M-Estimate for the stationary hyperbolic GARCH models

Lanciné Bamba (), Ouagnina Hili (), Abdou Ka Diongue and Assi N’Guessan ()
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Lanciné Bamba: Institut National Polytechnique Félix Houphouët-Boigny
Ouagnina Hili: Institut National Polytechnique Félix Houphouët-Boigny
Assi N’Guessan: Université de Lille

METRON, 2021, vol. 79, issue 3, No 4, 303-351

Abstract: 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.

Keywords: ARCH ( $$\infty $$ ∞; Long memory in volatility; M-estimate; BM-estimate; Outliers; 62M10; 62F12 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s40300-021-00221-w

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