Nonlinear Time Series Analysis

Abstract

The recent development of nonlinear time series analysis is primarily due to the efforts to overcome the limitations of linear models such as autoregressive moving-average (ARMA) models of Box and Jenkins (1976) in real applications. Two examples of such limitations are the non-ability to model sudden outbursts and the restriction to symmetry in the sense of reversible processes, whereas many processes observed in reality reveal irreversibility, well-known examples being the sunspot numbers and the Canadian Lynx data, see Tong (1990) for a discussion of these data sets with respect to nonlinearity and irreversibility. The increasing popularity of nonlinear time series models is also attributed to the development of nonlinear and nonparametric regression techniques which provides many useful tools. Advanced computational power and easy-to-use advanced softwares and graphics such as S-Plus(Venables and Ripley (1994)) and XploRe(Härdle, Klinke and Turlach (1995)) contribute to the increasing application of nonlinear time series analysis. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.