Nonparametric Modeling and Prediction for Time Series Analysis

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DMS9626113 Chen This research is concerned with nonparametric model building procedures and nonparametric prediction methods in nonlinear time series analysis. The first objective of this research is to develop a new nonparametric modeling procedure for nonlinear time series. The investigator studies the functional coefficient autoregressive models and makes the model easier to use in practice. In particular, a weighted local linear regression procedure is studied. This procedure differs from the classical local linear regression for curve fitting where the response function is of interest. Here, estimating the coefficient functions are of main interest. A procedure for detecting discontinuities in the coefficient functions is studied as well. The second objective of this research is concerned with multi-step predictions using nonparametric smoothing techniques. The investigator studies the properties of a multi-stage nonparametric predictor, which is closely related to the iterative integration procedures for multi-step prediction. Preliminary study shows that the new method does improve the accuracy of the prediction. The first goal is to show that the predictor is applicable to a wide class of nonlinear AR models. The second goal is to investigate the practical implementation of the method, particularly the automatic bandwidth selection method and prediction strategy. This research is concerned with model building procedures and prediction methods in nonlinear time series analysis. A time series is a set of data observed over a period of time. For example, daily ozone and pollutant readings for environmental study, quarterly unemployment rate or GNP for economical study and noisy telecommunication signals are all subjects of time series analysis. Time series analysis tries to reveal the generating mechanism of the observed time series and to provide sensible methods to predict future observations based on current and past information. Linear ti me series models assumes the future observations relate to the current and past observations in simple linear functions while nonlinear models assume complex relationship. In this research, the investigator follows the principle of `letting the data speak for themselves' and develops modeling procedures for nonlinear time series. It is used to overcome the difficulty encountered in real applications of choosing an appropriate model. The second objective of this research is concerned with multi-step predictions for nonlinear time series. Nonlinear time series models have been shown to have certain advantages in multi-step forecasting over linear models. In this research, the investigator studies the properties of a new predictor that improves the prediction accuracy. There are sufficient reasons to believe that the results of this research should have significant contributions in nonlinear time series analysis, which has many important applications in the fields of economics, telecommunication, meteorology, environment and many others.