Mathematical Sciences: Extreme Values and Inference in Time Series Models

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The principal investigator will use the asymptotic techniques that he developed along with Dr. Resnick, to find limits of sequences of point processes related to various time series. When the point processes are generated from normalized extreme value processes, general solutions are hard or possibly impossible to obtain. Dr. Davis will obtain results for a certain subclass of these processes. Results on convergence of the sample correlation functions lead directly to the estimation of the order of the autoregressive processes. The second area for the project is inference on the time series models. The prediction problems for high order autoregressive processes are computationally complex. Recursive prediction will be worked out using the univariate Kalman filtering results. Extensive numerical comparisons will be made with the standard least squares predictors. Rates of convergence of these estimates will be investigated as well.