DOI: https://doi.org/10.15587/1729-4061.2014.28172

“Caterpillar”-SSA and Box-Jenkins hybrid models and methods for time series forecasting

Виталий Николаевич Щелкалин

Abstract


Trend and decomposition approaches to non-stationary time series forecasting are considered in the paper. According to them, various hybrid models for non-stationary time series forecasting, as well as identification methods for these models based on the combined use of the “Caterpillar”-SSA and Box-Jenkins methods were proposed. Hybrid mathematical models of the trend approach to forecasting, based on the “Caterpillar”-SSA and Box-Jenkins methods lie in modeling the process as deviation of actual time series values with respect to the trend component, which is represented in the proposed models by the linear recurrence formula (LRF) of the “Caterpillar”-SSA method and its approximation by the SARIMA model. The main goal of the decomposition approach to forecasting based on the “Caterpillar”-SSA and Box-Jenkins methods is the decomposition of the original time series into multiple time series with a simpler structure, considered independently of each other using the “Caterpillar”-SSA method; forecasting the data of decomposition components by SARIMA models and calculating the total forecast by combining forecasts of the constructed simplified models.

The proposed models were tested on the electricity and natural gas consumption time series, and their forecasting results were compared with the results, obtained by classical probabilistic SARIMA models, generalized for the case of several seasonal components.

The obtained results allow to conclude that for effective forecasts, it is necessary to carry out decomposition of the studied time series and combine different models, describing both statistical and deterministic time series components that provides the best forecasting quality.


Keywords


time series forecasting; structural identification of model; decomposition model; Box-Jenkins method; “Caterpillar”-SSA method

References


1. Sedov, A. V. (2010). Modelirovanie obyektov s diskretno-raspredelennymi parametrami: dekompozitsionnyy podkhod. Moskow: Nauka, 438.

2. Benn, D. V., Farmer, E. D. (1987). Sravnitelnye modeli prognozirovaniya elektricheskoy nagruzki. Moskva: Energoatomizdat, 200.

3. Qiang Zhan, Ben De Wang, Bin He, Yong Peng, Ming Lei Ren. (2011). Singular Spectrum Analysis and ARIMA Hybrid Model for Annual Runnoff Forecasting. Water Resour Manage, 25 (11), 2683–2703 doi: 10.1007/s11269-011-9833-y

4. Evdokimov, A. G., Tevyashev, A. D. (1980). Operativnoe upravlenie potokoraspredeleniem v inzhenernykh setyakh. Kharkiv: Vishcha shkola, 144.

5. Lawrance, A. J., Kottegoda, N. T. (1977). Stochasting modelling of riverflow time series. J. R. Stat. Soc. A., 140 (1), 1–47. doi: 10.2307/2344516

6. Fernando, D. A. K., Jayawardena, W. A. (1994). Generation and forecasting of monsoon rainfall data. In Proc. of the 20th WEDC conference. Colombo, Sri Lanka, 310–313.

7. Yurekli, K., Kurunca, A., Ozturkb, F. (2005). Application of linear stochastic models to monthly flow data of Kelkit Stream. Ecol Model, 183 (1), 67–75. doi: 10.1016/j.ecolmodel.2004.08.001

8. Broomhead, D. S., King, G. P. (1986). Extracting qualitative dynamics from experimental data. Physica D, 20 (2-3), 217–236. doi: 10.1016/0167-2789(86)90031-x

9. Fraedrich, K. (1986). Estimating the dimension of weather and climate attractor. J. Atmos Sci, 43, 419–432.

10. Vautard, R., Ghil, M. (1989). Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series. Physica D, 35 (3), 395–424. doi: 10.1016/0167-2789(89)90077-8

11. Ghil, M., Vautard, R. (1991). Interdecadal oscillations and the warming trend in global temperature time series. Nature, 350 (6316), 324–327. doi: 10.1038/350324a0

12. Yiou, P., Baert, E., Loutre, M. F. (1996). Spectral analysis of climate data. Surv Geophys, 17 (6), 619–663. doi: 10.1007/bf01931784

13. Lisi, F., Nicolis, O., Sandri, M. (1995). Combination of singular spectrum analysis and auto regressive model for short term load forecasting. Neural Process Lett, 2 (4), 6–10.

