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Recursive Generalized M Estimates For Autoregressive Moving‐Average Models

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  • Hector Allende
  • Siegfried Heiler

Abstract

. Outliers in time series seriously affect conventional parameter estimates. In this paper a robust recursive estimation procedure for the parameters of auto‐regressve moving‐average models with additive outliers is proposed. Using ‘cleaned’ residuals from an initial robust fit of an autoregression of high order as input, bounded influence regression is applied recursively. The proposal follows certain ideas of Hannan and Rissanen, who suggested a three‐stage procedure for order and parameter estimation in a conventional setting. A Monte Carlo study is performed to investigate the robustness properties of the proposed class of estimates and to compare them with various other suggestions, including least squares, M estimates, residual autocovariance and truncated residual autocovariance estimates. The results show that the recursive generalized M estimates compare favourably with them. Finally, possible modifications to master even vigourous situations are suggested.

Suggested Citation

  • Hector Allende & Siegfried Heiler, 1992. "Recursive Generalized M Estimates For Autoregressive Moving‐Average Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(1), pages 1-18, January.
    • Handle: RePEc:bla:jtsera:v:13:y:1992:i:1:p:1-18
    DOI: 10.1111/j.1467-9892.1992.tb00091.x
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    Cited by:

    1. R. H. Glendinning, 2000. "Estimating the Inverse Autocorrelation Function from Outlier Contaminated Data," Computational Statistics, Springer, vol. 15(4), pages 541-565, December.
    2. Jean-Marie Dufour & Tarek Jouini, 2011. "Asymptotic Distributions for Some Quasi-Efficient Estimators in Echelon VARMA Models," CIRANO Working Papers 2011s-25, CIRANO.
    3. Lucas, Andre, 1995. "An outlier robust unit root test with an application to the extended Nelson-Plosser data," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 153-173.
    4. H. Glendinning, Richard, 2001. "Selecting sub-set autoregressions from outlier contaminated data," Computational Statistics & Data Analysis, Elsevier, vol. 36(2), pages 179-207, April.
    5. Hella, Heikki, 2003. "On robust ESACF identification of mixed ARIMA models," Bank of Finland Scientific Monographs, Bank of Finland, volume 0, number sm2003_027, July.

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