Maximum likelihood 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

50 Scopus citations


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 generate uncorrelated (white noise) time series, but these series are not independent in the non-Gaussian case. An approximate likelihood for a causal all-pass model is given and used to establish asymptotic normality for maximum likelihood estimators under general conditions. Behavior of the estimators for finite samples is studied via simulation. A two-step procedure using all-pass models to identify and estimate noninvertible autoregressive-moving average models is developed and used in the deconvolution of a simulated water gun seismogram.

Original languageEnglish (US)
Pages (from-to)1638-1659
Number of pages22
JournalJournal of Multivariate Analysis
Issue number7
StatePublished - Aug 2006


  • Gaussian mixture
  • Non-Gaussian
  • Noninvertible moving average
  • White noise

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


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