ABSTRACT
One task in modelling nonlinear time series data is to study the structural relationship between the present observation and the history of the data set. Since Tong (1990), which focuses mainly on parametric models, nonparametric techniques have been used extensively to model nonlinear time series data (see Auestad and Tjøstheim 1990; Tjøstheim 1994; Chapter 6 of Fan and Gijbels 1996; Ha¨rdle, Lu¨tkepohl and Chen 1997; Gao 1998; Chapter 6 of Ha¨rdle, Liang and Gao 2000; Fan and Yao 2003 and the references therein). Although nonparametric techniques appear feasible, there is a serious problem: the curse of dimensionality. For the independent and identically distributed case, this problem has been discussed and illustrated in several monographs and many papers. In order to deal with the curse of dimensionality problem for the time series case, several nonparametric and semiparametric approaches have been discussed in Chapters 2 and 3, including nonparametric time series single-index and projection pursuit modelling and additive nonparametric and semiparametric time series modelling. In addition to such nonparametric and semiparametric approaches to modelling nonlinear time series, variable selection criteria based on nonparametric techniques have also been discussed in the literature.
