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arXiv · 2507.22869

Inference on Common Trends in a Cointegrated Nonlinear SVAR

James A. Duffy·Xiyu Jiao
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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.

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James A. Duffy, Xiyu Jiao. 2025-07-30. Inference on Common Trends in a Cointegrated Nonlinear SVAR. https://arxiv.org/abs/2507.22869

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