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| Autori principali: | , , , |
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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2605.27859 |
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| _version_ | 1866910264405786624 |
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| author | Anne, Gael Lu, Yang Yu, Xuewen Zhou, Xiaowen |
| author_facet | Anne, Gael Lu, Yang Yu, Xuewen Zhou, Xiaowen |
| contents | Discrete-time affine processes are widely used in finance and economics and encompass count, positive, and nonnegative-valued processes. This paper develops near-unit-root asymptotic theory for this class of models. Unlike linear AR(1) processes, affine processes exhibit time-varying conditional variance that remains asymptotically non-negligible near unity, leading to qualitatively different scaling limits and estimator behavior. We show that the local-to-unity regime suffers from the usual nuisance-parameter problem, whereas the mildly explosive regime, while free of it, still does not allow consistent estimation of the intercept. By contrast, the mildly stationary framework is more tractable: the OLS estimator is asymptotically normal, the resulting trajectories are more realistic than those of linear AR(1) models, and inference is possible through both a plug-in method or bootstrap. The theoretical results are supported by simulation evidence and illustrated through applications to insurance and financial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27859 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Near-Unit-Root Theory for Affine Processes Anne, Gael Lu, Yang Yu, Xuewen Zhou, Xiaowen Statistics Theory Discrete-time affine processes are widely used in finance and economics and encompass count, positive, and nonnegative-valued processes. This paper develops near-unit-root asymptotic theory for this class of models. Unlike linear AR(1) processes, affine processes exhibit time-varying conditional variance that remains asymptotically non-negligible near unity, leading to qualitatively different scaling limits and estimator behavior. We show that the local-to-unity regime suffers from the usual nuisance-parameter problem, whereas the mildly explosive regime, while free of it, still does not allow consistent estimation of the intercept. By contrast, the mildly stationary framework is more tractable: the OLS estimator is asymptotically normal, the resulting trajectories are more realistic than those of linear AR(1) models, and inference is possible through both a plug-in method or bootstrap. The theoretical results are supported by simulation evidence and illustrated through applications to insurance and financial data. |
| title | Near-Unit-Root Theory for Affine Processes |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2605.27859 |