Nonparametric Modeling for Nonlinear Time Series

University Of North Carolina At Charlotte, Charlotte NC

Investigators

Abstract

This project covers a variety of methodological developments and foundational research. In particular, the object of this research is to develop some new nonparametric model building and identication procedures for high-dimensional nonlinear time series data. The investiga- tor studies both the varying-coefficient regression models and nonlinear additive regression models for nonlinear time series data and makes the models practically applicable. The first objectiveis to develop nonparametric estimation procedures for nonlinear time series. In particular, for varying-coefficient regression models, local polynomial regression techniques are used to estimate the coefficient functions and the asymptotic properties of the resulting estimators are studied. This procedure differs from the classical local linear regression for curve fitting where the response surface is of interest. Here, of interest is to estimate the coefficient functions. For nonlinear additive regression models, the investigator uses partial residual method to estimate unknown additive functions coupled with projection method and local polynomial fitting. The approach is divided into two steps. In the first step, the initial estimated values for all components are obtained by using the projection method. In the second step, a local polynomial technique is employed to estimate any one of compo- nents by using the initial estimated values of the rest of components. The second objective of this research is concerned with the model identification. For both models, a new goodness- of-fit test technique is proposed, based on the comparison of the residual sum of squares under the null and alternative models, to detect whether certain coefficient functions in the varying-coefficient models are constant or whether certain components in the additive mod- els are linear or whether any covariates are significant in the models. The null distribution of the test is estimated by a nonparametric bootstrap method. Also, the investigator studies the practical implementation of the methods, particularly the automatic bandwidth selection method based on a modified generalized cross-validation. A nonparametric version of Akaike information criterion is proposed for choosing the smoothing variable in varying-coefficient models and determining an appropriate model for given data. This research is concerned with model estimation and identification procedures in non- linear time series analysis. A time series is a set of data observed over a period of time. For example, daily ozone and pollutant levels from environmental study, quarterly earnings for a company or daily currency exchange rate from economical study, wild animals' popula- tion observed over years from ecological study, number of in uenza cases observed over time from epidemiology, and noisy telecommunication signals. The investigator has been active in this research area. Furthermore, the investigator has conducted preliminary work on the described problem area which has led to encouraging results. There are sufficient reasons to believe that by pursuing the topics outlined in this proposal, the results of this research should have significant contributions in nonlinear time series analysis, which has many impor- tant applications in the fields of economics, social science, medicine, epidemiology, biology, environment, physical sciences, engineering, and many others.