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.
Keywords
Cite
@article{arxiv.2507.22869,
title = {Inference on Common Trends in a Cointegrated Nonlinear SVAR},
author = {James A. Duffy and Xiyu Jiao},
journal= {arXiv preprint arXiv:2507.22869},
year = {2026}
}
Comments
ii + 39 pp.; author accepted manuscript