Estimating a GARCH-M Model by a Non-Parametric Heuristic Method and Its Advantages

The models from the GARCH family are often estimated by maximum likelihood method, either parametrically or non-parametrically. Since the parametric estimation procedure is based on an a priori distribution, its misspecification can lead to the inconsistency of the estimators. Therefore non-parametric approach, in which both model´s parameters and the distribution of error terms are estimated from the data, seems to be a better alternative. In our work, we propose a non-parametric technique with the use of a heuristic called differential evolution to estimate the parameters of a GARCH-M model. This technique can more likely reach to a global solution of maximum likelihood estimation (MLE) task. Further, it can also more effectively control the required properties of the estimates. The suitability of our approach is verified on modeling the CZK/USD and CZK/EURO forward exchange rate premium of period from 2007 to 2012 by a GARCH-M model.