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Prediction of Fractional Brownian Motion-Type Processes

By Akihiko Inoue and Vo V. Anh

Abstract

We introduce a class of continuous-time Gaussian processes with stationary increments via moving-average representation with good MA coefficient. The class includes fractional Brownian motion with Hurst index less than 1/2 as a typical example. It also includes processes which have different indices corresponding to the local and long-time properties, repsectively. We derive some basic properties of the processes, and, using the results, we establish a prediction formula for them. The prediction kernel in the formula is given explicitly in terms of MA and AR coefficients

Topics: 010406 Stochastic Analysis and Modelling, Fractional Brownian motion, Hurst index, Prediction
Publisher: Taylor & Francis
Year: 2007
DOI identifier: 10.1080/07362990701282971
OAI identifier: oai:eprints.qut.edu.au:15029

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