pesigan

Examples

n <- 5
beta0 <- matrix(
  data = c(
    0.7, 0.5, -0.1,
    0.0, 0.6, 0.4,
    0, 0, 0.5
  ),
  nrow = 3
)
vcov_beta_vec_l <- t(chol(0.001 * diag(9)))
# One scalar covariate per replication
beta1 <- matrix(data = 0, nrow = 9, ncol = 1)
beta1[1, 1] <- 0.10  # x shifts beta[1,1]
x <- list(c(0), c(1), c(-1), c(0.5), c(2))

SimBetaNCovariate(
  n = n,
  beta0 = beta0,
  vcov_beta_vec_l = vcov_beta_vec_l,
  beta1 = beta1,
  x = x
)
#> [[1]]
#>             [,1]        [,2]        [,3]
#> [1,]  0.73714275 -0.01569974 -0.01051835
#> [2,]  0.51045990  0.62092334 -0.02241639
#> [3,] -0.05715703  0.41446261  0.49795605
#> 
#> [[2]]
#>             [,1]        [,2]       [,3]
#> [1,]  0.79546249 0.000930592 0.01095603
#> [2,]  0.48309397 0.562960936 0.02006462
#> [3,] -0.09565399 0.404087614 0.47342670
#> 
#> [[3]]
#>             [,1]        [,2]         [,3]
#> [1,]  0.63629846 0.001422849  0.008760512
#> [2,]  0.50411427 0.588666045 -0.046495787
#> [3,] -0.06590982 0.419744641  0.526820311
#> 
#> [[4]]
#>            [,1]       [,2]        [,3]
#> [1,]  0.7799245 0.03766229 -0.01601237
#> [2,]  0.4905213 0.58185885 -0.04205268
#> [3,] -0.1251074 0.32625402  0.50291231
#> 
#> [[5]]
#>            [,1]          [,2]         [,3]
#> [1,]  0.8692902 -0.0004960935  0.047489421
#> [2,]  0.4895781  0.5295633964 -0.001605503
#> [3,] -0.1546900  0.3846987284  0.559527733
#>