Concepts of and tools for nonlinear time-series modelling

The aim of the paper is to examine some of the key issues in nonlinear time series analysis. Tools and approaches are provided for nonlinear modelling in econometrics. A wide range of topics is covered, including probabilistic properties, statistical inference and computational methods. The approach chosen in the present paper is to concentrate on tools and methods, rather than on models themselves. This choice was done for two reasons. First the number of imaginable nonlinear models is virtually infinite, whereas fundamental concepts like stationarity and ergodicity are of interest for all these models. Second, comprehensive reviews of the nonlinear models used in financial and macroeconomic time series are already available in the literature. We tried to make the text as self-consistent as possible, and to give the main ideas of the mathematical and computational arguments. Techniques and concepts are illustrated by various examples, Monte Carlo experiments and a real application. This paper is intended for a broad public of researchers in statistics or econometrics, coming either from theoretical domains or from applied areas.