Non-linear time series and Markov chains

It is shown how Markov chain theory can be exploited to study non-linear time series, the emphasis being on the classification into stationary and non-stationary models. A generalized h-step version of the Tweedie (1975), (1976) criteria is formulated, and applications are given to a number of non-linear models. New results are obtained, and known results are shown to emerge as special cases in both the scalar and vector case. A connection to stability theory is briefly discussed, and it is indicated how the Markov property can be utilized for estimation purposes.