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A Distribution Generating Equation for Unit-Root Statistics

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  • Abadir, Karim M

Abstract

A unified framework to derive the distribution of conventional statistics under a unit root is presented. It is based on formulae which can generate (analytically as well as numerically) the densities and distributions of statistics such as the t ratio, the normalized autocorrelation coefficient, and many more. The name density (or distribution) generating equation is given to these formulae. As a practical example, the numerical and analytical aspects of the distribution of the t ratio under a unit root are discussed. Suggestions for further applications and extensions of these formulae are also given. Copyright 1992 by Blackwell Publishing Ltd

Suggested Citation

  • 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.
    • Handle: RePEc:bla:obuest:v:54:y:1992:i:3:p:305-23
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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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