Functional modelling of telecommunications data
Abstract
This work deals with statistical modeling and forecasting of telecommunications data. Main mobile traffic events (SMS, Voice calls, Mobile data) are smoothed using B-spline functions and later analyzed in a functional framework. Functional linear auto-regression models are fitted using both bottom-up and topdown design methodologies. The advantages and disadvantages of both approaches for the prediction of mobile telephone users’ habits are discussed.
Keyword : functional data analysis, functional linear regression, telecommunications data, prediction
How to Cite
Birbilas, A., & Račkauskas, A. (2022). Functional modelling of telecommunications data. Mathematical Modelling and Analysis, 27(1), 117–133. https://doi.org/10.3846/mma.2022.14043
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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L. Aspirot, K. Bertin and G. Perera. Asymptotic normality of the Nadaraya – Watson estimator for nonstationary functional data and applications to telecommunications. Journal of Nonparametric Statistics, 21(5):535–551, 2009. https://doi.org/10.1080/10485250902878655
P. Bernard. Analyse de signaux physiologiques. Memoire Univ. Catholique Angers, 1997.
P. Besse and H. Cardot. Approximation spline de la prevision d’un processus fonctionnel autoregressif d’ordre 1. The Canadian Journal of Statistics, 24(4):467–487, 1996. https://doi.org/10.2307/3315328
P. Besse, H. Cardot and D.B. Stephenson. Autoregressive forecasting of some functional climatic variations. Scandinavian Journal of Statistics, 27(4):673–687, 2000. https://doi.org/10.1111/1467-9469.00215
D. Bosq. Linear processes in function spaces: theory and applications, vol. 149. Springer-Verlag New York, 2011. https://doi.org/10.1007/978-1-4612-1154-9
F. Calabrese, Z. Smoreda, V.D. Blondel and C. Ratti. Interplay between telecommunications and face-to-face interactions: A study using mobile phone data. PLOS One, 6(7):1–6, 2011. https://doi.org/10.1371/journal.pone.0020814
A. Cavallini, G.C. Montanari, M. Loggini, O. Lessi and M. Cacciaris. Nonparametric prediction of harmonic levels in electrical networks. Proceed. IEEE ICHPS VI, pp. 165–171, 1994.
P. Craven and G. Wahba. Smoothing noisy data with spline functions. Numerische Mathematik, 31(4):377–403, 1978. https://doi.org/10.1007/BF01404567
J. Damon and S. Guillas. The inclusion of exogenous variables in functional autoregressive ozone forecasting. Environmetrics, 13(7):759–774, 2002. https://doi.org/10.1002/env.527
F. Ferraty and P. Vieu. Nonparametric Functional Data Analysis: Theory and Practice. Springer Series in Statistics Springer, New York, 2006. https://doi.org/10.1007/0-387-36620-2
V.S. Frost and B. Melamed. Traffic modeling for telecommunication networks. IEEE Communications Magazine, 32(3):70–81, 1994. https://doi.org/10.1109/35.267444
D.J. Levitin, R.L. Nuzzo, B.W. Vines and J.O. Ramsay. Introduction to functional data analysis. Canadian Psychology/Psychologie canadienne, 48(3):135– 155, 2007. https://doi.org/10.1037/cp2007014
K.S. Meier-Hellstern, P.E. Wirth, Y. Yan and D.A. Hoeflin. Traffic models for ISDN data users: office automation application. ITC-13, pp. 167–172, 1991. Available from Internet: http://132.187.12.7/fileadmin/ITCBibDatabase/ 1991/meierhellstern911.pdf
F. Özgül, A. Çelik, C. Atzenbeck and N. Gergin. Investigating Terrorist Attacks Using CDR Data: A Case Study. Lecture Notes in Social Networks. Springer, Vienna, 2011. https://doi.org/10.1007/978-3-7091-0388-3_17
J. Ramsay, G. Hooker and S. Graves. Functional Data Analysis with R and MATLAB, 1st Edition. Springer, New York, 2009. https://doi.org/10.1007/978-0-387-98185-7_1
J. Ramsay and B.W. Silverman. Functional Data Analysis, 2nd Edition. Springer Series in Statistics Springer, New York, 2005. https://doi.org/10.1007/b98888
Y. Ben Slimen, S. Allio and J. Jacques. Anomaly prevision in radio access networks using functional data analysis. In GLOBECOM 2017 – 2017 IEEE Global Communications Conference, pp. 1–6, 2017. https://doi.org/10.1109/GLOCOM.2017.8254087
J.L. Wang, J.-M. Chiou and H.-G. Mu¨ller. Functional data analysis. Annual Review of Statistics and Its Application, 3(1):257–295, 2016. https://doi.org/10.1146/annurev-statistics-041715-033624
Y. Yan and D. Lambert. Fitting trees to functional data, with an application to time-of-day patterns. Journal of Computational and Graphical Statistics, 8(4):749–762, 1999. https://doi.org/10.1080/10618600.1999.10474847