SimPhiN2: Simulate Random Drift Matrices from the Multivariate Normal Distribution and Project to Hurwitz

Description

This function simulates random dirft matrices from the multivariate normal distribution then projects each draw to the Hurwitz-stable region using ProjectToHurwitz().

Usage

SimPhiN2(n, phi, vcov_phi_vec_l, margin = 0.001)

Value

Returns a list of random drift matrices.

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: Positive numeric. Target buffer so that the spectral abscissa is \(\le -\text{margin}\) (default 1e-3).

Author

Ivan Jacob Agaloos Pesigan

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

Examples

Run this code

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)))
SimPhiN2(n = n, phi = phi, vcov_phi_vec_l = vcov_phi_vec_l)