Prediction of Fractional Processes with Long-range Dependence

TL;DR

This paper introduces a new class of Gaussian processes with long-range dependence, providing explicit prediction formulas, including for fractional Brownian motion, enhancing understanding of their predictability.

Contribution

It defines a new class of Gaussian processes with stationary increments and long-range dependence, offering explicit prediction formulas in terms of MA and AR coefficients.

Findings

Explicit prediction formulas for the new class of processes.

Inclusion of fractional Brownian motion as a special case.

Enhanced understanding of long-range dependence in Gaussian processes.

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.