Efficient and Robust Estimation for Financial Returns: An Approach Based on q-Entropy

Abstract

We consider a new robust parametric estimation procedure, which minimizes an empirical version of the Havrda-Charvat-Tsallis entropy. The resulting estimator adapts according to the discrepancy between the data and the assumed model by tuning a single constant q, which controls the trade-o between robustness and eciency. The method is applied to expected re- turn and volatility estimation of financial asset returns under multivariate normality. Theoretical properties, ease of implementability and empirical re- sults on simulated and financial data make it a valid alternative to classic robust estimators and semi-parametric minimum divergence methods based on kernel smoothing.