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

Author

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  • Steve Lawford

    (LEEA - ENAC - Laboratoire d'Economie et d'Econométrie de l'Aérien - ENAC - Ecole Nationale de l'Aviation Civile)

  • Michalis P. Stamatogiannis

    (School of Economics - UON - University of Nottingham, UK, Department of Business Studies - Philips College)

Abstract

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.

Suggested Citation

  • Steve Lawford & Michalis P. Stamatogiannis, 2009. "The finite-sample effects of VAR dimensions on OLS bias, OLS variance, and minimum MSE estimators," Post-Print hal-00563603, HAL.
    • Handle: RePEc:hal:journl:hal-00563603
    DOI: 10.1016/j.jeconom.2008.10.004
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    Cited by:

    1. Diego Fresoli, 2022. "Bootstrap VAR forecasts: The effect of model uncertainties," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(2), pages 279-293, March.

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    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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