Comments on “A Nonparametric Test For Nonlinear Cointegration” By Jörg Breitung

Abstract

This paper provides a very appealing approach to testing for nonlinear cointegration in a way that avoids a drawback faced by standard tests, which will often reject the null of cointegration in the presence of nonlinear cointegration. Unlike previous work on nonlinear cointegration (e.g. Granger and Teräsvirta, 1993; Granger, 1995; Granger, Inoue, and Morin, 1997; Swanson, Corradi, and White, 1997), the test is based on ranks. For a time series x _t , t=1, …, T,R _T (x _t ) is the rank of x _t in the sample of size T. To test the null of no nonlinear cointegration between x _t and y _t , one forms where d _t = R _T (y _t ) −R _T (x _t ) is the difference in ranks. More sophisticated statistics are proposed, based on standardizing in reasonable ways, but it suffices for the present discussion to limit attention to these straightforward statistics.