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M-Estimate for the stationary hyperbolic GARCH models

Author

Listed:
  • Lanciné Bamba

    (Institut National Polytechnique Félix Houphouët-Boigny)

  • Ouagnina Hili

    (Institut National Polytechnique Félix Houphouët-Boigny)

  • Abdou Kâ Diongue

    (Université Gaston Berger de Saint-Louis)

  • Assi N’Guessan

    (Université de Lille)

Abstract

In this manuscrit, we propose two classes of M-estimates for the hyperbolic GARCH models. The first class called M-estimate is defined by minimizing of a convenient bounded loss function. The second, called BM-estimate is a modified version of the first with a mechanism that limits the propagation of the effect of outliers in the conditional variance. The asymptotic properties of these classes of M-estimates are established. According to the Monte Carlo study, we compare the performance of the M and BM-estimates with that of the quasi-maximum likelihood (QML) estimate. We show that the proposed M and BM-estimates are less affected by outliers than the QML-estimate. Moreover, in the last part, an empirical example indicates that the studied M-estimate is the best for the out-of-sample forecasting.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metron:v:79:y:2021:i:3:d:10.1007_s40300-021-00221-w
    DOI: 10.1007/s40300-021-00221-w
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    References listed on IDEAS

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