Second Order Expansion of the T-Statistic in AR(1) Models
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Second Order Expansion of the T-Statistic in Ar(1) Models.pdf
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174.62 KB
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Author(s)
Mikusheva, Anna
Date Issued
September 2014
Journal
Econometric Theory
Publisher
Cambridge University Press
Citation
Mikusheva, Anna. “Second Order Expansion of the T-Statiscic in AR(1) Models.” Econometric Theory 31.3 (2015): 426–448.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Economics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1017/s0266466614000383
