ABSTRACT
This chapter focuses on how to apply the local polynomial modelling technique to explore important structural information contained in dependent data. It discusses only certain aspects of nonlinear time series analysis that have a nonparametric flavor. The chapter shows how nonparametric regression techniques can be used for nonlinear prediction. The key conditions that enable one to apply local polynomial fitting are mixing conditions which indicate the strength of dependence of two time events in medium or long terms. Smoothed periodograms have a few drawbacks. Firstly, periodograms can often be highly heteroscedastic, making the task of local bandwidth selection hard. Secondly, the estimate can be unstable in the peak regions. Salient features of a nonlinear stochastic system include its sensitivity to initial values and noise amplification through time evolution. The sensitivity indicates how different two trajectories of the system can be given two nearby initial values.
