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

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.