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

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

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Mukhtar Ali

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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Article provided by Taylor and 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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repec:cup:etheor:v:9:y:1993:i:3:p:363-76 is not listed on IDEAS
Francis X. Diebold & Marc Nerlove, 1988. "Unit roots in economic time series: a selective survey," Finance and Economics Discussion Series 49, Board of Governors of the Federal Reserve System (U.S.).
Schwert, G. William, 1987. "Effects of model specification on tests for unit roots in macroeconomic data," Journal of Monetary Economics, Elsevier, vol. 20(1), pages 73-103, July. [Downloadable!] (restricted)
repec:cup:etheor:v:9:y:1993:i:1:p:81-93 is not listed on IDEAS

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