##### Department of Mathematics,

University of California San Diego

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### Math 288 - Special Statistics

## Beth Andrews

#### Colorado State University

## 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. 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 cannot be used for all-pass models. I discuss asymptotic properties of the two types of estimators, examine their behavior for finite samples via simulation, and consider an application for all-pass models--fitting noninvertible moving average models (known as nonminimum phase models in the engineering literature). I apply the results to stock market data. This is joint work with Jay Breidt and Richard Davis.

Host: Ian Abramson

### February 18, 2003

### 2:00 PM

### AP&M 6438

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