A New Robust Estimation Method for GARCH Models and Its Algorithmic Implementation

The maximum likelihood estimation (MLE) method is widely used for parameter estimation in GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models in time series analysis. However, its lack of robustness often results in discrepancies between model analysis results and real-world situations. To address this issue, this paper introduces a Robust Weighted Maximum Likelihood Estimation (RWMLE) method based on two key principles: Firstly, inspired by the 3-sigma rule in quality control, the Andrews weighting function is robustly modified to fully exploit information from the original observations. This modification aims to enhance the robustness of the estimation process. Secondly, the modified Andrews weighting function is applied to transform the original series, which is then utilized in the maximum likelihood estimation of GARCH model parameters. Simulation experiments and financial case analyses demonstrate that under uncontaminated data, the results of the traditional maximum likelihood estimation method are essentially consistent with those of the robust weighted maximum likelihood estimation method. However, in the presence of contamination, as the contamination rate increases, the results obtained from the traditional maximum likelihood estimation become unrecognizable, while the robust weighted maximum likelihood estimation exhibits only minor changes. The conclusions drawn from this study can be applied to the volatility modeling of financial assets that contain outliers.