matAR.RR.se {tensorTS}

Asymptotic Covariance Matrix of One-Term Reduced rank MAR(1) Model

Description

Asymptotic covariance matrix of the reduced rank MAR(1) model. If Sigma1 and Sigma2 is provided in input, we assume a separable covariance matrix, Cov(vec(E_t)) = \Sigma_2 \otimes \Sigma_1.

Usage

matAR.RR.se(A1,A2,k1,k2,method,Sigma.e=NULL,Sigma1=NULL,Sigma2=NULL,RU1=diag(k1),
RV1=diag(k1),RU2=diag(k2),RV2=diag(k2),mpower=100)

Arguments

A1

left coefficient matrix.

A2

right coefficient matrix.

k1

rank of A_1.

k2

rank of A_2.

method

character string, specifying the method of the estimation to be used.

"RRLSE",

Least squares.

"RRMLE",

MLE under a separable cov(vec(E_t)).

Sigma.e

only if method = "RRLSE". Cov(vec(E_t)) = Sigma.e: covariance matrix of dimension (d_1 d_2) \times (d_1 d_2)

Sigma1, Sigma2

only if method = "RRMLE". Cov(vec(E_t)) = \Sigma_2 \otimes \Sigma_1. \Sigma_i is d_i \times d_i, i=1,2.

RU1, RV1, RU2, RV2

orthogonal rotations of U_1,V_1,U_2,V_2, e.g., new_U1=U1 RU1.

mpower

truncate the VMA(\infty) representation of vec(X_t) at mpower for the purpose of calculating the autocovariances. The default is 100.

Value

a list containing the following:

Sigma

asymptotic covariance matrix of (vec(\hat A_1),vec(\hat A_2^T)).

Theta1.u

asymptotic covariance matrix of vec(\hat U_1).

Theta1.v

asymptotic covariance matrix of vec(\hat V_1).

Theta2.u

asymptotic covariance matrix of vec(\hat U_2).

Theta2.v

asymptotic covariance matrix of vec(\hat V_2).

References

Han Xiao, Yuefeng Han, Rong Chen and Chengcheng Liu, Reduced Rank Autoregressive Models for Matrix Time Series.