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Parametric Nonlinear Time Series Models

Part of the Springer Series in Statistics book series (SSS)

Abstract

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.

Keywords

Maximum Likelihood Estimator GARCH Model Stochastic Volatility Model Bilinear Model Time Series Plot 
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.

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Copyright information

© Springer Sciences+Business Media, Inc. 2005

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