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

摘要

In this paper we introduce a class of nonlinear data generating processes (DOGs) that are first order Markov and can be represented as the sum of a linear plus a bounded nonlinear component. We use the concepts of geometric ergodicity and of linear stochastic comovement, which correspond to the linear concepts of integratedness and cointeg-ratedness, to characterize the DGPs. We show that the stationarity test due to Kwiatowski et al. (1992, Journal of Econometrics, 54, 159-178) and the cointegrationtest of shin (1994, Econometric Theory, 10, 91-115) are applicable in the current context, although 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 presented which suggests that the test has useful finite sample power against a variety of nonlinear alternatives. An empirical illustration is also provided.