## The Annals of Statistics

### Rank-based 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 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

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

Dates
First available in Project Euclid: 5 July 2007

https://projecteuclid.org/euclid.aos/1183667296

Digital Object Identifier
doi:10.1214/009053606000001316

Mathematical Reviews number (MathSciNet)
MR2336871

Zentralblatt MATH identifier
1117.62089

#### Citation

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. https://projecteuclid.org/euclid.aos/1183667296

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