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SECOND ORDER EXPANSION OF THE T-STATISTIC IN AR(1) MODELS

Published online by Cambridge University Press:  15 September 2014

Anna Mikusheva
Anna Mikusheva*
Affiliation:
MIT
*
*Address correspondence to Anna Mikusheva, Department of Economics, MIT, E17-210, 77 Massachusetts Avenue, Cambridge, MA 02139; e-mail: amikushe@mit.edu.
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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.

Type
ARTICLES
Information
Econometric Theory , Volume 31 , Issue 3 , June 2015 , pp. 426 - 448
Copyright
Copyright © Cambridge University Press 2014 

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Footnotes

Financial support from the Castle-Krob Career Development Chair and Sloan Research Fellowship is gratefully acknowledged. I am grateful to Jim Stock, Marcelo Moreira, Gary Chamberlain, Peter Phillips, Denis Chetverikov, and three anonymous referees for helpful comments.

References

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