Application of Exponential Smoothing Models and Arima Models in Time Series Analysis from Telco Area

DOI 10.7160/aol.2019.110307
No 3/2019, September
pp. 73-84

Köppelová, J. and Jindrová, A. (2019) “Application of Exponential Smoothing Models and Arima Models in Time Series Analysis from Telco Area", AGRIS on-line Papers in Economics and Informatics, Vol. 11, No. 3, pp. 73-84. ISSN 1804-1930. DOI 10.7160/aol.2019.110307.


The use of ICT has been steadily increasing in both business and social life. Apparently, the most essential communication technology today is a mobile phone. However, the use of mobile phones also has its downside, which is their impact on the environment, which is not negligible. Despite the negative impact on the environment, few of us can imagine a life without a mobile phone. The mobile telecommunications market is one of the most important sectors of the modern economy. Analysing past developments - as well as predicting future developments - of indicators in this area plays a very important role in decision making, as in any other area of the national economy. The extrapolation methods have been the most often applied methods in the area of time series analysis and forecasting in practice. Currently, the combined methods in time series forecasting is more and more favoured. The main aim of this paper is an examination of applicability of the Box-Jenkins methodology models and the exponential smoothing models for providing extrapolation forecasts, but for past development modelling of selected indicators from the telecom area, too. Information on the indicators under study was collected on monthly and daily basis. Quality of the models selected was then assessed using the MAPE and AIC metric. In conclusion, a comparative analysis was performed of both the groups of models. The best individual models were further aggregated and quality of these was assessed using the same assessment criteria. SAS statistical system was applied for effective implementation of the analysis. The research has demonstrated that the exponential smoothing models can only be recommended for the analysis of indicators under study from the mobile telecom area. The detailed analysis has proved, anyway, a higher level of success with the combined models.


ICT and environment, ICT and sustainable rural development, mobile telco services; time series; exponential smoothing models; Box-Jenkins methodology; combined models


