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. ***
