Testing for stationarity-ergodicity and for comovements between nonlinear discrete time Markov processes

In this paper we introduce a class of nonlinear data generating processes ( DGPs) that are first order Markov and can be represented as the sum of a li near plus a bounded nonlinear component. We use the concepts of geometric e rgodicity and of linear stochastic comovement, which correspond to the line ar concepts of integratedness and cointegratedness, to characterize the DGP s. We show that the stationarity test due to Kwiatowski et ai. (1992, Journ al of Econometrics, 54, 159-178) and the cointegration test of Shin (1994, Econometric Theory, 10, 91-115) are applicable in the current context, alth ough the Shin test has a different limiting distribution. We also propose a consistent test which has a null of linear cointegration (comovement), and an alternative of 'non-linear cointegration'. Monte Carlo evidence is pres ented which suggests that the test has useful finite sample power against a variety of nonlinear alternatives. An empirical illustration is also provi ded, (C) 2000 Elsevier Science S.A. All rights reserved. JEL classification : C12; C22.