The Annals of Statistics

Rank-based estimation for all-pass time series models

Beth Andrews, Richard A. Davis, and F. Jay Breidt

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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.

Article information

Ann. Statist., Volume 35, Number 2 (2007), 844-869.

First available in Project Euclid: 5 July 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62E20: Asymptotic distribution theory 62F10: Point estimation

All-pass deconvolution non-Gaussian noninvertible moving average rank estimation white noise


Andrews, Beth; Davis, Richard A.; Breidt, F. Jay. Rank-based estimation for all-pass time series models. Ann. Statist. 35 (2007), no. 2, 844--869. doi:10.1214/009053606000001316.

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