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...
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| Format: | Article |
| Language: | en_US |
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Cambridge University Press
2016
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| Online Access: | http://hdl.handle.net/1721.1/105179 https://orcid.org/0000-0002-0724-5428 |
| _version_ | 1826208556105334784 |
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| author | Mikusheva, Anna |
| author2 | Massachusetts Institute of Technology. Department of Economics |
| author_facet | Massachusetts Institute of Technology. Department of Economics Mikusheva, Anna |
| author_sort | Mikusheva, Anna |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T14:07:29Z |
| format | Article |
| id | mit-1721.1/105179 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:07:29Z |
| publishDate | 2016 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | mit-1721.1/1051792022-10-01T19:21:08Z Second Order Expansion of the T-Statistic in AR(1) Models Mikusheva, Anna Massachusetts Institute of Technology. Department of Economics Mikusheva, Anna Mikusheva, Anna 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. Alfred P. Sloan Foundation. Sloan Research Fellowship Massachusetts Institute of Technology. Department of Economics (Castle-Krob Career Development Chair) 2016-11-03T17:07:11Z 2016-11-03T17:07:11Z 2014-09 Article http://purl.org/eprint/type/JournalArticle 0266-4666 1469-4360 http://hdl.handle.net/1721.1/105179 Mikusheva, Anna. “Second Order Expansion of the T-Statiscic in AR(1) Models.” Econometric Theory 31.3 (2015): 426–448. https://orcid.org/0000-0002-0724-5428 en_US http://dx.doi.org/10.1017/s0266466614000383 Econometric Theory Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Cambridge University Press Mikusheva |
| spellingShingle | Mikusheva, Anna Second Order Expansion of the T-Statistic in AR(1) Models |
| title | Second Order Expansion of the T-Statistic in AR(1) Models |
| title_full | Second Order Expansion of the T-Statistic in AR(1) Models |
| title_fullStr | Second Order Expansion of the T-Statistic in AR(1) Models |
| title_full_unstemmed | Second Order Expansion of the T-Statistic in AR(1) Models |
| title_short | Second Order Expansion of the T-Statistic in AR(1) Models |
| title_sort | second order expansion of the t statistic in ar 1 models |
| url | http://hdl.handle.net/1721.1/105179 https://orcid.org/0000-0002-0724-5428 |
| work_keys_str_mv | AT mikushevaanna secondorderexpansionofthetstatisticinar1models |