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Robust estimates for arch processes

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  • NORA MULER
  • VICTOR J. YOHAI

Abstract

In this paper, we present two robust estimates for ARCH(p) models: τ ‐ and filtered τ‐estimates. These are defined by the minimization of conveniently robustified likelihood functions. The robustification is achieved by replacing the mean square error of the standardized observations with the square of a robust τ‐scale estimate in the reduced form of the Gaussian likelihood function. The robust filtering procedure avoids the propagation of the effect of one outlier on subsequent conditional variances. A Monte‐Carlo study shows that the maximum likelihood estimate practically collapses when there is only a small percentage of outlier contamination, while both robust estimates perform much better.

Suggested Citation

  • Nora Muler & Victor J. Yohai, 2002. "Robust estimates for arch processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(3), pages 341-375, May.
    • Handle: RePEc:bla:jtsera:v:23:y:2002:i:3:p:341-375
    DOI: 10.1111/1467-9892.00268
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    Cited by:

    1. Andrea Bergesio & María Eugenia Szretter Noste & Víctor J. Yohai, 2021. "A robust proposal of estimation for the sufficient dimension reduction problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 758-783, September.
    2. Salibian-Barrera, Matias & Van Aelst, Stefan & Yohai, Víctor J., 2016. "Robust tests for linear regression models based on τ-estimates," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 436-455.
    3. Maronna, Ricardo A. & Yohai, Victor J., 2017. "Robust and efficient estimation of multivariate scatter and location," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 64-75.
    4. Boudt, Kris & Croux, Christophe, 2010. "Robust M-estimation of multivariate GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2459-2469, November.
    5. Sonja Rieder, 2012. "Robust parameter estimation for the Ornstein–Uhlenbeck process," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(4), pages 411-436, November.
    6. L. Grossi & G. Morelli, 2006. "Robust volatility forecasts and model selection in financial time series," Economics Department Working Papers 2006-SE02, Department of Economics, Parma University (Italy).
    7. Stella Kitromilidou & Konstantinos Fokianos, 2016. "Mallows’ quasi-likelihood estimation for log-linear Poisson autoregressions," Statistical Inference for Stochastic Processes, Springer, vol. 19(3), pages 337-361, October.
    8. M. Angeles Carnero & Daniel Peña & Esther Ruiz, 2004. "Spurious And Hidden Volatility," Working Papers. Serie AD 2004-45, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    9. Duchesne, Pierre, 2004. "On robust testing for conditional heteroscedasticity in time series models," Computational Statistics & Data Analysis, Elsevier, vol. 46(2), pages 227-256, June.
    10. Lanciné Bamba & Ouagnina Hili & Abdou Kâ Diongue & Assi N’Guessan, 2021. "M-Estimate for the stationary hyperbolic GARCH models," METRON, Springer;Sapienza Università di Roma, vol. 79(3), pages 303-351, December.
    11. M. Angeles Carnero & Daniel Peña & Esther Ruiz, 2008. "Estimating and Forecasting GARCH Volatility in the Presence of Outiers," Working Papers. Serie AD 2008-13, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).

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