M-Quantile Estimation for GARCH Models

M-regression and quantile methods have been suggested to estimate generalized autoregressive conditionally heteroscedastic (GARCH) models. In this paper, we propose an M-quantile approach, which combines quantile and M-regression to obtain a robust estimator of the conditional volatility when the data have abrupt observations or heavy-tailed distributions. Monte Carlo experiments are conducted to show that the M-quantile approach is more resistant against additive outliers than M-regression and quantile methods. The usefulness of the method is illustrated on two financial datasets.