2025/07/30 by Duffy, James A., Jiao, Xiyu
#60G65 (Secondary) #62E20 #62M10 (Primary) #91B84 #Econometrics (econ.EM) #FOS: Economics and business #FOS: Mathematics #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2507.22869
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-linear 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.