Distribution of the Least Squares Estimator in a First-Order Autoregressive Model

Mukhtar M. Ali
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Mukhtar M. Ali: University of Kentucky

Econometrics from University Library of Munich, Germany

Abstract: This paper investigates the finite sample distribution of the least squares estimator of the autoregressive parameter in a first-order autoregressive model. 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 exists 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.

Keywords: Unit Root; Saddlepoint Approximation; Asymptotic expansion (search for similar items in EconPapers)
JEL-codes: C13 C22 (search for similar items in EconPapers)
Pages: 29 pages
Date: 1996-10-23
Note: Type of Document - Word for Windows (V. 6/7) binary document; prepared on IBM PC compatible; to print on HP; pages: 29 . Revision of ewp-em/9604001 (UK-E-188-96)
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