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

Author

Listed:
  • Steve Lawford
  • Michalis P Stamatogiannis

Abstract

Vector autoregressions (VAR's) are an important tool in time series analysis. However, relatively little is known about the finite-sample behaviour of parameter estimators. We address this issue here, by investigating maximum likelihood estimators (MLE's) in the context of a purely nonstationary first-order VAR. Using Monte Carlo simulation and numerical optimization, we derive response surfaces for MLE bias, in terms of VAR dimensions, given correct and over-parameterization of the model. We study non-zero initial values, and show that univariate bias nonmonotonicity disappears in the multivariate case. Lastly, we examine MLE variance and the correction factors required for the MLE to attain minimum mean squared error (MSE). Contact Details (for paper requests) : Dr. Steve Lawford ECARES Universite Libre de Bruxelles 50 Avenue F. D. Roosevelt CP 114 B-1050 Brussels Belgium Fax: +32 (0)2 650 4475 e-mail: steve_lawford@yahoo.co.uk

Suggested Citation

  • Steve Lawford & Michalis P Stamatogiannis, "undated". "The Finite-Sample Effects of VAR Dimensions on MLE Bias, MLE Variance and Minimum MSE Estimators: Purely Nonstationary Case," Discussion Papers 02/04, Department of Economics, University of York.
  • Handle: RePEc:yor:yorken:02/04
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    More about this item

    Keywords

    Finite sample bias; Monte Carlo simulation; Nonstationary time series; Response surfaces; Vector autoregression;

    JEL classification:

    • 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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