Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 397454, 9 pages
doi:10.1155/2010/397454
Research Article

On the Predictability of Long-Range Dependent Series

Ming Li1 and Jia-Yue Li2

1School of Information Science & Technology, East China Normal University, Dong-Chuan Road no. 500, Shanghai 200241, China
2Key Laboratory of Geographical Information Science, Ministry of Education of China; School of Resources and Environment Science, East China Normal University, Shanghai 200062, China

Received 23 January 2010; Accepted 7 February 2010

Academic Editor: Cristian Toma

Copyright © 2010 Ming Li and Jia-Yue Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.