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A Note on the Saddlepoint Approximation in the First Order Non-Circular Autoregression

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Abstract

In approximating the small sample distribution of the least squares estimator of the coefficient in a non-circular autoregression the saddlepoint method is complicated by the presence of a branch point of the integrand within the natural contour of integration. Some new approximations are given based on a contour looping around the branch point; and a uniform approximation which is valid as the saddlepoint crosses branch point is also developed.

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  • Peter C.B. Phillips, 1978. "A Note on the Saddlepoint Approximation in the First Order Non-Circular Autoregression," Cowles Foundation Discussion Papers 487, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:487
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d04/d0487.pdf
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    1. Peter C.B. Phillips, 1981. "A New Approach to Small Sample Theory," Cowles Foundation Discussion Papers 608, Cowles Foundation for Research in Economics, Yale University.

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