Optimal break tests for large linear time series models
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914091415633920 |
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| author | Gupta, Abhimanyu Seo, Myung Hwan |
| author_facet | Gupta, Abhimanyu Seo, Myung Hwan |
| contents | We develop a class of optimal tests for a structural break occurring at an unknown date in infinite and growing-order time series regression models, such as AR($\infty$), linear regression with increasingly many covariates, and nonparametric regression. Under an auxiliary i.i.d. Gaussian error assumption, we derive an average power optimal test, establishing a growing-dimensional analog of the exponential tests of Andrews and Ploberger (1994) to handle identification failure under the null hypothesis of no break. Relaxing the i.i.d. Gaussian assumption to a more general dependence structure, we establish a functional central limit theorem for the underlying stochastic processes, which features an extra high-order serial dependence term due to the growing dimension. We robustify our test both against this term and finite sample bias and illustrate its excellent performance and practical relevance in a Monte Carlo study and a real data empirical example. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_12262 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal break tests for large linear time series models Gupta, Abhimanyu Seo, Myung Hwan Econometrics Statistics Theory 62M10, 62G10, 62R07 We develop a class of optimal tests for a structural break occurring at an unknown date in infinite and growing-order time series regression models, such as AR($\infty$), linear regression with increasingly many covariates, and nonparametric regression. Under an auxiliary i.i.d. Gaussian error assumption, we derive an average power optimal test, establishing a growing-dimensional analog of the exponential tests of Andrews and Ploberger (1994) to handle identification failure under the null hypothesis of no break. Relaxing the i.i.d. Gaussian assumption to a more general dependence structure, we establish a functional central limit theorem for the underlying stochastic processes, which features an extra high-order serial dependence term due to the growing dimension. We robustify our test both against this term and finite sample bias and illustrate its excellent performance and practical relevance in a Monte Carlo study and a real data empirical example. |
| title | Optimal break tests for large linear time series models |
| topic | Econometrics Statistics Theory 62M10, 62G10, 62R07 |
| url | https://arxiv.org/abs/2510.12262 |