7 - Nonparametric Time Series Modeling

Summary

Introduction

As the previous chapters have shown, parametric time series modeling offers a great wealth of modeling tools. Linear time series models are generally the starting point for modeling both univariate and multivariate time series data. Such data may also exhibit nonstationary behavior caused by the presence of unit roots, structural breaks, seasonal influences, and the like. If one is interested in nonlinear dynamics, it is no longer sufficient to consider linear models. This situation arises if, for example, the strength of economic relationships depends on the state of the business cycle or if the adjustment speed toward long-run equilibrium relationships is not proportional to the deviation from the long-run equilibrium. Chapter 6 discusses how to build nonlinear parametric models for various kinds of nonlinear dynamics, including those of business cycles. There it is also explained how the parameter estimates can be used to understand the underlying nonlinear dynamic behavior.

However, nonlinear parametric modeling also has its drawbacks. Most importantly, it requires an a priori choice of parametric function classes for the function of interest. The framework of smooth transition regression models discussed in Chapter 6, for example, is widely used. Although it is an appropriate modeling framework for many empirical problems, it may not always capture features that are relevant to the investigator. In the latter case, one has to choose alternative nonlinear parametric models like neural networks or Markov-switching models to name a few. Thus, nonlinear parametric modeling implies the difficult choice of a model class.

In contrast,when using the nonparametric modeling approach, one can avoid this choice.