Modelling Autoregressive Processes with a Shifting Mean

In this paper we introduce an autoregressive model with a deterministically shifting intercept. This implies that the model has a shifting mean and is thus nonstationary but stationary around a nonlinear deterministic component. The shifting intercept is defined as a linear combination of logistic transition functions with time as the transition variables. The number of transition functions is determined by selecting the appropriate functions from a possibly large set of alternatives using a sequence of specification tests. This selection procedure is a modification of a similar technique developed for neural network modelling by White (2006). A Monte Carlo experiment is conducted to show how the proposed modelling procedure and some of its variants work in practice. The paper contains two applications in which the results are compared with what is obtained by assuming that the time series used as examples may contain structural breaks instead of smooth transitions and selecting the number of breaks following the technique of Bai and Perron (1998).

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SNDE recognizes that advances in statistics and dynamical systems theory can increase our understanding of economic and financial markets. The journal seeks both theoretical and applied papers that characterize and motivate nonlinear phenomena. Researchers are required to assist replication of empirical results by providing copies of data and programs online. Algorithms and rapid communications are also published.