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Zbl 1191.62160
Li, Ming; Li, Jia-Yue
On the predictability of long-range dependent series. (English)
[J] Math. Probl. Eng. 2010, Article ID 397454, 9 p. (2010). ISSN 1024-123X; ISSN 1563-5147/e

Summary: 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 a Hilbert space.

MSC 2000:: *62M20 Prediction, etc. (statistics)
62M10 Time series, etc. (statistics)
46N30 Appl. of functional analysis in probability theory and statistics

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