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Rank-based estimation for all-pass time series models. (English) Zbl 1117.62089

Summary: 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 L. A. Jaeckel [Ann. Math. Stat. 43, 1449–1458 (1972; Zbl 0277.62049)]. 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.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F12 Asymptotic properties of parametric estimators
62F35 Robustness and adaptive procedures (parametric inference)
62E20 Asymptotic distribution theory in statistics
86A15 Seismology (including tsunami modeling), earthquakes

Citations:

Zbl 0277.62049
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References:

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