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Maximum likelihood estimation for all-pass time series models

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

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 97 (2006)
    Issue (Month): 7 (August)
    Pages: 1638-1659

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    Handle: RePEc:eee:jmvana:v:97:y:2006:i:7:p:1638-1659
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    1. Jian Huang, 2000. "Quasi-likelihood Estimation of Non-invertible Moving Average Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 689-702.
    2. Lii, Keh-Shin & Rosenblatt, Murray, 1992. "An approximate maximum likelihood estimation for non-Gaussian non-minimum phase moving average processes," Journal of Multivariate Analysis, Elsevier, vol. 43(2), pages 272-299, November.
    3. Lii, Keh-Shin & Rosenblatt, Murray, 1988. "Nonminimum phase non-Gaussian deconvolution," Journal of Multivariate Analysis, Elsevier, vol. 27(2), pages 359-374, November.
    4. Breid, F. Jay & Davis, Richard A. & Lh, Keh-Shin & Rosenblatt, Murray, 1991. "Maximum likelihood estimation for noncausal autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 36(2), pages 175-198, February.
    5. Davis, Richard A. & Knight, Keith & Liu, Jian, 1992. "M-estimation for autoregressions with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 145-180, February.
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