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Saddlepoint And Estimated Saddlepoint Approximations For Optimal Unit Root Tests

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  • Marsh, Patrick

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 proved to yield valid asymptotic inference. Numerical evidence, considered over a range of models, demonstrates some finite-sample superiority over approximations for a directly comparable test based on simulation of its limiting stochastic representation.

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  • Marsh, Patrick, 2011. "Saddlepoint And Estimated Saddlepoint Approximations For Optimal Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 27(5), pages 1026-1047, October.
    • Handle: RePEc:cup:etheor:v:27:y:2011:i:05:p:1026-1047_00
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    Cited by:

    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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