Exact 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 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. Only rarely the accuracy improves by including further term beyond the first term of this expansion in the approximation. As a matter of fact, often the accuracy of such an approximation with additional term(s) deteriorates. An application of the finding is illustrated with examples.

Keywords: Unit Root; Saddlepoint Approximation; Asymptotic Expansion (search for similar items in EconPapers)
JEL-codes: C12 C13 C22 (search for similar items in EconPapers)
Pages: 22 pages
Date: 1996-04-03
Note: Type of Document - Binary WordPerfect (V5.1) Document; prepared on IBM PC - Compatible; to print on HP LaserJet II; pages: 22. Contains many special characters and equations created with WordPerfect's Equation Editor. Conversion to other formats may cause problems.
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