On the Use of the Kolmogorov–Wiener Filter for Heavy-tail Process Prediction

Abstract

This paper is devoted to the investigation of the applicability of the Kolmogorov–Wiener filter to the prediction of heavy-tail processes. As is known, telecommunication traffic in systems with data packet transfer is considered to be a heavy-tail process. There are a lot of rather sophisticated approaches to traffic prediction; however, in the rather simple case of stationary traffic sophisticated approaches may not be needed, and a simple approach, such as the Kolmogorov–Wiener filter, may be applied. However, as far as we know, this approach has not been considered in recent papers. In our previous papers, we theoretically developed a method for obtaining the filter weight function in the continuous case. The Kolmogorov–Wiener filter may be applied only to stationary processes, but in some models telecommunication traffic is treated as a stationary process, and thus the use of the Kolmogorov–Wiener filter may be of practical interest. In this paper, we generate stationary heavy-tail modeled data similar to fractional Gaussian noise and investigate the applicability of the Kolmogorov–Wiener filter to data prediction. Both non-smoothed and smoothed processes are investigated. It is shown that both the discrete and the continuous Kolmogorov–Wiener filter may be used in a rather accurate short-term prediction of a heavy-tail smoothed stationary random process. The paper results may be used for stationary telecommunication traffic prediction in systems with packet data transfer.