On the Predictability of Long‐Range Dependent Series

This paper points out that the predictability analysis of conventional time series may in general be invalid for long‐range dependent (LRD) series since the conventional mean‐square error (MSE) may generally not exist for predicting LRD series. To make the MSE of LRD series prediction exist, we introduce a generalized MSE. With that, the proof of the predictability of LRD series is presented in Hilbert space.