SimBetaN: Simulate Transition Matrices from the Multivariate Normal Distribution

Description

This function simulates random transition matrices from the multivariate normal distribution. The function ensures that the generated transition matrices are stationary using TestStationarity() with a rejection sampling approach.

Usage

SimBetaN(
  n,
  beta,
  vcov_beta_vec_l,
  margin = 1,
  beta_lbound = NULL,
  beta_ubound = NULL,
  bound = FALSE,
  max_iter = 100000L
)

Value

Returns a list of random transition matrices.

Arguments

n: Positive integer. Number of replications.
beta: Numeric matrix. The transition matrix (\(\boldsymbol{\beta}\)).
vcov_beta_vec_l: Numeric matrix. Cholesky factorization (t(chol(vcov_beta_vec))) of the sampling variance-covariance matrix of \(\mathrm{vec} \left( \boldsymbol{\beta} \right)\).
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.

Author

Ivan Jacob Agaloos Pesigan

Other Simulation of State Space Models Data Functions: LinSDE2SSM(), LinSDECovEta(), LinSDECovY(), LinSDEMeanEta(), LinSDEMeanY(), ProjectToHurwitz(), ProjectToStability(), SSMCovEta(), SSMCovY(), SSMInterceptEta(), SSMInterceptY(), SSMMeanEta(), SSMMeanY(), SimAlphaN(), SimBetaN2(), SimBetaNCovariate(), SimCovDiagN(), SimCovN(), SimIotaN(), SimNuN(), SimPhiN(), SimPhiN2(), SimPhiNCovariate(), SimSSMFixed(), SimSSMIVary(), SimSSMLinGrowth(), SimSSMLinGrowthIVary(), SimSSMLinSDEFixed(), SimSSMLinSDEIVary(), SimSSMOUFixed(), SimSSMOUIVary(), SimSSMVARFixed(), SimSSMVARIVary(), SpectralRadius(), TestPhi(), TestPhiHurwitz(), TestStability(), TestStationarity()

Examples

Run this code

n <- 10
beta <- 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)))
SimBetaN(n = n, beta = beta, vcov_beta_vec_l = vcov_beta_vec_l)