Stationary covariance of a VAR(1) process

Solves \(\Sigma = \Phi \Sigma \Phi' + \Psi\) by vectorization.

Usage

stationary_cov(Phi, Psi)

Arguments

Phi

Lagged-coefficient matrix.

Psi

Innovation covariance matrix.

Value

The stationary covariance matrix (same dimension as Phi). An error is raised when Phi is not stable.

Examples

p <- default_params()
round(diag(stationary_cov(p$Phi, p$Psi)), 3)
#> [1] 1 1 1 1
S <- stationary_cov(p$Phi, p$Psi)
all.equal(S, p$Phi %*% S %*% t(p$Phi) + p$Psi)
#> [1] "Attributes: < Length mismatch: comparison on first 1 components >"