"Nonparametric Regression Methods For Nonlinear Time Series Models"

本项目的目的是发展的方法估计和测试非线性时间序列模型涉及大量的预测变量。关键思想是采用非参数回归理论中使用的一些技术，这些技术可以在适当的证明之后转移到时间序列设置中。此外，本文还首次建立了所得估计量的决策理论性质。这是通过建立非参数回归与各种非线性时间序列模型之间的渐近等价结果来实现的。本项目中研究的模型在不同的应用领域中非常常见。其中许多是涉及联邦战略利益的领域。例如，人们可以提到预测未来洪水的水平和预测许多工业领域的产量。另一个非常重要的应用领域是建立解释海洋表面温度长期变化的模型，通过这样做，有助于解释和预测未来全球气候的变化。上述所有模型通常都包含大量的预测变量，这使得在实践中选择所需的模型非常困难。根据本项目提出的方法和试验，可以制定有效的模型选择程序，对选择正确的模型有很大的帮助。在选择了正确的模型之后，可以获得高质量的预测，这些预测不仅对科学研究人员感兴趣，而且对整个社会也有好处。

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.