matAR.RR.se: 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)

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(\(\hat V_2\)).

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.

References

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