Inference on Common Trends in a Cointegrated Nonlinear SVAR

TL;DR

This paper develops a robust statistical test for identifying common trends in cointegrated nonlinear SVAR models, addressing limitations of existing methods with a novel asymptotic analysis.

Contribution

It introduces a modified variance ratio test that accurately infers the number of common trends in nonlinear cointegrated systems, supported by new theoretical results.

Findings

The modified test correctly identifies the number of common trends.

Unmodified tests tend to overestimate the number of trends in nonlinear cointegration.

The paper proves a new LLN-type result for nonstationary autoregressive processes.

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.