FRACTIONAL-INTEGRATION AND INTERVAL PREDICTION

The motivation for fractional integration in terms of low-frequency sp ectral behavior and long-lag autocorrelation behavior is well known. U sing results on the rate of growth of variances of sums of integrated random variables, we provide additional and complementary time-domain motivation for fractional integration in terms of the long-horizon beh avior of (1) the variance-time function, and (2) confidence intervals for predictions. The results are illustrated with an empirical applica tion to real interest rate forecasting.