FRACTIONAL PROCESSES WITH LONG-RANGE DEPENDENCE

Abstract. We introduce a class of Gaussian processes with stationary in-crements which exhibit long-range dependence. The class includes fractional Brownian motion with Hurst parameter H> 1/2 as a typical example. We es-tablish 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 inequal-ity, which concerns the L1-estimate of the difference between the finite and infinite past predictor coefficients. 1