Inference on Common Trends in a Cointegrated Nonlinear SVAR
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910114120728576 |
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| author | Duffy, James A. Jiao, Xiyu |
| author_facet | Duffy, James A. Jiao, Xiyu |
| contents | We consider the problem of performing inference on the number of common stochastic trends when data is generated by a cointegrated CKSVAR (a two-regime, piecewise affine SVAR; Mavroeidis, 2021), using a modified version of the Breitung (2002) multivariate variance ratio test that is robust to the presence of nonlinear cointegration (of a known form). To derive the asymptotics of our test statistic, we prove a fundamental LLN-type result for a class of stable but nonstationary autoregressive processes, using a novel dual linear process approximation. We show that our modified test yields correct inferences regarding the number of common trends in such a system, whereas the unmodified test tends to infer a higher number of common trends than are actually present, when cointegrating relations are nonlinear. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_22869 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inference on Common Trends in a Cointegrated Nonlinear SVAR Duffy, James A. Jiao, Xiyu Econometrics Statistics Theory 62M10 (Primary), 91B84, 62E20, 60G65 (Secondary) We consider the problem of performing inference on the number of common stochastic trends when data is generated by a cointegrated CKSVAR (a two-regime, piecewise affine SVAR; Mavroeidis, 2021), using a modified version of the Breitung (2002) multivariate variance ratio test that is robust to the presence of nonlinear cointegration (of a known form). To derive the asymptotics of our test statistic, we prove a fundamental LLN-type result for a class of stable but nonstationary autoregressive processes, using a novel dual linear process approximation. We show that our modified test yields correct inferences regarding the number of common trends in such a system, whereas the unmodified test tends to infer a higher number of common trends than are actually present, when cointegrating relations are nonlinear. |
| title | Inference on Common Trends in a Cointegrated Nonlinear SVAR |
| topic | Econometrics Statistics Theory 62M10 (Primary), 91B84, 62E20, 60G65 (Secondary) |
| url | https://arxiv.org/abs/2507.22869 |