14. Sivapragasam, C., Liong, S. Y., Pasha, M. F. K. (2001). Rainfall and discharge forecasting with SSA-SVM approach. J. Hydroinform, 3 (7), 141–152.

15. Golyandina, N., Nekrutkin, V. Zhigljavsky, A. (2001). Analysis of time series structure: SSA and related techniques. Chapman and Hall/CRC. New York. doi: 10.1201/9781420035841

16. Marques, C. A. F., Ferreira, J. A., Rocha, A., Castanheira, J. M., Melo-Goncalves, P., Vaz., N., Dias, J. M. (2005). Singular spectrum analysis and forecasting of hydrological time series. In Meeting of the European-Union-of-Geosciences.Vienna,Austria.

17. Hassani, H., Heravi, S., Zhigljavscky, A. (2009). Forecasting European industrial production with singular spectrum analysis. Int. J. Forecast, 25 (1), 103–118. doi: 10.1016/j.ijforecast.2008.09.007

18. Dai, W., Lu, C.-J. (2008). Financial Time Series Forecasting Using A Compound Model Based on Wavelet Frame and Support Vector Regression. In the 4th International Conference on Neural Computation, 328–332. doi: 10.1109/icnc.2008.455

19. Kurbatskii, V. G., Sidorov, D. N., Spiryaev, V. A., Tomin, N. V. (2011). On the Neural Network Approach for Forecasting of Nonstationary Time Series on The Basis of the Hilbert-Huang Transform. Automation and Remote Control, 72 (7), 1405–1414. doi: 10.1134/s0005117911070083

20. Zhang, W. Q., Xu C. (2011). Time series forecasting method based on Huang transform and BP neural network. In Proc. Of the 7thInternational Conference on Computational Intelligence and Security, 497–502. doi: 10.1109/cis.2011.116

21. Lu, C.-J., Wu, J.-Y., Lee, T.-S. (2009). ICA-Based Signal Reconstruction Scheme with Neural Network in Time Series Forecasting. In First Conference on Intelligent Information and Database Systems, 318–323. doi: 10.1109/aciids.2009.28

22. Xiang, L., Zhu, Y., Tang, G.-J. (2009). A hybrid support vector regression for time series forecasting. In World Congress on Software Engineering, 161–165. doi: 10.1109/wcse.2009.130

23. Sallehuddin, R., Shamsuddin, S. M., Hashim, S. Z. M. (2008). Hybridization Model of Linear and Nonlinear Time Series Data for Forecasting. In Second Asia International Conference on Modelling & Simulation, 597–602. doi: 10.1109/ams.2008.142

24. Hippert, H. S., Pedreira, C. E., Souza, R. C. (2000). Combining Neural Networks and ARIMA Models for Hourly Temperature Forecast. In Proceedings of the International Joint Conference on Neural Networks, 1–6. doi: 10.1109/ijcnn.2000.860807

25. Xuemei, L., Lixing, D., Ming, S., Gang, X., Jibin, L. (2009). A Novel Air-conditioning Load Prediction Based on ARIMA and BPNN Model. In Asia-Pacific Conference on Information Processing, 51–54. doi: 10.1109/apcip.2009.21

26. Tian, F. P., Ma, L. L. (2010). Forecast of Cerebral Infraction Incidence Rate Based on BP Neural Network and ARIMA Combined Model. In International Symposium on Intelligence Information Processing and Trusted Computing, 216–219. doi: 10.1109/iptc.2010.7

27. Kong, F., Wu, X. (2008). Time Series Forecasting Model with Error Correction by Structure Adaptive Support Vector Machine. In International Conference on Computer Science and Software Engineering, 1067–1070. doi: 10.1109/csse.2008.88

28. Lo, J.-H. (2012). A Data-Driven Model for Software Reliability Prediction. In International Conference on Granular Computing, 1–6. doi: 10.1109/grc.2012.6468581