  1. Bastianin, A., Galeotti, M., and Manera, M. (2016) "Statistical and Economic Evaluation of Time Series Models for Forecasting Arrivals at Call Centers". [Online]. Working Papers, 2017, Vol. 6., pp. 1–26. [Online]. Available: cgi?article=2188&context=feem. [Accessed: 15 April 2019].
  2. Billah, B., King, M. L., Snyder, R. D. and Koehler, A. B. (2006) "Exponential smoothing model selection for forecasting", International Journal of Forecasting, Vol. 22, No. 2, pp. 239-247. ISSN 0169-2070. DOI 10.1016/j.ijforecast.2005.08.002.
  3. Bolin, D., Guttorp, P., Januzzi, A., Jones, D., Novak, M., Podschwit, H., Richardson, L., Sé, A., Sowder, C. and Zimmerman, A. (2015) "Statistical prediction of global sea level from global temperature", Statistica Sinica, pp. 351-367. ISSN 10170405. DOI 10.5705/ss.2013.222w.
  4. Bozdogan, H. (2000) "Akaike's Information Criterion and Recent Developments in Information Complexity", Journal Of Mathematical Psychology, Vol 44, No. 4, pp. 62-91. ISSN 0022-2496. DOI 10.1006/jmps.1999.1277.
  5. Cipra, T. (1986) "Analýza časových řad s aplikacemi v ekonomii" (in Czech), 1st ed., Prague, SNTL/Alfa, textbook.
  6. Cipra, T. (1992) "Robust exponential smoothing", Journal of Forecasting, Vol. 11, No. 1, pp. 57-69. ISSN 0169-2070. DOI 10.1002/for.3980110106.
  7. Corberán-Vallet, A., Bermúdez, J. D. and Vercher, E. (2011) "Forecasting correlated time series with exponential smoothing models", International Journal of Forecasting, Vol. 27, No. 2, pp. 252-265. ISSN 0169-2070. DOI 10.1016/j.ijforecast.2010.06.003.
  8. Deb, Ch., Zhang, F., Yang, J., Lee, S. E. and Shah, K. W. (2017) "A review on time series forecasting techniques for building energy consumption", Renewable and Sustainable Energy Reviews, Vol. 74, pp. 902-924. ISSN 1364-0321. DOI 10.1016/j.rser.2017.02.085.
  9. Fildes, R., Hibon, M., Makridakis, S. and Meade, N. (1998) "Generalising about univariate forecasting methods: further empirical evidence", International Journal of Forecasting, Vol. 14, No. 3, pp. 339-358. ISSN 0169-2070. DOI 10.1016/S0169-2070(98)00009-0.
  10. Findley, D. F. (2005) "Asymptotic second moment properties of out-of-sample forecast errors of misspecified regARIMA models and the optimality of GLS", Statistica Sinica, pp. 447-476. ISSN 10170405.
  11. Gardner, E. S. (2006) "Exponential smoothing: The state of the art–Part II", International Journal of Forecasting, Vol. 22, No. 4, pp. 637-666. ISSN 0169-2070. DOI 10.1016/j.ijforecast.2006.03.005.
  12. Gardner, E. S. and Diaz-Saiz, J. (2008) "Exponential smoothing in the telecommunications data", International Journal of Forecasting, Vol. 24, No. 1, pp. 170-174. ISSN 0169-2070. DOI 10.1016/j.ijforecast.2007.05.002.
  13. Gelper, S., Fried, R. and Croux, C. (2010) "Robust forecasting with exponential and Holt–Winters smoothing", Journal of forecasting, Vol. 29, No. 3, pp. 285-300. E-ISSN 1099-131X. DOI 10.2139/ssrn.1089403.
  14. Ghosh, H. and Paul, R. K. (2010) "Functional coefficient autoregressive nonlinear time-series model for forecasting Indian lac export data", Model assisted statistics and applications, Vol. 5, No. 2, pp. 101-108. E.ISSN 1875-9068, ISSN 1574-1699. DOI 10.3233/MAS-2010-0147.
  15. Guo, J., Peng, Y., Peng, X., Chen, Q., Yu, J. and Dai, Y. (2009) "Traffic forecasting for mobile networks with multiplicative seasonal arima models", Electronic Measurement & Instruments, 2009, ICEMI'09, 9th International Conference, pp. 3–377, IEEE. DOI 10.1109/ICEMI.2009.5274287.
  16. Hilas, C. S., Goudos, S. K. and Sahalos, J. N. (2006) "Seasonal decomposition and forecasting of telecommunication data: A comparative case study", Technological Forecasting and Social Change, Vol. 73, No. 5, pp. 495-509. ISSN 0040-1625.DOI 10.1016/j.techfore.2005.07.002
  17. Hindls, R., Hronová, S. and Novák, I. (2000) "Metody statistické analýzy pro ekonomy" (in Czech), Management press, 1st ed., 249 p. ISBN 80-85943-44-1.
  18. Hloušková, Z., Ženíšková, P. and Prášilová, M. (2018) "Comparison of Agricultural Costs Prediction Approaches", Agris On-Line Papers in Economics and Informatics, Vol. 10, No. 1, pp. 3-13. ISSN 1804-1930. DOI 10.7160/aol.2018.100101.
