Repetitive Stochastic Guesstimation for Estimating Parameters in a GARCH(1,1) Model

A behavioral algorithm for optimization - Repetitive Stochastic Guesstimation (RSG) - is adapted, with complete proofs for its global convergence, for estimating parameters in a GARCH(1,1) model, based on a very small number of observations. Estimators delivered by this algorithm for the example of a GARCH(1,1) model are dependent on some computational capabilities - namely number of iterations and replications performed. In this context, the Large Numbers Law might be applied in a completely different dimension. An alternative toward waiting until the historical data series are recorded (while the underling process may change several times) is to use computers for correctly extracting information from the most recent data. Given the existent computational support, it is also possible to determine estimates for the rates of convergence. As a result, potential benefits of this econometric technique can be gained in case of very young financial markets from Eastern European countries. Also, prediction and political decisions based on these estimations are properly grounded.