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A Comparison of Minimum MSE and Maximum Power for the nearly Integrated Non-Gaussian Model

Author

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  • Karim M. Abadir

    (University of York)

  • Andre Lucas

    (Vrije Universiteit Amsterdam)

Abstract

This discussion paper resulted in a publication in the Journal of Econometrics (2004). Volume 119, p. 45. We study the optimal choice of quasi-likelihoods for nearly integrated,possibly non-normal, autoregressive models. It turns out that the two mostnatural candidate criteria, minimum Mean Squared Error (MSE) and maximumpower against the unit root null, give rise to different optimalquasi-likelihoods. In both cases, the functional specification of theoptimal quasi-likelihood is the same: it is a combination of the truelikelihood and the Gaussian quasi-likelihood. The optimal relativeweights, however, depend on the criterion chosen and are markedlydifferent. Throughout, we base our results on exact limiting distributiontheory. We derive a new explicit expression for the joint density of theminimal sufficient functionals of Ornstein-Uhlenbeck processes, which alsohas applications in other fields, and we characterize its behaviour forextreme values of its arguments. Using these results, we derive theasymptotic power functions of statistics which converge weakly tocombinations of these sufficient functionals. Finally, we evaluatenumerically our computationally-efficient formulae.

Suggested Citation

  • Karim M. Abadir & Andre Lucas, 2000. "A Comparison of Minimum MSE and Maximum Power for the nearly Integrated Non-Gaussian Model," Tinbergen Institute Discussion Papers 00-033/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20000033
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    References listed on IDEAS

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    1. Larsson, Rolf, 1995. "The Asymptotic Distributions Of Some Test Statistics in Near-Integrated AR Processes," Econometric Theory, Cambridge University Press, vol. 11(2), pages 306-330, February.
    2. Karim Abadir, 1999. "An introduction to hypergeometric functions for economists," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 287-330.
    3. Rothenberg, Thomas J. & Stock, James H., 1997. "Inference in a nearly integrated autoregressive model with nonnormal innovations," Journal of Econometrics, Elsevier, vol. 80(2), pages 269-286, October.
    4. Perron, Pierre, 1991. "A Continuous Time Approximation to the Unstable First-Order Autoregressive Process: The Case without an Intercept," Econometrica, Econometric Society, vol. 59(1), pages 211-236, January.
    5. Abadir, Karim M, 1992. "A Distribution Generating Equation for Unit-Root Statistics," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 305-323, August.
    6. Lucas, André, 1995. "Unit Root Tests Based on M Estimators," Econometric Theory, Cambridge University Press, vol. 11(2), pages 331-346, February.
    7. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    8. Abadir, Karim M. & Lucas, Andre, 2000. "Quantiles for t-statistics based on M-estimators of unit roots," Economics Letters, Elsevier, vol. 67(2), pages 131-137, May.
    9. Perron, Pierre, 1989. "The Calculation of the Limiting Distribution of the Least-Squares Estimator in a Near-Integrated Model," Econometric Theory, Cambridge University Press, vol. 5(2), pages 241-255, August.
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    Cited by:

    1. J. Roderick McCrorie, 2021. "Moments in Pearson's Four-Step Uniform Random Walk Problem and Other Applications of Very Well-Poised Generalized Hypergeometric Series," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 244-281, November.

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