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Saddlepoint Approximations for Optimal Unit Root Tests

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  • Patrick Marsh

Abstract

This paper provides a (saddlepoint) tail probability approximation for the distribution of an optimal unit root test. Under restrictive assumptions, Gaussianity and known covariance structure, the order of error of the approximation is given. More generally, when innovations are a linear process in martingale differences, the estimated saddlepoint is proven to yield valid asymptotic inference. Numerical evidence demonstrates superiority over approximations for a directly comparable test based on simulation of its limiting stochastic representation. In addition, because the saddlepoint offers an explicit representation P-value sensitivity to model specification is easily analyzed, here in the context of the Nelson and Plosser data.

Suggested Citation

  • Patrick Marsh, "undated". "Saddlepoint Approximations for Optimal Unit Root Tests," Discussion Papers 09/31, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:09/31
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    1. Patrick Marsh, 2019. "Properties of the power envelope for tests against both stationary and explosive alternatives: the effect of trends," Discussion Papers 19/03, University of Nottingham, Granger Centre for Time Series Econometrics.

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