VARMAcov function

Autocovariance Matrices of a VARMA Model

Uses psi-weights to compute the autocovariance matrices of a VARMA model

VARMAcov(Phi = NULL, Theta = NULL, Sigma = NULL, lag = 12, trun = 120)

Arguments

• Phi: A k-by-kp matrix consisting of VAR coefficient matrices, Phi = [Phi1, Phi2, ..., Phip].
• Theta: A k-by-kq matrix consisting of VMA coefficient matrices, Theta = [Theta1, Theta2, ..., Thetaq]
• Sigma: Covariance matrix of the innovations (k-by-k).
• lag: Number of cross-covariance matrices to be computed. Default is 12.
• trun: The lags of pis-weights used in calculation. Default is 120.

Details

Use psi-weight matrices to compute approximate autocovariance matrices of a VARMA model.

Returns

• autocov: Autocovariance matrices

• ccm: Auto correlation matrices

References

Tsay (2014, Chapter 3). Multivariate Time Series Analysis with R and Financial Applications. John Wiley. Hoboken, NJ.

Author(s)

Ruey S. Tsay

Examples

Phi=matrix(c(0.2,-0.6,0.3,1.1),2,2)
Sig=matrix(c(4,1,1,1),2,2)
VARMAcov(Phi=Phi,Sigma=Sig)