29. He, Y., Zhu, Y., Duan, D. (2006). Research on Hybrid ARIMA and Support Vector Machine Model in Short Term Load Forecasting. In Proceedings of the Sixth International Conference on Intelligent Systems Design and Applications, 1–5. doi: 10.1109/isda.2006.229

30. Ngo, L. B., Apon, A., Hoffman, D. (2012). An Empirical Study on Forecasting using Decomposed Arrival Data of an Enterprise Computing System. In 9th International Conference on Information Technology- New Generations, 756–763. doi: 10.1109/itng.2012.36

31. Hou, Z., Makarov, Y. V., Samaan, N. A., Etingov, P. V. (2013). Standardized Software for Wind Load Forecast Error Analyses and Predictions Based on Wavelet-ARIMA Models – Applications at Multiple Geographically Distributed Wind Farms. In Hawaii International Conference on System Sciences, 5005–5011. doi: 10.1109/hicss.2013.495

32. Shchelkalin, V. N. (2012). Trendovyy podkhod prognozirovaniya vremennykh ryadov na osnove metoda «Gusenitsa»-SSA. Materialy 14-y Mezhdunarodnoy nauchno-tekhnicheskoy konferentsii SAIT. Kiev, 258–259.

33. Vahabie, A. H., Yousefi, M. M. R., Araabi, B. N., Lucas, C., Barghinia, S. (2007). Combination of Singular Spectrum Analysis and Autoregressive Model for short term load forecasting. IEEE LAUSANNE POWERTECH, 1090–1093. doi: 10.1109/pct.2007.4538467

34. Shchelkalin, V. N. (2012). Dekompozitsionnyy podkhod prognozirovaniya vremennykh ryadov na osnove metoda «Gusenitsa»-SSA. Materialy 14-y Mezhdunarodnoy nauchno-tekhnicheskoy konferentsii SAIT. Kiev, 258–259.

35. Golyandina, N. E. (2004). Metod «Gusenitsa»-SSA: prognoz vremennykh ryadov. Sankt-Peterburg: S. Peterburgskiy gosudarstvennyy universitet, 52.


GOST Style Citations


1. Седов, А. В. Моделирование объектов с дискретно-распределёнными параметрами: декомпозиционный подход [Текст] / А. В. Седов. – Южный научный центр РАН. – М. : Наука, 2010. – 438 с.

2. Бэнн, Д. В. Сравнительные модели прогнозирования электрической нагрузки [Текст] / Д. В. Бэнн, Е. Д. Фармер; пер. с англ. – М. : Энергоатомиздат, 1987. – 200 с.

3. Qiang, Z. Singular Spectrum Analysis and ARIMA Hybrid Model for Annual Runnoff Forecasting [Text] / Z. Qiang, D. W. Ben, H. Bin, P. Yong, L. R. Ming // Water Resour Manage. – 2011. – Vol. 25, Issue 11. – P. 2683–2703. doi: 10.1007/s11269-011-9833-y 

4. Евдокимов, А. Г. Оперативное управление потокораспределением в инженерных сетях [Текст] / А. Г. Евдокимов, А. Д. Тевяшев. – Х.: Вища школа, 1980. – 144 с.

5. Lawrance, A. J. Stochasting modelling of riverflow time series [Text] / A. J. Lawrance, N. T. Kottegoda // J. R. Stat. Soc. A. – 1977. – Vol. 140, issue 1. – P. 1–47. doi: 10.2307/2344516 

6. Fernando, D. A. K. Generation and forecasting of monsoon rainfall data [Text] / D. A. K. Fernando, W. A. Jayawardena // In Proc. of the 20th WEDC conference. Colombo, Sri Lanka, 1994. – P. 310–313.

7. Yurekli, K. Application of linear stochastic models to monthly flow data of Kelkit Stream [Text] / K. Yurekli, A. Kurunca, F. Ozturkb // Ecol Model. – 2005. – Vol. 183, Issue 1. – P. 67–75. doi: 10.1016/j.ecolmodel.2004.08.001 

8. Broomhead, D. S. Extracting qualitative dynamics from experimental data [Text] / D. S. Broomhead, G. P. King // Physica D. – 1986. – Vol. 20, Issue 2-3. – P. 217–236. doi: 10.1016/0167-2789(86)90031-x 

9. Fraedrich, K. Estimating the dimension of weather and climate attractor [Text] / K. Fraedrich // J. Atmos Sci. – 1986. – Vol. 43. – P. 419–432.

