Forecasting High-Frequency Financial Data with the ARFIMA-ARCH Model

Financial data series are often described as exhibiting two non-standard time series features. First, variance often changes over time, with alternating phases of high and low volatility. Such behaviour is well captured by ARCH models. Second, long memory may cause a slower decay of the autocorrelation function than would be implied by ARMA models. Fractionally integrated models have been offered as explanations. Recently, the ARFIMA-ARCH model class has been suggested as a way of coping with both phenomena simultaneously. 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 period 1986-89, the ARFIMA-ARCH (5,d,2/4) model with non-integer d is selected by AIC. Model-based out-of-sample forecasts for the mean are better than predictions based on conditionally homoscedastic white noise only for longer horizons (tau > 40). Regarding volatility forecasts, however, the selected ARFIMA-ARCH models dominate. Copyright © 2001 by John Wiley & Sons, Ltd.