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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:
62M20Prediction; filtering (statistics)
62M10Time series, auto-correlation, regression, etc. (statistics)
46N30Applications of functional analysis in probability theory and statistics