THE ASYMPTOTIC INFLUENCE OF VAR DIMENSIONS ON ESTIMATOR BIASES

Paper number: 94/06

Year: 1994

Paper Category: Discussion Paper

Authors

Karim M.Abadir

Kaddour Hadri

Elias Tzavalis

University of Exeter

Abstract

We show that in a purely nonstationary Vector Autoregression (VAR), the biases of Maximum Likelihood and Least Squares Estimators are asymptotically proportional to the dimension of the system, even when the equations and regressors are generated independantly of each other. When some stable linear combinations exist, as when the variables are cointegrated, these biases are in general asymptotically proportional to the sum of the characteristic roots of the VAR. Adding irrelevant variables to a VAR is thus shown to have more serious negative consequences in integrated time series than in classical ergodic or cross section analyses.

Keywords: Asymptotic biases, Vector AutoRegression (VAR), Error Correction Mechanism (ECM), Unit roots, Integrated Series, Spurious regressions, Cointegration, Common trends, Maximum Likelihood Estimator (MLE), Least Squares Estimators (LSE), Functional Central Limit Theorum (FCLT), Jordan decomposition.

Corresponding author: Karim M.Abadir, Department of Economics, Amory Building, Rennes Drive, University of Exeter, Exeter EX4 4RJ, England.
E-mail: kmabadir@exeter.ac.uk
Phone: England + 392 + 263200
Fax: England + 392 + 263242