Parameter Estimation for All-Pass Time Series Models
Beth Andrews
Colorado State University
Ph.D. Candidate

Thursday, 31 July 2003
1:00 PM
E202 Engineering
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 least absolute deviations, maximum likelihood, and rank techniques to obtain parameter estimates.  Least absolute deviations and maximum likelihood estimation have already been studied for autoregressive-moving average models.  However, the parameters in the autoregressive and moving average polynomials of an all-pass model are dependent, so the results for autoregressive-moving average models cannot be used for all-pass models. All-pass processes with both finite and infinite variance are considered.  I discuss asymptotic properties of the estimators, examine their behavior for finite samples via simulation, and consider an application for all-pass models—fitting noninvertible autoregressive-moving average models.  The results are applied to the deconvolution of a simulated water gun seismogram.



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