A comparative analysis of the effectiveness of prediction using PRT and RIA approaches, using, respectively, exclusively the linear component of long-term memory and, along with the linear, non-linear component, is given. The noise immunity of prediction is considered in both approaches in the presence of ad-ditive noise with a normal or uniform distribution.
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Abdullayev, N. T. , Dyshin, O. A. , Ibrahimova, I. D. and Ahmadova, K. R. (2019). Analysis of the Noise Immunity of Emission Prediction in the Dynamics of the Heartbeat Using Information about Short-Term and Long-Term Dependencies. Open Access Library Journal, 6, e5888. doi: http://dx.doi.org/10.4236/oalib.1105888.
Bogachev, M.I. (2008) Statistical Analysis and Prediction of the Dynamics of Random Processes in Telecommunication Networks Using Multifractal Traffic Models. Radio Elektronika, No. 2, 34-45.
Bogachev, M.I. (2009) On the Issue of Predictability of Emissions of Dynamic Series with Fractal Properties When Using Information about the Linear and Nonlinear Components of the Long-Term Dependence. Radio Electronics, No. 5, 31-40.
Bogachev, M.I. (2010) Comparative Analysis of Noise Immunity of Methods for Predicting Emissions of Random Signals with Fractal Properties When Using Information about Short-Term and Long-Term Dependencies. News of Russian Universities, No. 1, 11-21.
Bogachev, M.I. and Bunde, A. (2011) On the Predictability of Extreme Events in Record with Linear and Nonlinear Long-Range Memory. Physica A, 390, 2240-2250. https://doi.org/10.1016/j.physa.2011.02.024
Bogachev, M.I. and Markelov, O.A. (2012) Noise Immunity of Forecasting of Emissions of Time Series with Long-Term Dependence. News of Russian Universities, No. 5, 15-19.
Bogachev, M.I., Eichner, J.F. and Bunde, A. (2007) Effect of Nonlinear Correlations of the Statistic of Return Intervals in Multifractal Data Sets. Physical Review Letters, 99, 240601-240604. https://doi.org/10.1103/PhysRevLett.99.240601
Bogachev, M.I., Kireenkov, I.S., Nifontov, E. and Bunde, A. (2009) Statistics of Return Intervals between Long Heartbeat Intervals and Their Usability for Online Prediction of Disorders. New Journal of Physics, 11, Article ID: 063036. https://doi.org/10.1088/1367-2630/11/6/063036
Kantelhardt, J.W., Zschiegner, S.A., Koscielny-Bunde, E., Halvin, S., Bunde, A. and Stanley, H.E. (2002) Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series. Physica A: Statistical Mechanics and Its Applications, 316, 87-114. https://doi.org/10.1016/S0378-4371(02)01383-3
Hennig, F., Maass, P.J., Hayano, J. and Heinrichs, S. (2006) Exponential Distribution of Long Heart Beat Intervals during Atrial Fibrillation and Their Relevance for White Noise Behavior in Power Spectrum. Journal of Biological Physics, 32, 383-392. https://doi.org/10.1007/s10867-006-9022-z
Adler, R.J., Feldman, R.E. and Taqqu, M.S. (1998) Practical Guide to Heavy Tails: Statistical Techniques and Applications. Brikhauser, Boston, MA, 534 p.
Barford, P. and Crovella, M. (1998) Generating Representative Web Workloads for Network and Server Performance Evaluation. Proceedings of the 1998 ACM SIGMETRICS Joint International Conference on Measurement and Modeling of Computer Systems, Madison, WI, 22-26 June 1998, 151-160. https://doi.org/10.1145/277858.277897
Bunde, A., Eichner, J., Halvin, S. and Kantelhardt, J.W. (2004) Return Intervals of Rare Events in Records with Long-Term Persistence. Physica A, 342, 308-314. https://doi.org/10.1016/j.physa.2004.01.069
Bogachev, M.I., Eichner, J.F. and Bunde, A. (2008) The Effects of Multifractality on the Statistics of Return Intervals. The European Physical Journal Special Topics, 61, 181-193. https://doi.org/10.1140/epjst/e2008-00760-5
Bogachev, M.I., Eichner, J.F. and Bunde, A. (2008) On the Occurrence of Extreme Events in long-term Correlated and Multifractal Data Sets. Pure and Applied Geophysics, 165, 1195-2007. https://doi.org/10.1007/s00024-008-0353-5
Hallerberg, S., Altmann, E.G., Holstein, D. and Kantz, H. (2007) Precursors of Extreme Increments. Physical Review E, 75, Article ID: 016706. http://arxiv.orq/pdf/phesics0604167 https://doi.org/10.1103/PhysRevE.75.016706
Hallerberg, S. and Kantz, H. (2008) Influence of the Event Magnitude on the Predictability of an Extreme Event. Physical Review E, 77, Article ID: 011108. https://doi.org/10.1103/PhysRevE.78.029902