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Robust Estimation for ARCH Models

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  • Mendes, Beatriz Vaz de Melo
  • Júnior, Antonio Marcos Duarte

Abstract

This article introduces the class of the constrained M-estimators for ARCH models. The new estimators are defined based on the minimization of a bounded function of the squared residuals standardized by a robust scale. Their robustness and efficiency properties are derived. Using Monte Carlo experiments, it is shown that under small percentages of contaminations the robust estimates are still able to capture the dynamics of the process. The robust procedure is used to estimate the volatility of four Brazilian financial series.

Suggested Citation

  • Mendes, Beatriz Vaz de Melo & Júnior, Antonio Marcos Duarte, 1999. "Robust Estimation for ARCH Models," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 19(1), May.
    • Handle: RePEc:sbe:breart:v:19:y:1999:i:1:a:2795
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    Cited by:

    1. Fajardo, José & Farias, Aquiles, 2004. "Generalized Hyperbolic Distributions and Brazilian Data," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 24(2), November.
    2. Reyna, Fernando R. Q. & Júnior, Antonio M. Duarte & Mendes, Beatriz V. M. & Porto, Oscar, 2005. "Optimal Portfolio Structuring in Emerging Stock Markets Using Robust Statistics," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 25(2), November.
    3. Fajardo, J. & Cajueiro, D. O., 2003. "Volatility Estimation and Option Pricing with Fractional Brownian Motion," Finance Lab Working Papers flwp_53, Finance Lab, Insper Instituto de Ensino e Pesquisa.
    4. Barbachan, José Fajardo & Schuschny, Andrés Ricardo & Silva, André de Castro, 2001. "Lévy processes and the Brazilian market," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 21(2), November.

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