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**On the predictability of long-range dependent series.**
*(English)*
Zbl 1191.62160

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:

62M20 | Inference from stochastic processes and prediction |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

46N30 | Applications of functional analysis in probability theory and statistics |

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\textit{M. Li} and \textit{J.-Y. Li}, Math. Probl. Eng. 2010, Article ID 397454, 9 p. (2010; Zbl 1191.62160)

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