Fractional integration and interval prediction

The motivation for fractional integration in terms of low-frequency spectral behavior and long-lag auto-correlation behavior is well known. Using 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 behavior of (1) the variance-time function, and (2) confidence intervals for predictions. The results are illustrated with an empirical application to real interest rate forecasting.