Volatility and covariance matrix forecasting is very important area in Financial Economics, since research in this field helped to solve effectively such tasks asset allocation, valuation of various financial instruments, and management of financial risks.
During the last twenty years there was developed a number of forecasting models for volatility and covariance matrix. The accuracy of these forecasting models may be tested using various criteria. All of them may be grouped into two main categories - statistical and operational or economical. Statistical criteria assess the accuracy of the average of probability distribution of forecasts, while operational criteria strive to a .. es the accuracy of tails of probability distribution of forecasts.
Using six time series of main USA dollar exchange rates, covering the period from 23.02.2000 till 08.07.2002, it was empirically tested the accuracy of three forecasting models (BIS, EWMA, and GARCH (1,1) using both statistical and operational criteria. According to statistical criteria the preference should be given to the EWMA model, but according to operational criteria - to BIS and GARCH (1,1) models. Despite that, it was not achieved such level of accuracy that one could state that the accuracy of both forecasting models is very good. So directions for the future research may be the following - using operational criteria to test GARCH models and stochastic models with more sophisticated specifications.