"Nonparametric Regression Methods For Nonlinear Time Series Models"

Purdue University, West Lafayette IN

Investigators

Abstract

The aim of this project is to develop the methodology for estimation and testing of the nonlinear time series models involving a large number of predictor variables. The key idea is to adapt a number of techniques that are used in the nonparametric regression theory and that can be, after suitable justification, transferred to the time series setting. In addition to the above, the decision-theoretic properties of the resulting estimators are established for the first time. This is achieved by establishing asymptotic equivalence results between the nonparametric regression and various nonlinear time series models. The models studied in this project are very commonly encountered in different areas of application. Many of these are the areas of federal strategic interest. As an example, one can mention forecasting the levels of future flooding and predicting the volume of production in many areas of industry. Another very important area of application is building the models that explain long-term changes in sea surface temperature and, by doing so, help explain and predict the future changes in the global climate. All of the above models often include a lot of predictor variables and this makes the choice of the model needed very difficult in practice. Based on the methods and tests proposed in this project, efficient model selection procedures can be enacted that can greatly help in choosing the right model. After the right model is chosen, high quality forecasts can be obtained that are not only of interest for researchers in science, but that also benefit society as a whole.