Maximum likelihood estimation for all-pass time series models

Beth Andrews; Richard A. Davis; F. Jay Breidt

doi:10.1016/j.jmva.2006.01.005

Maximum likelihood estimation for all-pass time series models

Beth Andrews^*, Richard A. Davis, F. Jay Breidt

^*Corresponding author for this work

Statistics and Data Science

Research output: Contribution to journal › Article › peer-review

52 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1638-1659
Number of pages	22
Journal	Journal of Multivariate Analysis
Volume	97
Issue number	7
DOIs	https://doi.org/10.1016/j.jmva.2006.01.005
State	Published - Aug 2006

Funding

We would like to thank two anonymous reviewers for their helpful comments and Professor Keh-Shin Lii for supplying the water gun wavelet used in Section 4.3. Also, the work reported here was developed in part under STAR Research Assistance Agreement CR-829095 awarded by the U.S. Environmental Protection Agency (EPA) to Colorado State University. This manuscript has not been formally reviewed by EPA. The views expressed here are solely those of the authors. EPA does not endorse any products or commercial services mentioned in this report. ∗Corresponding author. E-mail address: [email protected] (B. Andrews). 1Supported in part by NSF Grants DMS9972015 and DMS0308109. 2Supported in part by EPA STAR Grant CR-829095.

Keywords

Gaussian mixture
Non-Gaussian
Noninvertible moving average
White noise

ASJC Scopus subject areas

Statistics and Probability
Numerical Analysis
Statistics, Probability and Uncertainty

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10.1016/j.jmva.2006.01.005

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title = "Maximum likelihood estimation for all-pass time series models",

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.",

keywords = "Gaussian mixture, Non-Gaussian, Noninvertible moving average, White noise",

author = "Beth Andrews and Davis, {Richard A.} and {Jay Breidt}, F.",

note = "Funding Information: We would like to thank two anonymous reviewers for their helpful comments and Professor Keh-Shin Lii for supplying the water gun wavelet used in Section 4.3. Also, the work reported here was developed in part under STAR Research Assistance Agreement CR-829095 awarded by the U.S. Environmental Protection Agency (EPA) to Colorado State University. This manuscript has not been formally reviewed by EPA. The views expressed here are solely those of the authors. EPA does not endorse any products or commercial services mentioned in this report. Funding Information: ∗Corresponding author. E-mail address: [email protected] (B. Andrews). 1Supported in part by NSF Grants DMS9972015 and DMS0308109. 2Supported in part by EPA STAR Grant CR-829095.",

year = "2006",

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doi = "10.1016/j.jmva.2006.01.005",

language = "English (US)",

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AU - Jay Breidt, F.

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N2 - 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.

AB - 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.

KW - Gaussian mixture

KW - Non-Gaussian

KW - Noninvertible moving average

KW - White noise

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Maximum likelihood estimation for all-pass time series models

Abstract

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Keywords

ASJC Scopus subject areas

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