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An optimized time series combined forecasting method based on neural networks

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Abstract

In the field of time series forecasting, combining forecasts from multiple models significantly improves the forecasting precision as well as often produces better forecasts than each constituent model. The linear method is the main method in the current literatures for it is simpler and more efficient, and usually gives good results. However, the selection of the basic unit models and the determination of combination weights always bring difficulties to combined forecasting model. In addition, there is usually more time consuming in the combining model. To address these problems, this paper proposes an optimized time series combined forecasting method based on neural networks. The principle of the proposed method adheres to two primary aspects. (a) A multi-threaded grid search method is proposed to quickly determine the number of hidden layer nodes in a neural network for a scenario. (b) A method based on sample dynamic partitioning to explore the weight generation mode is proposed to determine the combined forecasting. Empirical results from six real-world time series show that the superiority of our approach in forecasting accuracies.

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References

  1. Maier HR, Dandy GC (2000) Neural networks for the prediction and forecasting of water resources variables: a review of modelling issues and applications. Environ Model 15(1):101–124

    Google Scholar 

  2. Li H-Z, Guo S, Li C-J, Sun J-Q (2013) A hybrid annual power load forecasting model based on generalized regression neural network with fruit fly optimization algorithm. Knowl Based Syst 37:378–387

    Google Scholar 

  3. Bodyanskiy Y, Popov S (2006) Neural network approach to forecasting of quasiperiodic financial time series. Eur J Oper Res 175(3):1357–1366

    MathSciNet  MATH  Google Scholar 

  4. Song H, Li G (2008) Tourism demand modelling and forecasting—a review of recent research. Tour Manag 29(2):203–220

    Google Scholar 

  5. Chen C-F, Lai M-C, Yeh C-C (2012) Forecasting tourism demand based on empirical mode decomposition and neural network. Knowl Based Syst 26:281–287

    Google Scholar 

  6. Lu X, Wang J, Cai Y, Zhao J (2015) Distributed HS-ARTMAP and its forecasting model for electricity load. Appl Soft Comput 32:13–22

    Google Scholar 

  7. Box GE, Jenkins GM, Reinsel GC, Ljung GM (2015) Time series analysis: forecasting and control. Wiley, Hoboken

    MATH  Google Scholar 

  8. Pellegrini S, Ruiz E, Espasa A (2011) Prediction intervals in conditionally heteroscedastic time series with stochastic components. Int J Forecast 27(2):308–319

    Google Scholar 

  9. Suykens JA, Vandewalle J (1999) Least squares support vector machine classifiers. Eural Process Lett 9(3):293–300

    Google Scholar 

  10. Vapnik V (2013) The nature of statistical learning theory. Springer, Berlin

    MATH  Google Scholar 

  11. Zhang GP (2007) A neural network ensemble method with jittered training data for time series forecasting. Inf Sci 177(23):5329–5346

    Google Scholar 

  12. Bates JM, Granger CW (1969) The combination of forecasts. J Oper Res Soc 20(4):451–468

    Google Scholar 

  13. Hoeting JA, Madigan D, Raftery AE, Volinsky CT (1999) Bayesian model averaging: a tutorial. Stat Sci 14(4):382–401

    MathSciNet  MATH  Google Scholar 

  14. Jose VRR, Winkler RL (2008) Simple robust averages of forecasts: some empirical results. Int J Forecast 24(1):163–169

    Google Scholar 

  15. De Gooijer JG, Hyndman RJ (2006) 25 years of time series forecasting. Int J Forecast 22(3):443–473

    Google Scholar 

  16. Armstrong JS (2001) Principles of forecasting: a handbook for researchers and practitioners, vol 30. Springer, Berlin

    Google Scholar 

  17. Aksu C, Gunter SI (1992) An empirical analysis of the accuracy of SA, OLS, ERLS and NRLS combination forecasts. Int J Forecast 8(1):27–43

    Google Scholar 

  18. Granger CW, Ramanathan R (1984) Improved methods of combining forecasts. J Forecast 3(2):197–204

    Google Scholar 

  19. Lemke C, Gabrys B (2010) Meta-learning for time series forecasting and forecast combination. Neurocomputing 73(10–12):2006–2016

    Google Scholar 

  20. Bunn DW (1975) A Bayesian approach to the linear combination of forecasts. J Oper Res Soc 26(2):325–329

    MATH  Google Scholar 

  21. Aiolfi M, Timmermann A (2006) Persistence in forecasting performance and conditional combination strategies. J Econom 135(1–2):31–53

    MathSciNet  MATH  Google Scholar 

  22. Andrawis RR, Atiya AF, El-Shishiny H (2011) Forecast combinations of computational intelligence and linear models for the NN5 time series forecasting competition. Int J Forecast 27(3):672–688

