On the numerical evaluation of the theoretical variance‐covariance matrix of least squares estimators for echelon‐form varma models

Abstract

This paper is concerned with the development of a fast and efficient procedure for evaluating the asymptotic varianc:e-c.((variance matrix of least squares estimators with respect to stationary and invertible vector autoregressive moving average models. The models are presumed to be represented in reversed echelon canonical form. The proposed procedure takes advantage of some properties of the covariance matrix that have not been fully exploited in the existing literature to achieve a substantial reduction in computation time and storage requirements. These attributes make it possible to implement the suggested procedure on computers with limited memory capacity. Comparisons with the existing approach, in terms of analytical arguments and numerical examples, are made to illustrate the feasibility and computational efficiency of the proposed method

Keywords:

• Asymptotic variance‐covariance matrix
• Computational efficiency
• Echelon canonical form
• Vector autoregressive moving average models