Saddlepoint Approximation for the Least Squares Estimation in First-Order Autoregression

Offer Lieberman

No 267631, Department of Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: In an earlier article, Phillips (1978) extended Daniels' (1956) approximation to the density of a modified correlation coefficient to obtain a saddlepoint approximation to the density of the least squares estimator in the first order non-circular autoregression. It was demonstrated that the resulting approximation is undefined in a substantial part of the tails. In this note, we establish that a suitable deformation of the contour of integration leads to a different type of saddlepoint approximation which is defined everywhere on the support of the density. It is further shown that the relative error of this approximation is bounded in the extreme tails.

Keywords: Research; Methods/Statistical; Methods (search for similar items in EconPapers)
Pages: 13
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Persistent link: https://EconPapers.repec.org/RePEc:ags:monebs:267631

DOI: 10.22004/ag.econ.267631

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