Generalised vec operators and the seemingly unrelated regression equations model with vector correlated disturbances

• Published in: Journal of econometrics Vol. 99; no. 2; pp. 225 - 253
• Main Author: Turkington, Darrell
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.12.2000; Elsevier; Elsevier Sequoia S.A
• Series: Journal of Econometrics
• Subjects: Calculus; Correlation; Econometrics; Economic models; Economic theory; Exact sciences and technology; Generalised vec; Inference from stochastic processes; time series analysis; Linear inference, regression; Mathematical economics; Mathematics; Matrix algebra; Multivariate analysis; Probability and statistics; Regression analysis; Sciences and techniques of general use; Statistics; Studies; SURE model; Vector correlated disturbances; C30; C10; SURE model; Vector correlated disturbances; Generalised vec; Regression equation; Data analysis; Autoregressive disturbance; Time series; Statistical association; Statistical estimation; Multivariate analysis; Stochastic process; Statistical regression; Hypothesis test; Lagrange multiplier; Log likelihood function; Correlation analysis; Regression model; Least squares method; Vec operator; Hessian matrix; Linear estimation; Maximum likelihood; Autocorrelation; Likelihood function
• ISSN: 0304-4076; 1872-6895
• DOI: 10.1016/S0304-4076(00)00025-7

This paper introduces operators which are generalisations of the vec operator. Properties of these operators are discussed, some theorems involving these operators are presented and their relevance to matrix calculus demonstrated. These operators are used to facilitate the complicated differentiation required in applying classical statistical procedures to the SURE model with vector correlated disturbances. It is then shown that well-known statistical results concerning the linear regression model with autoregressive and moving average distrubances generalise to the SURE model with vector autoregressive and moving average disturbances.