Mathematical Sciences: Nonlinear Time Series Analysis

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This project is concerned with nonlinear time series analysis. It has four main objectives. The first objective is to develop new methods for modeling nonlinear time series via nonparametric smoothing techniques. This research is a continuation of the work on functional coefficient AR models and nonlinear additive AR models by the PI and Tsay over the last several years. See Chen and Tsay (1993a, 1993b). The results obtained under this research will increase the applicability of nonlinear time series models. The second objective of the proposed research is to investigate binary-process driven switching regression models. A unified treatment is proposed for the general switching structures and a testing procedure is introduced for discriminating a random (independent) switching regression model from a Markov-chain driven model. The third objective is to study new approaches in finding the indicator variable for an open-loop threshold AR model. Several approaches are suggested to overcome the difficulties encountered in using the open-loop threshold AR models. In particular, two algorithms and some graphical tools are proposed to identify an appropriate indicator variable. The final objective is to investigate the ergodicity conditions of some nonlinear time series models. The results obtained will provide a better understanding of the nonlinear models as well as a foundation on which asymptotic properties of various nonparametric statistics for nonlinear time series analysis can be established.