Empirical comparison of Box-Jenkins models, artificial neural network and singular spectrum analysis in forecasting time series. (Persian. English summary) Zbl 1413.91060

Summary: The Box-Jenkins model is applied as a parametric method for time series analysis and fitting seasonal and non-seasonal autoregressive moving average models. But this procedure is not useful for short length and non stationary time series data. To overcome these problems, two nonparametric methods i.e. artificial neural network and singular spectrum analysis are introduced. These procedures do not require any statistical assumptions about normality of errors and could be used for short time series data. In this article, after introducing the above methods, their accuracy in forecasting sales of four types of food products, pharmaceutical and health care of a distribution corporation are compared. Then using simulation studies, the effectiveness of these methods for short-term and long-term predictions are evaluated. The results show the superiority of singular spectrum analysis compared to the other two methods in terms of the root mean square error of forecasting.


91B84 Economic time series analysis
68T05 Learning and adaptive systems in artificial intelligence
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P20 Applications of statistics to economics
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[1] Box, G.E.P., Jenkins, G.M. and Reinsel, G.C. (2008). Time Series Analysis: Forecasting and Control, 4nd ed., Hoboken, New Jersey: John Wiley & Sons. · Zbl 1154.62062
[2] Krose, B. and Smagt, P.V.D. (1996). An Introduction to Neural Networks, 8\^{}{th} ed. University of Amsterdam.
[3] Dunne, R.A. (2007). A Statistical Approach to Neural Networks for Pattern Recognition, Hoboken, New Jersey: John Wiley & Sons. · Zbl 1183.62165
[4] Rao, A.R. and Cecchi, G.A. (eds), (2012). The Relevance of the Time Domain to Neural Network Models, Springer.
[5] Dreyfus, G. (2005). Neural Networks: Methodology and Applications, Springer. · Zbl 1119.92003
[6] Tirozzi, B., Puca, S., Pittalis, S., Bruschi, A., Morucci, S., Ferraro, E. and Corsini, S. (2005). Neural Networks and Sea Time Series: Reconstruction and Extreme-Event Analysis, Boston, Birkhauser. · Zbl 1094.62121
[7] Petridis, V. and Kehagias, A. (1998). Predictive Modular Neural Networks: Applications to Time Series, Springer, New York. · Zbl 0959.93057
[8] Chatfield, C. (2000). Time Series Forecasting, Chapman & Hall/CRC.
[9] Hyndman, R.J. and Khandakar, Y. (2008). Automatic Time Series Forecasting: The forecast Package for R. Journal of Statistical Software, 27 (3), 1-22.
[10] Hyndman, R.J. and Athanasopoulos, G. (2013). Forecasting: principles and practice. Section 9/3. http://otexts.org/fpp/9/3. Accessed on 2016-02-02.
[11] De Prony, G. (1795). Essai expérimental et analytique sur les lois de la dilatabilité des fluids élastiques et sur celles de la force expansive de la vapeur de l’eau et la vapeur de l’alkool à différentes températures. J de l’Ecole Polytechnique. 1(2), 24–76.
[12] Broomhead, D. and King, G. (1986). Extracting qualitative dynamics from experimental data. Physica D, 20, 217–236. · Zbl 0603.58040
[13] Broomhead, D., King, G. (1986b). On the qualitative analysis of experimental dynamical systems. In: Sarkar S (ed) Nonlinear Phenomena and Chaos. Adam Hilger, Bristol, 113–144.
[14] Elsner, J.B. and Tsonis, A.A. (1996). Singular spectrum analysis: a new tool in time series analysis. New York: Springer.
[15] Danilov, D. and Zhigljavsky, A. (Eds), (1997). Principal components of time series: the “Caterpillar” method. St.Petersburg Press, St. Petersburg (in Russian).
[16] Golyandina, N., Nekrutkin V. and Zhigljavsky, A. (2001). Analysis of time series structure: SSA and related techniques, Boca Raton: Chapman and Hall/CRC. · Zbl 0978.62073
[17] Golyandina, N. and Zhigljavsky, A. (2013). Singular Spectrum Analysis for Time Series, London: Springer. · Zbl 1276.62053
[18] Sanei, S. and Hassani, H. (2016). Singular Spectrum Analysis of Biomedical Signals, Taylor & Francis/CRC.
[19] Zhigljavsky, A. (2010). Singular Spectrum Analysis for Time Series: Introduction to this Special Issue, Statistics and Its Interface, 3, 255-258. · Zbl 1245.62114
[20] Hassani, H. (2007). Singular Spectrum Analysis: Methodology and Comparison. Journal of DataScience,5(2), 239–257.
[21] Hassani, H. and Thomakos, D. (2010). A review on Singular Spectrum Analysis for Economic and Financial Time Series, Statistics and Its Interface, 3, 377-397. · Zbl 1245.91078
[22] Mahmoudvand, R.; Alehosseini, F.; Rodrigues, C.P. (2015). Forecasting Mortality Rate by Singular Spectrum Analysis. RevStat-Statistical Journal, 13, 193-206. · Zbl 1369.62280
[23] Mahmoudvand, R. and Rodrigues, P.C. (2016). Missing value imputation in time series using Singular Spectrum Analysis. International Journal of Energy and Statistics, 4 (1), 1650005.
[24] Rodrigues, C.P. and Mahmoudvand, R. (2016). Correlation Analysis in Contaminated Data by Singular Spectrum Analysis. Quality and Reliability Engineering International, 32(6), 2127-2137.
[25] Ghanati, R; Kazemhafizi, M; Mahmoudvand, R. and Fallahsafari, M. (2016). Filtering and parameter estimation of surface-NMR data using singular spectrum analysis. Journal of Applied Geophysics, 130, 118-130.
[26] Hassani, H., Mahmoudvand, R. and Zokaei, M. (2011). Separability and window length in singular spectrum analysis. Comptes Rendus Mathematique, 349 (17–18), 987-990. · Zbl 1232.62122
[27] Mahmoudvand, R. and Zokaei, M. (2012). On the Singular Values of the Hankel Matrix with Application in Singular Spectrum Analysis. Chilean Journal of Statistics, ‎3, 43-56.‎‎
[28] Hassani, H., Webster, A., Silva, E. S. and Heravi, S., (2015). Forecasting U.S. Tourist arrivals using optimal Singular Spectrum Analysis, Tourism Management, 46, 322-335.
[29] Golyandina, N.
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