Fractional Processes with Long-range Dependence
نویسنده
چکیده
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-estimate of the difference between the finite and infinite past predictor coefficients.
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