One-dimensional inference in autoregressive models with the potential presence of a unit root
This paper examines the problem of testing and confidence set construction for one-dimensional functions of the coefficients in autoregressive (AR(p)) models with potentially persistent time series. The primary example concerns inference on impulse responses. A new asymptotic framework is suggested...
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| Format: | Article |
| Language: | en_US |
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The Econometric Society
2012
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| Online Access: | http://hdl.handle.net/1721.1/72467 https://orcid.org/0000-0002-0724-5428 |
| _version_ | 1826213039463989248 |
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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 | This paper examines the problem of testing and confidence set construction for one-dimensional functions of the coefficients in autoregressive (AR(p)) models with potentially persistent time series. The primary example concerns inference on impulse responses. A new asymptotic framework is suggested and some new theoretical properties of known procedures are demonstrated. I show that the likelihood ratio (LR) and LR± statistics for a linear hypothesis in an AR(p) can be uniformly approximated by a weighted average of local-to-unity and normal distributions. The corresponding weights depend on the weight placed on the largest root in the null hypothesis. The suggested approximation is uniform over the set of all linear hypotheses. The same family of distributions approximates the LR and LR± statistics for tests about impulse responses, and the approximation is uniform over the horizon of the impulse response. I establish the size properties of tests about impulse responses proposed by Inoue and Kilian (2002) and Gospodinov (2004), and theoretically explain some of the empirical findings of Pesavento and Rossi (2007). An adaptation of the grid bootstrap for impulse response functions is suggested and its properties are examined. |
| first_indexed | 2024-09-23T15:42:23Z |
| format | Article |
| id | mit-1721.1/72467 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:42:23Z |
| publishDate | 2012 |
| publisher | The Econometric Society |
| record_format | dspace |
| spelling | mit-1721.1/724672022-10-02T03:32:56Z One-dimensional inference in autoregressive models with the potential presence of a unit root Mikusheva, Anna Massachusetts Institute of Technology. Department of Economics Mikusheva, Anna Mikusheva, Anna This paper examines the problem of testing and confidence set construction for one-dimensional functions of the coefficients in autoregressive (AR(p)) models with potentially persistent time series. The primary example concerns inference on impulse responses. A new asymptotic framework is suggested and some new theoretical properties of known procedures are demonstrated. I show that the likelihood ratio (LR) and LR± statistics for a linear hypothesis in an AR(p) can be uniformly approximated by a weighted average of local-to-unity and normal distributions. The corresponding weights depend on the weight placed on the largest root in the null hypothesis. The suggested approximation is uniform over the set of all linear hypotheses. The same family of distributions approximates the LR and LR± statistics for tests about impulse responses, and the approximation is uniform over the horizon of the impulse response. I establish the size properties of tests about impulse responses proposed by Inoue and Kilian (2002) and Gospodinov (2004), and theoretically explain some of the empirical findings of Pesavento and Rossi (2007). An adaptation of the grid bootstrap for impulse response functions is suggested and its properties are examined. 2012-08-30T15:45:53Z 2012-08-30T15:45:53Z 2012-01 Article http://purl.org/eprint/type/JournalArticle 0012-9682 1468-0262 http://hdl.handle.net/1721.1/72467 Mikusheva, Anna. “One-Dimensional Inference in Autoregressive Models With the Potential Presence of a Unit Root.” Econometrica 80.1 (2012): 173-212. https://orcid.org/0000-0002-0724-5428 en_US http://dx.doi.org/10.3982/ecta9371 Econometrica Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf The Econometric Society MIT web domain |
| spellingShingle | Mikusheva, Anna One-dimensional inference in autoregressive models with the potential presence of a unit root |
| title | One-dimensional inference in autoregressive models with the potential presence of a unit root |
| title_full | One-dimensional inference in autoregressive models with the potential presence of a unit root |
| title_fullStr | One-dimensional inference in autoregressive models with the potential presence of a unit root |
| title_full_unstemmed | One-dimensional inference in autoregressive models with the potential presence of a unit root |
| title_short | One-dimensional inference in autoregressive models with the potential presence of a unit root |
| title_sort | one dimensional inference in autoregressive models with the potential presence of a unit root |
| url | http://hdl.handle.net/1721.1/72467 https://orcid.org/0000-0002-0724-5428 |
| work_keys_str_mv | AT mikushevaanna onedimensionalinferenceinautoregressivemodelswiththepotentialpresenceofaunitroot |