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April 2007 Rank-based estimation for all-pass time series models
Beth Andrews, Richard A. Davis, F. Jay Breidt
Ann. Statist. 35(2): 844-869 (April 2007). DOI: 10.1214/009053606000001316


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 are useful for identifying and modeling noncausal and noninvertible autoregressive-moving average processes. We establish asymptotic normality and consistency for rank-based estimators of all-pass model parameters. The estimators are obtained by minimizing the rank-based residual dispersion function given by Jaeckel [Ann. Math. Statist. 43 (1972) 1449–1458]. These estimators can have the same asymptotic efficiency as maximum likelihood estimators and are robust. The behavior of the estimators for finite samples is studied via simulation and rank estimation is used in the deconvolution of a simulated water gun seismogram.


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Beth Andrews. Richard A. Davis. F. Jay Breidt. "Rank-based estimation for all-pass time series models." Ann. Statist. 35 (2) 844 - 869, April 2007.


Published: April 2007
First available in Project Euclid: 5 July 2007

zbMATH: 1117.62089
MathSciNet: MR2336871
Digital Object Identifier: 10.1214/009053606000001316

Primary: 62M10
Secondary: 62E20 , 62F10

Keywords: All-pass , Deconvolution , non-Gaussian , noninvertible moving average , rank estimation , White noise

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 2 • April 2007
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