Estimation of Volatility on the Small Sample with Generalized Maximum Entropy

Abstract

Generalized autoregressive conditional heteroscedasticity (GARCH) provides useful techniques for modeling the dynamic volatility model. Several estimation techniques have been developed over the years, for examples Maximum likelihood, Bayesian, and Entropy. Among these, entropy can be considered an efficient tool for estimating GARCH model since it does not require any distribution assumptions which must be given in Maximum likelihood and Bayesian estimators. Moreover, we address the problem of estimating GARCH model characterized by ill-posed features. We introduce a GARCH framework based on the Generalized Maximum Entropy (GME) estimation method. Finally, in order to better highlight some characteristics of the proposed method, we perform a Monte Carlo experiment and we analyze a real case study. The results show that entropy estimator is successful in estimating the parameters in GARCH model and the estimated parameters are close to the true values.