{"ID":2888888,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.22869","arxiv_id":"2507.22869","title":"Inference on Common Trends in a Cointegrated Nonlinear SVAR","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2507.22869","url_pdf":"https://arxiv.org/pdf/2507.22869v2","authors":"[\"James A. Duffy\",\"Xiyu Jiao\"]","published":"2025-07-30T17:44:07Z","proceeding":"econ.EM","tasks":"[\"econ.EM\",\"math.ST\"]","methods":"[]","has_code":false}