Common Persistence in Nonlinear Autoregressive Models.

In this paper we propose to consider a measure of the persistence of shocks in linear combinations of nonlinear processes, in order to investigate the possible presence of common long-run properties. We argue that such common persistence for nonlinear time series corresponds to the concept of cointegration for linear time series. Additionally, persistence can be used to examine other common properties such as nonlinearity, which in turn may be used to identify simplifying structures. The calculation of our persistence measure is based on Monte Carlo integration. An application to logistic smooth transition autoregressive models and artificial neural networks for industrial production in Belgium, Germany and the USA yields that Belgium and Germany display common persistence, while the USA - Germany relation seems to be much weaker. In addition, we find that the Germany and USA data display common nonlinearity.