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Second Order Expansion Of The T-Statistic In Ar(1) Models

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  • Mikusheva, Anna

Abstract

The purpose of this paper is to differentiate between several asymptotically valid methods for confidence set construction for the autoregressive coefficient in AR(1) models. We show that the nonparametric grid bootstrap procedure suggested by Hansen (1999, Review of Economics and Statistics 81, 594–607) achieves a second order refinement in the local-to-unity asymptotic approach when compared with a modified version of Stock’s (1991, Journal of Monetary Economics 28, 435–459) and Andrews’ (1993, Econometrica 61, 139–165) grid testing procedures. We establish a second order expansion of the t-statistic in an AR(1) model in the local-to-unity asymptotic approach, which differs drastically from the usual Edgeworth-type expansions by approximating the statistic around a nonstandard and nonpivotal limit.

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  • Mikusheva, Anna, 2015. "Second Order Expansion Of The T-Statistic In Ar(1) Models," Econometric Theory, Cambridge University Press, vol. 31(3), pages 426-448, June.
  • Handle: RePEc:cup:etheor:v:31:y:2015:i:03:p:426-448_00
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    Cited by:

    1. Eric Benhamou, 2019. "T-statistic for Autoregressive process," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 8(1), pages 1-2.
    2. Yiu Lim Lui & Weilin Xiao & Jun Yu, 2022. "The Grid Bootstrap for Continuous Time Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1390-1402, June.
    3. Marcus J. Chambers & Maria Kyriacou, 2018. "Jackknife Bias Reduction in the Presence of a Near-Unit Root," Econometrics, MDPI, vol. 6(1), pages 1-28, March.

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