    Google Scholar 

  23. Lin C-C, Lin C-L, Shyu JZ (2014) Hybrid multi-model forecasting system: a case study on display market. Knowl Based Syst 71:279–289

    Google Scholar 

  24. Adhikari R (2015) A neural network based linear ensemble framework for time series forecasting. Neurocomputing 157:231–242

    Google Scholar 

  25. Zhou Z-H, Wu J, Tang W (2002) Ensembling neural networks: many could be better than all. Artif Intell 137(1–2):239–263

    MathSciNet  MATH  Google Scholar 

  26. Adhikari R (2015) A mutual association based nonlinear ensemble mechanism for time series forecasting. Appl Intell 43(2):233–250

    Google Scholar 

  27. Rumelhart DE, McClelland JL (1986) Parallel distributed processing: explorations in the microstructure of cognition. MIT Press, Cambridge, MA

    Google Scholar 

  28. Shen W, Guo X, Wu C, Wu D (2011) Forecasting stock indices using radial basis function neural networks optimized by artificial fish swarm algorithm. Knowl Based Syst 24(3):378–385

    Google Scholar 

  29. Wang S, Zhang N, Wu L, Wang Y (2016) Wind speed forecasting based on the hybrid ensemble empirical mode decomposition and GA-BP neural network method. Renew Energy 94:629–636

    Google Scholar 

  30. Yu F, Xu X (2014) A short-term load forecasting model of natural gas based on optimized genetic algorithm and improved BP neural network. Appl Energy 134:102–113

    Google Scholar 

  31. Wang D, Luo H, Grunder O, Lin Y, Guo H (2017) Multi-step ahead electricity price forecasting using a hybrid model based on two-layer decomposition technique and BP neural network optimized by firefly algorithm. Appl Energy 190:390–407

    Google Scholar 

  32. Zhang GP (2003) Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing 50:159–175

    MATH  Google Scholar 

  33. Wang L, Zeng Y, Zhang J, Huang W, Bao Y (2006) The criticality of spare parts evaluating model using artificial neural network approach. In: International Conference on Computational Science. Springer, pp 728–735

  34. Wang L, Zeng Y, Chen T (2015) Back propagation neural network with adaptive differential evolution algorithm for time series forecasting. Expert Syst Appl 42(2):855–863

    Google Scholar 

  35. Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735–1780

    Google Scholar 

  36. Gers FA, Schmidhuber J, Cummins F (1999) Learning to forget: continual prediction with LSTM. Neural Comput 12(10):2451–2471

    Google Scholar 

  37. Zhao Z, Chen W, Wu X, Chen PC, Liu J (2017) LSTM network: a deep learning approach for short-term traffic forecast. IET Intel Transp Syst 11(2):68–75

    Google Scholar 

  38. Zheng H, Yuan J, Chen L (2017) Short-term load forecasting using EMD-LSTM neural networks with a Xgboost algorithm for feature importance evaluation. Energies 10(8):1168

    Google Scholar 

  39. Jaeger H (2001) The “echo state” approach to analysing and training recurrent neural networks-with an erratum note. Bonn Ger Ger Natl Res Center Inf Technol GMD Tech Rep 148(34):13

    Google Scholar 

  40. Jaeger H, Haas H (2004) Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication. Science 304(5667):78–80

    Google Scholar 

  41. Jaeger H (2007) Echo state network. Scholarpedia 2(9):2330

    Google Scholar 

  42. Chatzis SP, Demiris Y (2011) Echo state Gaussian process. IEEE Trans Neural Netw 22(9):1435–1445

    Google Scholar 

  43. Bianchi FM, Scardapane S, Uncini A, Rizzi A, Sadeghian A (2015) Prediction of telephone calls load using Echo State Network with exogenous variables. Neural Netw 71:204–213

    Google Scholar 

  44. Chouikhi N, Ammar B, Rokbani N, Alimi AM (2017) PSO-based analysis of Echo State Network parameters for time series forecasting. Appl Soft Comput 55:211–225

    Google Scholar 

  45. Shen L, Chen J, Zeng Z, Yang J, Jin J (2018) A novel echo state network for multivariate and nonlinear time series prediction. Appl Soft Comput 62:524–535

    Google Scholar 

  46. Cho K, Van Merriënboer B, Gulcehre C, Bahdanau D, Bougares F, Schwenk H, Bengio Y (2014) Learning phrase representations using RNN encoder-decoder for statistical machine translation. arXiv:1406.1078 (preprint)

  47. Chung J, Gulcehre C, Cho K, Bengio Y (2014) Empirical evaluation of gated recurrent neural networks on sequence modeling. arXiv:1412.3555 (preprint)

