Robust and efficient estimation of GARCH models based on Hellinger distance

Area of Science:

• Econometrics
• Financial Statistics
• Statistical Modeling

Background:

• Financial data often exhibit outliers, compromising standard GARCH model estimation.
• Likelihood-based GARCH estimators are typically non-robust to these outlying observations.
• Minimum distance methods offer a robust alternative but are underexplored for GARCH models.

Purpose of the Study:

• To propose and investigate novel robust estimators for GARCH models using the minimum Hellinger distance.
• To introduce a minimum profile Hellinger distance estimator (MPHDE) for situations with unspecified innovation distributions.
• To assess the robustness and efficiency of these new estimators compared to existing methods.

Main Methods:

• Development of a minimum Hellinger distance estimator (MHDE) for GARCH parameter estimation.
• Construction of a minimum profile Hellinger distance estimator (MPHDE) for GARCH models.
• Theoretical analysis including proof of consistency and bias derivation for MHDE.
• Finite-sample performance evaluation via simulation studies.

Main Results:

• The proposed MHDE and MPHDE demonstrate superior performance compared to Maximum Likelihood Estimation (MLE)-based methods when financial data contain outliers.
• MHDE and MPHDE maintain competitive efficiency in clean data scenarios.
• The estimators exhibit robustness and efficiency, outperforming traditional MLE, Gaussian Quasi-MLE, Non-Gaussian Quasi-MLE, and Least Absolute Deviation estimators in contaminated data.

Conclusions:

• The minimum Hellinger distance estimators (MHDE and MPHDE) provide a robust and efficient alternative for estimating GARCH models, particularly in the presence of financial data outliers.
• These novel estimators address the limitations of traditional likelihood-based methods in handling contaminated data.
• The findings support the practical utility of MHD-type estimations in robust financial time series analysis.