Mathematical Sciences: Time Series Models and Extreme Value Theory

Proposal: DMS 9504596 PI(s): Richard Davis, Murray Rosenblatt, Peter Brockwell Institution: Colorado State Title: Times Series Models and Extreme Value Theory Abstract: The research is concerned with problems of estimation and research for time series models whose theory is not yet fully understood. The standard linear Gaussian models for time series data are inadequate to describe many of the time series observed in practice so it is important to develop techniques for estimation and prediction based on more general models. Efficient estimation procedures and prediction techniques for non-causal and non-invertible ARMA processes are developed and a study made of the theory and application of continuous-time linear and non-linear ARMA processes.还研究了线性和非线性模型的极值理论。 Existing methods of forecasting are based on assumptions which are frequently not satisfied by observed economic and scientific time series data. This research develops methods of analysis and forecasting for a more general class of time series models, leading to more accurate forecasting of series which do not meet the restrictive assumptions of the classical theory.

Proposal: DMS 9504596 PI(s): Richard Davis, Murray Rosenblatt, Peter Brockwell Institution: Colorado State Title: Times Series Models and Extreme Value Theory Abstract: The research is concerned with problems of estimation and research for time series models whose theory is not yet fully understood. The standard linear Gaussian models for time series data are inadequate to describe many of the time series observed in practice so it is important to develop techniques for estimation and prediction based on more general models. Efficient estimation procedures and prediction techniques for non-causal and non-invertible ARMA processes are developed and a study made of the theory and application of continuous-time linear and non-linear ARMA processes. Extreme value theory for linear and non-linear models is also investigated. Existing methods of forecasting are based on assumptions which are frequently not satisfied by observed economic and scientific time series data. This research develops methods of analysis and forecasting for a more general class of time series models, leading to more accurate forecasting of series which do not meet the restrictive assumptions of the classical theory.