The Finite-Sample E ects of VAR Dimensions on OLS Bias, OLS Variance, and Minimum MSE Estimators

Vector autoregressions (VARs) are important tools in time series analysis. However, relatively little is known about the nite-sample behaviour of parameter estimators. We address this issue, by investigating 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 response surfaces for OLS bias and variance, in terms of VAR dimensions, given correct speci cation 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 that are required for the least squares estimator to attain minimum mean squared error (MSE). Our results improve and extend one of the main nite-sample multivariate analytical bias results of Abadir, Hadri and Tzavalis (Econometrica 67 (1999) 163), generalize the univariate variance and MSE ndings of Abadir (Economics Letters 47 (1995) 263) to the multivariate setting, and complement various asymptotic studies.