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Distribution Of The Least Squares Estimator In A First-Order Autoregressive Model

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  • Mukhtar Ali
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    Abstract

    This paper investigates the finite sample distribution of the least squares estimator of the autoregressive parameter in a first-order autoregressive model. A uniform asymptotic expansion for the distribution applicable to both stationary and nonstationary cases is obtained. Accuracy of the approximation to the distribution by a first few terms of this expansion is then investigated. It is found that the leading term of this expansion approximates well the distribution. The approximation is, in almost all cases, accurate to the second decimal place throughout the distribution. In the literature, there exist a number of approximations to this distribution which are specifically designed to apply in some special cases of this model. The present approximation compares favorably with those approximations and in fact, its accuracy is, with almost no exception, as good as or better than these other approximations. Convenience of numerical computations seems also to favor the present approximations over the others. An application of the finding is illustrated with examples.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

    Volume (Year): 21 (2002)
    Issue (Month): 1 ()
    Pages: 89-119

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    Handle: RePEc:taf:emetrv:v:21:y:2002:i:1:p:89-119

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    Related research

    Keywords: Unit root; Saddlepoint approximation; Asymptotic expansion; JEL Classification: C13; C22;

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    References

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    1. Perron, P., 1987. "The Calculation of the Limiting Distribution of the Least Squares Estimator in Near-Integrated Model," Cahiers de recherche 8748, Universite de Montreal, Departement de sciences economiques.
    2. Stock, James H. & Watson, Mark W., 1989. "Interpreting the evidence on money-income causality," Journal of Econometrics, Elsevier, vol. 40(1), pages 161-181, January.
    3. Perron,P., 1988. "A Continuous Time Approximation To The Unstable First- Order Autoregressive Process: The Case Without An Intercept," Papers 337, Princeton, Department of Economics - Econometric Research Program.
    4. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
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    7. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
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    15. Tsui, Albert K. & Ali, Mukhtar M., 1994. "Exact distributions, density functions and moments of the last squares estimator in a first-order autoregressive model," Computational Statistics & Data Analysis, Elsevier, vol. 17(4), pages 433-454, May.
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