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A comparison of minimum MSE and maximum power for the nearly integrated non-Gaussian model

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  • Abadir, Karim M.
  • Lucas, Andre

Abstract

We study the optimal choice of quasi-likelihoods for nearly integrated, possibly non-normal, autoregressive models. It turns out that the two most natural candidate criteria, minimum Mean Squared Error (MSE) and maximum power against the unit root null, give rise to different optimal quasi-likelihoods. In both cases, the functional specification of the optimal quasi-likelihood is the same: it is a combination of the true likelihood and the Gaussian quasi-likelihood. The optimal relative weights, however, depend on the criterion chosen and are markedly different. Throughout, we base our results on exact limiting distribution theory. We derive a new explicit expression for the joint density of the minimal sufficient functionals of Ornstein-Uhlenbeck processes, which also has applications in other fields, and we characterize its behaviour for extreme values of its arguments. Using these results, we derive the asymptotic power functions of statistics which converge weakly to combinations of these sufficient functionals. Finally, we evaluate numerically our computationally-efficient formulae.
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  • Abadir, Karim M. & Lucas, Andre, 2004. "A comparison of minimum MSE and maximum power for the nearly integrated non-Gaussian model," Journal of Econometrics, Elsevier, vol. 119(1), pages 45-71, March.
  • Handle: RePEc:eee:econom:v:119:y:2004:i:1:p:45-71
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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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