Fractional Processes with Long-range Dependence

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. We apply the formulas to prove an analogue of Baxter's inequality, which concerns the L^1-estimate of the difference between the finite and infinite past predictor coefficients.