On the use of the continuous wiener filter to generalized fractional gaussian noise

Abstract

The paper is devoted to the investigation of the continuous Kolmogorov–Wiener filter weight function for forecasting of the process described by the generalized fractional Gaussian noise model. Such a model may describe telecommunication traffic, see [1, 2]. Our recent papers were devoted to the corresponding weight function obtaining for the processes in the power-law structure function model [3–5], іn the “usual“ fractional Gaussian noise model [6–8] and in the Gaussian fractional sum-difference model [9]; see also a review in [10]. However, the corresponding investigation for the generalized fractional Gaussian noise model is not yet done. In [11] it is shown, in particular, that the continuous Kolmogorov–Wiener filter may be applied to prediction of smoothed heavy-tail processes. So, the problem under consideration is of interest.