10. Vautard, R. Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series [Text] / R. Vautard, M. Ghil // Physica D. – 1989. – Vol. 35, Issue 3. – P. 395–424. doi: 10.1016/0167-2789(89)90077-8 

11. Ghil, M. Interdecadal oscillations and the warming trend in global temperature time series [Text] / M. Ghil, R. Vautard // Nature. – 1991. – Vol. 350, Issue 6316. – P. 324–327. doi: 10.1038/350324a0 

12. Yiou, P. Spectral analysis of climate data [Text] / P. Yiou, E. Baert, M.F. Loutre // Surv Geophys. – 1996. – Vol. 17, Issue 6. – P. 619–663. doi: 10.1007/bf01931784 

13. Lisi, F. Combination of singular spectrum analysis and auto regressive model for short term load forecasting [Text] / F. Lisi, O. Nicolis, M. Sandri // Neural Process Lett. – 1995. – Vol. 2, Issue 4. – P. 6–10.

14. Sivapragasam, C. Rainfall and discharge forecasting with SSA-SVM approach [Text] / C. Sivapragasam, S.Y. Liong, M.F.K. Pasha // J. Hydroinform. – 2001. – Vol. 3, Issue 7. – P. 141–152.

15. Golyandina, N. Analysis of time series structure: SSA and related techniques [Text] / N. Golyandina, V. Nekrutkin, A. Zhigljavsky // Chapman and Hall/CRC, New York, 2001. doi: 10.1201/9781420035841 

16. Marques, C. A. F. Singular spectrum analysis and forecasting of hydrological time series [Text] / C. A. F. Marques, J. A. Ferreira, A. Rocha, J. M. Castanheira // In Meeting of the European-Union-of-Geosciences.Vienna,Austria, 2005.

17. Hassani, H. Forecasting European industrial production with singular spectrum analysis [Text] / H. Hassani, S. Heravi, A. Zhigljavscky // Int. J. Forecast. – 2009. – Vol. 25, Issue 1. – P. 103–118. doi: 10.1016/j.ijforecast.2008.09.007 

18. Wensheng, D. Financial Time Series Forecasting Using A Compound Model Based on Wavelet Frame and Support Vector Regression [Text] / D. Wensheng, Lu Chi-Jie // In the 4th International Conference on Neural Computation, 2008. – P. 328–332. doi: 10.1109/icnc.2008.455 

19. Kurbatskii, V. G. On the Neural Network Approach for Forecasting of Nonstationary Time Series on The Basis of the Hilbert-Huang Transform [Text] / V. G. Kurbatskii, D. N. Sidorov, V. A. Spiryaev, N. V. Tomin // Automation and Remote Control. – 2011. – Vol. 72, Issue 7. – P. 1405–1414. doi: 10.1134/s0005117911070083 

20. Zhang, W. Q. Time series forecasting method based on Huang transform and BP neural network [Text] / W. Q. Zhang, C. Xu // In Proc. Of the 7thInternational Conference on Computational Intelligence and Security, 2011. – P. 497–502. doi: 10.1109/cis.2011.116 

21. Lu, C.-J. ICA-Based Signal Reconstruction Scheme with Neural Network in Time Series Forecasting [Text] / C.-J. Lu, J.-Yu Wu, T.-S. Lee // In First Conference on Intelligent Information and Database Systems, 2009. – P. 318–323. doi: 10.1109/aciids.2009.28 

22. Xiang, L. A hybrid support vector regression for time series forecasting [Text] / L. Xiang, Y. Zhu, G.-J. Tang // In World Congress on Software Engineering, 2009. – P. 161–165. doi: 10.1109/wcse.2009.130 

23. Sallehuddin, R. Hybridization Model of Linear and Nonlinear Time Series Data for Forecasting [Text] / R. Sallehuddin, S. M. Shamsuddin, S. Z. M. Hashim // In Second Asia International Conference on Modelling & Simulation, 2008. – P. 597–602. doi: 10.1109/ams.2008.142 

