Nonlinear Cointegration and Nonlinear Error Correction: Record Counting Cointegration Tests

摘要

In this article we propose a record counting Cointegration (RCC) test that is robust to nonlinearities and certain types of structural breaks. The RCC test is based on the synchronicity property of the jumps (new records) of cointegrated series, counting the number of jumps that simultaneously occur in both series. We obtain the rate of convergence of the RCC statistics under the null and alternative hypothesis. Since the asymptotic distribution of RCC under the null hypothesis of a unit root depends on the short-run dependence of the cointegrated series, we propose a small sample correction and show by Monte Carlo simulation techniques their excellent small sample behaviour. Finally, we apply our new Cointegration test statistic to several financial and macroeconomic time series that have certain structural breaks and nonlinearities.