Econometric inference in models with nonstationary time series - Stamatogiannis, Michalis P. (2010)
We investigate the finite sample behaviour of the ordinary least squares (OLS) estimator in vector autoregressive (VAR) models. The data generating process is assumed to be a purely nonstationary first-order VAR. Using Monte Carlo simulation and numerical optimization we derive response surfaces for OLS bias and variance in terms of VAR dimensions both under correct model specification and under several types of over-parameterization: we include a constant, a constant and trend, and introduce excess autoregressive lags. Correction factors are introduced that minimise the mean squared error (MSE) of the OLS estimator. Our analysis improves and extends one of the main finite-sample multivariate analytical bias results of Abadir, Hadri and Tzavalis (1999), generalises the univariate variance and MSE results of Abadir (1995) to a multivariate setting, and complements various asymptotic studies.