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

Abstract

Vector autoregressions (VARs) are an important tool in time series analysis. However, relatively little is known about the nite-sample behaviour of parameter estimators. We address this issue, by investi- gating ordinary least squares (OLS) estimators given a data generating process that is a purely nonstationary rst-order VAR. Speci cally, we use Monte Carlo simulation and numerical optimization to derive re- sponse surfaces for OLS bias and variance, in terms of VAR dimensions, given correct and (several types of) over-parameterization of the model: we include a constant, and a constant and trend, and introduce excess lags. We then examine the correction factors required for the least squares estimator to attain minimum mean squared error (MSE). Our results improve and extend one of the main nite-sample analytical bias results of Abadir, Hadri and Tzavalis (Econometrica 67 (1999) 163), generalize the univariate variance and MSE ndings of Abadir (Econ. Lett. 47 (1995) 263), and complement various asymptotic studies.