Hokkaido Mathematical Journal

INOUE Akihiko, ANH Vo V.,

Prediction of fractional processes with long-range dependence.

Hokkaido Mathematical Journal, 41 (2012) pp.157-183

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Abstract

We introduce a class of Gaussian processes with stationary increments which exhibit long-range dependence. The class includes fractional Brownian motion with Hurst parameter H > 1/2 as a typical example. We establish infinite and finite past prediction formulas for the processes in which the predictor coefficients are given explicitly in terms of the MA(∞) and AR(∞) coefficients.

MSC(Primary)60G25
MSC(Secondary)60G15
Uncontrolled KeywordsPredictor coefficients, prediction, fractional Brownian motion, long-range dependence