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

小行星9409273 作者提出研究非线性时间序列分析中的几个开放性问题，目标是将非参数回归建模和线性时间序列分析技术相结合，并将其扩展到非线性时间序列框架。特别是，作者计划研究非参数回归技术建模的非线性过程具有非常缓慢的衰减序列相关性，称为长程依赖的适当性。 修改现有的程序，考虑到在一个系列的相关性的金额将进行调查。 此外，作者将调查适当的方法来测试模型假设的基础上使用非线性回归算法时，算法应用于时间序列。 作者还计划扩展现有的方法，在单变量序列的非线性检验的多变量的情况下。数据驱动的方法获得完整的多元非线性模型将进行调查。 最后，作者将考虑的优势，在预测方面，使用数据驱动的非线性模型的数据，这表明一个非线性的生成过程。 ***

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. ***