Research Planning Grant: Data-driven Modeling and Forecasting of Nonlinear Time Series Systems

9409273雷，作者建议研究非线性时间序列分析中的几个公开问题，目的是将非参数回归建模和线性时间序列分析的技术结合起来，并将其扩展到非线性时间序列框架。特别是，作者计划调查非参数回归技术对具有非常缓慢衰减的序列相关性的非线性过程建模的适宜性，这种非线性过程被称为长期相关性。将对考虑到一系列相关程度的现有程序的修改进行调查。此外，当非线性回归算法应用于时间序列时，作者将研究检验模型假设的适当方法。作者还计划将现有的关于单变量序列非线性检验的方法推广到多变量情况。我们将研究数据驱动的方法来获得完全多变量的非线性模型。最后，作者将考虑在预测方面的优势，对数据使用数据驱动的非线性模型，该模型暗示了一个非线性生成过程。***

9409273 Ray The author proposes to investigate several open problems in nonlinear time series analysis, with the goal of combining techniques from nonparametric regression modeling and linear time series analysis and extending them to the nonlinear time series framework. In particular, the author plans to investigate the appropriateness of nonparametric regression techniques for modeling nonlinear processes having very slowly decaying serial correlation, known as long-range dependence. Modifications of existing procedures that take into account the amount of correlation in a series will be investigated. Additionally, the author will investigate appropriate methods of testing model assumptions underlying the use of nonlinear regression algorithms when the algorithms are applied to time series. The author also plans to extend existing methodology concerning tests of nonlinearity in univariate series to the multivariate case. Data-driven methods for obtaining full multivariate nonlinear models will be investigated. Finally, the author will consider the advantages, in terms of forecasting, of using a data-driven nonlinear model for data which suggests a nonlinear generating process. ***