  19. Christodoulos, C., Michalakelis, C. and Varoutas, D. (2010) "Forecasting with limited data: Combining ARIMA and diffusion models", Technological Forecasting and Social Change, Vol. 77, No. 4, pp. 558-565. ISSN 0040-1625. DOI 10.1016/j.techfore.2010.01.009.
  20. Christodoulos, Ch., Michalakelis, CH. and Varoutas, D. (2011) "On the combination of exponential smoothing and diffusion forecasts: An application to broadband diffusion in the OECD area", Technological Forecasting and Social Change, Vol. 78, No. 1, pp. 163-170. ISSN 0040-1625. DOI 10.1016/j.techfore.2010.08.007.
  21. Lim, J., Nama, Ch., Kim S., Rhee, H., Lee, E. and Lee, H. (2012) "Forecasting 3G mobile subscriptionin China: A study based on stochastic frontier analysis and a Bass diffusion model", Telecommunications Policy, Vol. 36, pp. 858-871. ISSN 0308-5961. DOI 10.1016/j.telpol.2012.07.016.
  22. Mabert, V. A. (1985) "Short interval forecasting of emergency phone call (911) work loads", Journal of Operations Management, Vol. 5, No. 3, pp. 259-271. ISSN 0272-6963. DOI 10.1016/0272-6963(85)90013-0.
  23. Madden, G. and Tan, J. (2007) "Forecasting telecommunications data with linear models", Telecommunications Policy, Vol. 31, No. 1, pp. 31-44. ISSN 0308-5961. DOI 10.1016/j.telpol.2006.11.004.
  24. Mastorocostas, P. and Hilas, C. (2012) "A computational intelligence-based forecasting system for telecommunications time series", Engineering Applications of Artificial Intelligence, Vol. 25, No. 1, pp. 200-2006. ISSN 0952-1976. DOI 10.1016/j.engappai.2011.04.004.
  25. Mastorocostas, P. and Hilas, C. (2014) "SCOLS-FuM: A Hybrid Fuzzy Modeling Method for Telecommunications Time-Series Forecasting", Informatica, Vol. 25, No. 2, pp. 221-239. E-ISSN 1822-8844, ISSN 0868-4952.
  26. Mirzavand, M. and Ghazavi, R. (2015) "A stochastic modelling technique for groundwater level forecasting in an arid environment using time series methods", Water resources management, Vol. 29, No. 4, pp.1315-1328. E-ISSN 09204741, ISSN 15731650. DOI 10.1007/s11269-014-0875-9.
  27. Murat, M., Malinowska, I., Hoffmann, H. and Baranowski, P. (2016) "Statistical modelling of agrometeorological time series by exponential smoothing", International Agrophysics, Vol. 30, No. 1, pp. 57-65. ISSN 23008725. DOI 10.1515/intag-2015-0076.
  28. Nimesh, R., Arora, S., Mahajan, K. K. and Gill, A. N. (2014) "Predicting air quality using ARIMA, ARFIMA and HW smoothing", Model Assisted Statistics and Applications, Vol. 9, No. 2, pp. 137–149. E-ISSN 1875-9068, ISSN 1574-1699. DOI 10.3233/mas-130285.
  29. Papic-Blagojevic, N., Vujko, A. and Gajic, T. (2016) "Comparative analysis of exponentials smoothing models to tourists’ aarivals in Serbia, Ekonomika Poljoprivrede, Vol. 63, No. 3, pp. 835-845. E-ISSN 2334-8453, ISSN 0352-3462. DOI 10.5937/ekopolj1603835p.
  30. Rafiy, M., Ernawati, Adam, P. and Rostin (2016) “The Demand of Services for Information Technology Industry in Indonesia", AGRIS on-line Papers in Economics and Informatics, Vol. 8, No. 4, pp. 125 - 132. ISSN 1804-1930. DOI 10.7160/aol.2016.080411.
  31. Seger, J. and Hindls, R. (1993) "Statistické metody v ekonomii" (In Czech) 1st ed., Prague H+H, 445 p. ISBN 80-85787-26-1.
  32. Svatošová, L. and Köppelová, J. (2017) “The Use of Combined Models in the Construction of Foodstuffs Consumption Forecasting in the Czech Republic", AGRIS on-line Papers in Economics and Informatics, Vol. 9, No. 4, pp. 81-89. ISSN 1804-1930. DOI 10.7160/aol.2017.090408.
  33. Sbrana, G. and Silvestrini, A. (2014) "Random switching exponential smoothing and inventory forecasting", International Journal of Production Economics, Vol. 156, pp. 283-294. ISSN 0925-5273. DOI 10.1016/j.ijpe.2014.06.016.
  34. Tavakkoli, A., Hemmasi, A. H., Talaeipour, M., Bazyar, B. and Tajdini, B. (2015) "Forecasting of Particleboard Consumption in Iran Using Univariate Time Series Models", Bio Resources, Vol. 10, No. 2, pp. 2032–2043. ISSN 1930-2126.
  35. Wei, X. and Yang, Y. (2012) "Robust combination of model selection methods for prediction", Statistica Sinica, Vol. 22, No. 3, pp. 1021-1040. E-ISSN 19968507, ISSN 10170405. DOI 10.5705/ss.2010.023.

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