Second Order Expansion of the T-Statistic in AR(1) Models
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...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Cambridge University Press
2016
|
| Online Access: | http://hdl.handle.net/1721.1/105179 https://orcid.org/0000-0002-0724-5428 |
| Summary: | 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. |
|---|