On the edge eigenvalues of the precision matrices of nonstationary autoregressive processes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866909989045534720 |
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| author | Yang, Junho |
| author_facet | Yang, Junho |
| contents | This paper investigates structural changes in the parameters of first-order autoregressive models by analyzing the edge eigenvalues of the precision matrices. Specifically, edge eigenvalues in the precision matrix are observed if and only if there is a structural change in the autoregressive coefficients. We show that these edge eigenvalues correspond to the zeros of a determinantal equation. Additionally, we propose a consistent estimator for detecting outliers within the panel time series framework, supported by numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_02204 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the edge eigenvalues of the precision matrices of nonstationary autoregressive processes Yang, Junho Methodology Statistics Theory This paper investigates structural changes in the parameters of first-order autoregressive models by analyzing the edge eigenvalues of the precision matrices. Specifically, edge eigenvalues in the precision matrix are observed if and only if there is a structural change in the autoregressive coefficients. We show that these edge eigenvalues correspond to the zeros of a determinantal equation. Additionally, we propose a consistent estimator for detecting outliers within the panel time series framework, supported by numerical experiments. |
| title | On the edge eigenvalues of the precision matrices of nonstationary autoregressive processes |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2109.02204 |