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Inference on Common Trends in a Cointegrated Nonlinear SVAR

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  • James A. Duffy
  • Xiyu Jiao

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.

Suggested Citation

  • James A. Duffy & Xiyu Jiao, 2025. "Inference on Common Trends in a Cointegrated Nonlinear SVAR," Papers 2507.22869, arXiv.org, revised Apr 2026.
    • Handle: RePEc:arx:papers:2507.22869
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    References listed on IDEAS

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    1. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
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    Cited by:

    1. Duffy, James A. & Mavroeidis, Sophocles & Wycherley, Sam, 2025. "Cointegration with occasionally binding constraints," Journal of Econometrics, Elsevier, vol. 252(PA).

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