Rank-based estimation for all-pass time series models

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 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 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.

Original languageEnglish (US)
Pages (from-to)844-869
Number of pages26
JournalAnnals of Statistics
Volume35
Issue number2
DOIs
StatePublished - Apr 2007

Keywords

  • All-pass
  • Deconvolution
  • Non-Gaussian
  • Noninvertible moving average
  • Rank estimation
  • White noise

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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