Nonparametric Modeling and Prediction for Time Series Analysis

本文主要研究非线性时间序列分析中的非参数模型建立过程和非参数预测方法。本研究的第一个目标是开发一种新的非线性时间序列的非参数建模方法。研究了函数系数自回归模型，使模型在实际应用中更易于使用。特别地，研究了加权局部线性回归过程。这个过程不同于曲线拟合的经典局部线性回归，其中响应函数是感兴趣的。在这里，估计系数函数是主要的兴趣。研究了一种检测系数函数不连续的方法。本研究的第二个目标是使用非参数平滑技术进行多步预测。研究了多阶段非参数预测器的性质，这与多阶段预测的迭代积分过程密切相关。初步研究表明，新方法确实提高了预测的精度。第一个目标是表明预测器适用于广泛的非线性AR模型。第二个目标是研究该方法的实际实现，特别是自动带宽选择方法和预测策略。本文研究了非线性时间序列分析中的模型建立步骤和预测方法。时间序列是在一段时间内观察到的一组数据。例如，用于环境研究的每日臭氧和污染物读数、用于经济研究的季度失业率或国民生产总值以及嘈杂的电信信号都是时间序列分析的对象。时间序列分析试图揭示观测时间序列的产生机制，并根据当前和过去的信息提供合理的方法来预测未来的观测。线性时间序列模型假设未来的观测值与当前和过去的观测值以简单的线性函数相关联，而非线性模型则假设两者之间存在复杂的关系。在本研究中，研究者遵循“让数据说话”的原则，并开发了非线性时间序列的建模程序。它用于克服在实际应用中遇到的选择合适模型的困难。本研究的第二个目标是非线性时间序列的多步预测。非线性时间序列模型在多步预测方面比线性模型具有一定的优势。在这项研究中，研究者研究了一种新的预测器的性质，以提高预测精度。我们有充分的理由相信，本研究的结果对非线性时间序列分析有重大的贡献，非线性时间序列分析在经济、电信、气象、环境等许多领域都有重要的应用。

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.