  The autocorrelation function of volatility in financial time series is fitted
well by a superposition of several exponents. Such a case admits an explicit
analytical solution of the problem of constructing the best linear forecast of
a stationary stochastic process. We describe and apply the proposed analytical
method for forecasting volatility. The leverage effect and volatility
clustering are taken into account. Parameters of the predictor function are
determined numerically for the Dow Jones 30 Industrial Average. Connection of
the proposed method to the popular ARCH models is discussed.
