ON THE CONTINUOUS KOLMOGOROV–WIENER FILTER FOR PREDICTION OF MODELED SMOOTHED HEAVY-TAIL PROCESS
DOI:
https://doi.org/10.32782/IT/2023-1-2Keywords:
continuous Kolmogorov–Wiener filter, prediction, heavy-tail data, Walsh functions, fractional Gaussian noise, time shiftAbstract
The telecommunication traffic nowadays is treated as a heavy-tail random process. The traffic prediction is an important problem for telecommunications. The paper is devoted to the use of the continuous Kolmogorov– Wiener filter for prediction of modeled smoothed heavy-tail process similar to fractional Gaussian noise, which may describe traffic in a simple model. This process is generated on the basis of the symmetric moving average approach with the use of the exponential smoothing algorithm. In our recent paper we investigated the applicability of the use of both discrete and continuous Kolmogorov–Wiener filter for the prediction of the above-described smoothed heavy-tail modeled data. In particular, it was shown that not only discrete, but also continuous Kolmogorov–Wiener filter may be used to the corresponding prediction, but the accuracy of the discrete filter is slightly higher than the accuracy of the continuous one. In fact, as it was seen from the graphs of the actual and predicted processes, the process predicted on the basis of the continuous filter has some time delay in comparison with the actual process. So, it is logical enough to make a time shift of the predicted process in order to delete the corresponding delay. So, in this paper we propose an enhancement of the corresponding algorithm by using an artificially chosen time shift for the predicted process. The aim of the work is to enhance the accuracy of the continuous Kolmogorov–Wiener filter prediction for the smoothed modeled heavy-tail process. The methodology consists in the solving of the Wiener-Hopf integral equation on the basis of the Walsh functions with further use of the time shift for the obtained process. The scientific novelty consists in the enhancement of the corresponding prediction accuracy on the basis of the use of the artificially chosen time shift for the predicted process. The conclusions are as follows. The use of the corresponding time shift allows one to decrease the prediction mean absolute percentage error.
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