Seminars and Events - Research Colloquia

Special Colloquia, Department of Statistics

Friday, January 17, 2003
4:30 PM in REC 303

Ms. Beth Andrews
Colorado State University

will speak on

Maximum Likelihood and Rank Estimation for All-Pass Time Series Models

Abstract

All-pass models are autoregressive-moving average models in which the roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa. They generate uncorrelated (white noise) time series, but these series are not independent in the non-Gaussian case. All-pass models are useful for fitting noninvertible moving average models (known as nonminimum phase models in the engineering literature). Because all-pass series are uncorrelated, estimation methods based on Gaussian likelihood, least-squares, or related second-order moment techniques cannot identify all-pass models. Consequently, I use maximum likelihood and rank techniques to obtain parameter estimates. Maximum likelihood estimation has already been studied for autoregressive-moving average models. However, the parameters in the autoregressive polynomial of an all-pass model are functions of parameters in the moving average polynomial and vice versa, so the results for autoregressive-moving average models are not directly applicable to all-pass models. I discuss the asymptotic properties of the two types of estimators, examine their behavior for finite samples via simulation, and apply the results to real data. This is joint work with Jay Breidt and Richard Davis.