On the choice of a genetic algorithm for estimating GARCH models

The GARCH models have been found difficult to build by classical methods, and several other approaches have been proposed in literature, including metaheuristic and evolutionary ones. In the present paper we employ Genetic Algorithms to estimate the parameters of GARCH(1,1) models, assuming a fixed computational time (measured in number of fitness function evaluations) that is variously allocated in number of generations, number of algorithm restarts and number of chromosomes in the population, in order to gain some indications about the impact of each of these factors on the estimates. Results from this simulation study show that if the main purpose is to reach a high quality solution with no time restrictions the algorithm should not be restarted and an average population size is recommended, while if the interest is focused on driving rapidly to a satisfactory solution then for moderate population sizes it is convenient to restart the algorithm, even if this means to have a small number of generations.