M-Estimate for the stationary hyperbolic GARCH models

摘要

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.