Spring Seminar Series - January 30, 2003
University of Minnesota
School of Statistics
College of Liberal Arts
Maximum Likelihood and Rank Estimation
for All-Pass Time Series Models
Beth Andrews
Department of Statistics
Colorado State University
Thursday, January 30, 2003
4:00 PM, 115
Ford Hall
Minneapolis, East Bank Campus
Social at 3:30 PM, 300
Ford Hall
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 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.