Parametric Nonlinear Time Series Models
The long-lasting popularity of ARMA models convincingly justifies the usefulness of linear models for analyzing time series data. Nevertheless, in view of the fact that any statistical model is an approximation to the real world, a linear model is merely a first step in representing an unknown dynamic relationship in terms of a mathematical formula. The truth is that the world is nonlinear! Therefore, it is not surprising that there exists an abundance of empirical evidence indicating the limitation of the linear ARMA family. To model a number of nonlinear features such as dependence beyond linear correlation, we need to appeal to nonlinear models. In this chapter, we present some parametric nonlinear time series models and their statistical inferences. §4.1 provides an introduction to the threshold modeling for conditional mean functions. §4.2 is devoted to ARCH modeling of nonconstant conditional variance functions—a phenomenon called conditional heteroscedasticity. A brief account on bilinear models is given in §4.3.
KeywordsMaximum Likelihood Estimator GARCH Model Stochastic Volatility Model Bilinear Model Time Series Plot
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