Forecasting high-frequency financial data with the ARFIMA-ARCH model

Financial data series are often described as exhibiting two non-standard ti me series features. First, variance often changes over time, with alternati ng phases of high and low volatility. Such behaviour is well captured by AR CH models. Second, long memory may cause a slower decay of the autocorrelat ion function than would be implied by ARMA models. Fractionally integrated models have been offered as explanations. Recently, the ARFIMA-ARCH model c lass has been suggested as a way of coping with both phenomena simultaneous ly. For estimation we implement the bias correction of Cox and Reid (1987). For daily data on the Swiss 1-month Euromarket interest rate during the pe riod 1986-1989, the ARFIMA-ARCH (5,d,2/4) model with non-integer d is selec ted by AIC. Model-based out-of-sample forecasts for the mean are better tha n predictions based on conditionally homoscedastic white noise only for lon ger horizons (tau > 40). Regarding volatility forecasts, however, the selec ted ARFIMA-ARCH models dominate. Copyright (C) 2001 John Wiley & Sons, Ltd.