Maximum likelihood estimation for all-pass time series models

Authors:
Beth Andrews;Richard A. Davis;F. Jay Breidt
Affiliations:
Northwestern University, IL;Colorado State University;Colorado State University
Venue:
Journal of Multivariate Analysis
Year:
2006

Citing 7
Cited 1

Time series: theory and methods

Time series: theory and methods
Nonminimum phase non-Gaussian deconvolution

Journal of Multivariate Analysis
Maximum likelihood estimation for noncausal autoregressive processes

Journal of Multivariate Analysis
An approximate maximum likelihood estimation for non-Gaussian non-minimum phase moving average processes

Journal of Multivariate Analysis
A new identification algorithm for allpass systems by higher-order statistics

Signal Processing
`` Direct Search'' Solution of Numerical and Statistical Problems

Journal of the ACM (JACM)
Parametric cumulant based phase estimation of 1-D and 2-Dnonminimum phase systems by allpass filtering

IEEE Transactions on Signal Processing

Maximum likelihood estimation of a noninvertible ARMA model with autoregressive conditional heteroskedasticity

Journal of Multivariate Analysis

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Abstract

An autoregressive-moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models generate uncorrelated (white noise) time series, but these series are not independent in the non-Gaussian case. An approximate likelihood for a causal all-pass model is given and used to establish asymptotic normality for maximum likelihood estimators under general conditions. Behavior of the estimators for finite samples is studied via simulation. A two-step procedure using all-pass models to identify and estimate noninvertible autoregressive-moving average models is developed and used in the deconvolution of a simulated water gun seismogram.