The Finite-Sample Effects of VAR Dimensions on MLE Bias, MLE Variance and Minimum MSE Estimators: Purely Nonstationary Case.

Vector autoregressions (VAR's) are an important tool in time series analysis. However, relatively little is known about the finite-sample behaviour of parameter estimators. We address this issue here, by investigating maximum likelihood estimators (MLE's) in the context of a purely nonstationary first-order VAR. Using Monte Carlo simulation and numerical optimization, we derive response surfaces for MLE bias, in terms of VAR dimensions, given correct and over-parameterization of the model. We study non-zero initial values, and show that univariate bias nonmonotonicity disappears in the multivariate case. Lastly, we examine MLE variance and the correction factors required for the MLE to attain minimum mean squared error (MSE). Contact Details (for paper requests) : Dr. Steve Lawford ECARES Universite Libre de Bruxelles 50 Avenue F. D. Roosevelt CP 114 B-1050 Brussels Belgium Fax: +32 (0)2 650 4475 e-mail: steve_lawford@yahoo.co.uk