24. Henrique, S. H. Combining Neural Networks and ARIMA Models for Hourly Temperature Forecast [Text] / H. S. Hippert, C. E. Pedreira, R. C. Souza // In Proceedings of the International Joint Conference on Neural Networks, 2000. – P. 1–6. doi: 10.1109/ijcnn.2000.860807 

25. Xuemei, L. A Novel Air-conditioning Load Prediction Based on ARIMA and BPNN Model [Text] / L. Xuemei, D. Lixing, S. Ming, X. Gang, L. Jibin // In Asia-Pacific Conference on Information Processing, 2009. – P. 51–54. doi: 10.1109/apcip.2009.21 

26. Tian, F. P. Forecast of Cerebral Infraction Incidence Rate Based on BP Neural Network and ARIMA Combined Model [Text] / F. P. Tian, L. L. Ma // In International Symposium on Intelligence Information Processing and Trusted Computing, 2010. – P. 216–219. doi: 10.1109/iptc.2010.7 

27. Feng, K. Time Series Forecasting Model with Error Correction by Structure Adaptive Support Vector Machine [Text] / K. Feng, W. Xiaojuan // In International Conference on Computer Science and Software Engineering, 2008. – P. 1067–1070. doi: 10.1109/csse.2008.88 

28. Lo, J.-H. A Data-Driven Model for Software Reliability Prediction [Text] / J.-H. Lo // In International Conference on Granular Computing, 2012. – P. 1–6. doi: 10.1109/grc.2012.6468581 

29. He, Y. Research on Hybrid ARIMA and Support Vector Machine Model in Short Term Load Forecasting [Text] / Y. He, Y. Zhu, D. Duan // In Proceedings of the Sixth International Conference on Intelligent Systems Design and Applications, 2006. – P. 1–5. doi: 10.1109/isda.2006.229 

30. Linh, B. N. An Empirical Study on Forecasting using Decomposed Arrival Data of an Enterprise Computing System [Text] / B. N. Linh, A. Amy, H. Doug // In 9th International Conference on Information Technology- New Generations, 2012. – P. 756–763. doi: 10.1109/itng.2012.36 

31. Hou, Z. Standardized Software for Wind Load Forecast Error Analyses and Predictions Based on Wavelet-ARIMA Models – Applications at Multiple Geographically Distributed Wind Farms [Text] / Z. Hou, Y. V. Makarov, N. A. Samaan, P. V. Etingov // In Hawaii International Conference on System Sciences, 2013. – P. 5005–5011. doi: 10.1109/hicss.2013.495 

32. Щелкалин, В. Н. Трендовый подход прогнозирования временных рядов на основе метода «Гусеница»-SSA [Текст] / Материалы 14-й Международной научно-технической конференции SAIT 2012, Киев, 24 апреля2012 г. / В .Н. Щелкалин // УНК “ИПСА” НТУУ “КПИ”. – К.: УНК “ИПСА” НТУУ “КПИ”, 2012. – С. 258 – 259.

33. Vahabie, A. H. Combination of Singular Spectrum Analysis and Autoregressive Model for short term load forecasting [Text] / A. H. Vahabie, M. M. R. Yousefi, B. N. Araabi, C. Lucas, S. Barghinia // IEEE LAUSANNE POWERTECH, 2007. – P. 1090–1093. doi: 10.1109/pct.2007.4538467 

34. Щелкалин, В. Н. Декомпозиционный подход прогнозирования временных рядов на основе метода «Гусеница»-SSA [Текст] : матер. 14-й Междун. науч.-тех. конф. SAIT / В. Н. Щелкалин // УНК “ИПСА” НТУУ “КПИ”. – К.: УНК “ИПСА” НТУУ “КПИ”, 2012. – С. 260–261.

35. Голяндина, Н. Э. Метод «Гусеница»-SSA: прогноз временных рядов [Текст]: уч. пос. / Н. Э. Голяндина. – СПб. : С.-Петербургский государственный университет, 2004. – 52 с.






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