Non‑linear Cointegration Test, Based on Record Counting Statistic

Abstract

Traditional tests fail to detect the presence of nonlinearities in series that are cointegrated, so in this paper a new procedure for cointegration tests is proposed by modifying the two-step Engle and Granger (EG) test (Engle and Granger in Econometrica 55:251–276, 1987), incorporating the RUR and the FB-RUR test of Aparicio et al. (J Time Ser Anal 27:545–576, 2006). The statistics of these non-parametric tests, which are constructed as functions of order statistics, endow the test with desirable properties such as invariance to non-linear transformations of the series and robustness to the presence of significant parameter shifts. As no prior estimation of the cointegrating parameter is required, the new tests lead to parameter-free asymptotic null distributions. Monte Carlo simulations are used to analyze the test properties and evaluate the power at different sample sizes. The robustness of the procedure is tested by performing a comparison of different tests of cointegration in real exchange rate relationships. These tests are able to find evidence of cointegration while standard cointegration tests fail to detect it.