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M-estimators of some GARCH-type models; computation and application

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Abstract

In this paper, we consider robust M-estimation of time series models with both symmetric and asymmetric forms of heteroscedasticity related to the GARCH and GJR models. The class of estimators includes least absolute deviation (LAD), Huber’s, Cauchy and B-estimator as well as the well-known quasi maximum likelihood estimator (QMLE). Extensive simulations are used to check the relative performance of these estimators in both models and the weighted resampling methods are used to approximate the sampling distribution of M-estimators. Our study indicates that there are estimators that can perform better than QMLE and even outperform robust estimator such as LAD when the error distribution is heavy-tailed. These estimators are also applied to real data sets.

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Authors and Affiliations

  1. Dept. of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK

    Farhat Iqbal & Kanchan Mukherjee

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  1. Farhat Iqbal
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  2. Kanchan Mukherjee
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Correspondence to Kanchan Mukherjee.

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Iqbal, F., Mukherjee, K. M-estimators of some GARCH-type models; computation and application. Stat Comput 20, 435–445 (2010). https://doi.org/10.1007/s11222-009-9135-x

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  • DOI: https://doi.org/10.1007/s11222-009-9135-x

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