Candidate: Kirk Anderson

Degree of: Doctor of Philosophy

Department: Statistics

Title: Robust Residuals and Diagnostics in Autoregressive Time Series

Committee:
Dr. Joe McKean, Chair
Dr. Daniel Mihalko
Dr. Mike Stoline
Dr. Joshua Naranjo
Dr. Bradley Huitema

Date: Friday, November 8, 2002 3:00 p.m.-5:00 p.m.
3302 Rood

Abstract:
One of the goals of model diagnostics is outlier detection. In particular, we would like to use the residuals, appropriately standardized, to "flag" outliers. Hopefully, our (robust) procedure has yielded a fit that resists undue influence by outlying points, while simultaneously drawing attention to these interesting points via residual analysis.

In this study we consider several different methods of standardizing the residuals resulting from autoregression. A large sample approximation for the variance of rank-based first order autoregressive time series residuals is developed. This provides studentized residuals, specific to the time series model and estimation procedure.

Simulation studies are presented that illustrate outlier detection ability among different standardization methods, and differences in fits among estimation procedures in the presence of innovation and additive outliers.

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