The finite-sample effects of VAR dimensions on OLS bias, OLS variance, and minimum MSE estimators

Steve Lawford, Michalis P Stamatogiannis

Research output: Contribution to journalArticlepeer-review

3 Citations (SciVal)


Vector autoregressions (VARs) are important tools in time series analysis. However, relatively little is known about the finite-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 first-order VAR. Specifically, we use Monte Carlo simulation and numerical optimisation to derive response surfaces for OLS bias and variance, in terms of VAR dimensions, given correct specification and several types of over-parameterisation 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 the minimum mean squared error (MSE). Our results improve and extend one of the main finite-sample multivariate analytical bias results of Abadir, Hadri and Tzavalis [Abadir, K.M., Hadri, K., Tzavalis, E., 1999. The influence of VAR dimensions on estimator biases. Econometrica 67, 163–181], generalise the univariate variance and MSE findings of Abadir [Abadir, K.M., 1995. Unbiased estimation as a solution to testing for random walks. Economics Letters 47, 263–268] to the multivariate setting, and complement various asymptotic studies.
Original languageEnglish
Pages (from-to)124-130
Number of pages7
JournalJournal of Econometrics
Issue number2
Early online date21 Oct 2008
Publication statusPublished - Feb 2009


  • finite-sample bias
  • nonstationary time series
  • vector autoregression
  • response surface
  • Monte Carlo simulation


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