  48. Wang S, Zhao X, Li M, Wang H (2018) TRSWA-BP neural network for dynamic wind power forecasting based on entropy evaluation. Entropy 20(4):283

    Google Scholar 

  49. Shao-Jiang L, Jia-Ying C, Zhi-Xue L (2018) A EMD-BP integrated model to forecast tourist number and applied to Jiuzhaigou. J Intell Fuzzy Syst 34(2):1045–1052

    Google Scholar 

  50. Wentao X, Jianjun H, Aiguo S, Xinyu Z (2017) An improved forecast of ship sway based on ESN. In: 2017 4th International Conference on Information, Cybernetics and Computational Social Systems (ICCSS). IEEE, pp 422–425

  51. Li J, Li Q (2015) Medium term electricity load forecasting based on CEEMDAN-permutation entropy and ESN with leaky integrator neurons. Electr Mach Control 8:012

    Google Scholar 

  52. Sagheer A, Kotb M (2019) Time series forecasting of petroleum production using deep LSTM recurrent networks. Neurocomputing 323:203–213

    Google Scholar 

  53. Baek Y, Kim HY (2018) ModAugNet: a new forecasting framework for stock market index value with an overfitting prevention LSTM module and a prediction LSTM module. Expert Syst Appl 113:457–480

    Google Scholar 

  54. Tokgöz A, Ünal G (2018) A RNN based time series approach for forecasting turkish electricity load. In: 2018 26th Signal Processing and Communications Applications Conference (SIU). IEEE, pp 1–4

  55. Zu X, Song R (2018) Short-term wind power prediction method based on wavelet packet decomposition and improved GRU. In: Journal of Physics: Conference Series, vol 2. IOP Publishing, p 022034

  56. Freitas PS, Rodrigues AJ (2006) Model combination in neural-based forecasting. Eur J Oper Res 173(3):801–814

    MathSciNet  MATH  Google Scholar 

  57. De Menezes LM, Bunn DW, Taylor JW (2000) Review of guidelines for the use of combined forecasts. Eur J Oper Res 120(1):190–204

    MATH  Google Scholar 

  58. Timmermann A (2006) Forecast combinations. Handb Econ Forecast 1:135–196

    Google Scholar 

  59. Hyndman RJ (2019) Time series data library. https://datamarket.com/data/list/?q=provider:tsdl

  60. Kingma DP, Ba J (2014) Adam: a method for stochastic optimization. arXiv:1412.6980. Accessed 14 Nov 2018 (preprint)

  61. Sutskever I, Martens J, Dahl G, Hinton G (2013) On the importance of initialization and momentum in deep learning. In: International Conference on Machine Learning, pp 1139–1147

  62. Dozat T (2016) Incorporating nesterov momentum into adam. Dostupnéz. http://cs229.stanford.edu/proj/054_report.pdf

  63. Wang L, Wang Z, Qu H, Liu S (2018) Optimal forecast combination based on neural networks for time series forecasting. Appl Soft Comput 66:1–17

    Google Scholar 

  64. Steel RGD, Torrie JH (1960) Principles and procedures of statistics: with special reference to the biological sciences. McGraw-Hill, New York

    MATH  Google Scholar 

  65. Glantz SA, Slinker BK, Neilands TB (1990) Primer of applied regression and analysis of variance, vol 309. McGraw-Hill, New York

    Google Scholar 

  66. Draper NR, Smith H (2014) Fitting a straight line by least squares. Wiley

  67. Box GE, Jenkins GM (1970) Time series analysis forecasting and control. Wisconsin Univ Madison Dept of Statistics, Madison

    MATH  Google Scholar 

  68. Ziegel ER, Box GEP, Jenkins GM, Reinsel GC (1995) Time series analysis, forecasting, and control. Technometrics 37(2):238

    Google Scholar 

  69. Zhang G, Patuwo BE, Hu MY (1998) Forecasting with artificial neural networks: the state of the art. Int J Forecast 14(1):35–62

    Google Scholar 

  70. Elman JL (1990) Finding structure in time. Cogn Sci 14(2):179–211

    Google Scholar 

  71. Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2(5):359–366

    MATH  Google Scholar 

  72. Lim CP, Goh WY (2007) The application of an ensemble of boosted elman networks to time series prediction: a benchmark study. World Acad Sci Eng Technol Int J Electr Comput Energ Electron Commun Eng 1(10):1518–1525

    Google Scholar 

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Correspondence to Ruizhi Sun.

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Zhao, K., Li, L., Cai, S. et al. An optimized time series combined forecasting method based on neural networks. J Supercomput 76, 2986–3012 (2020). https://doi.org/10.1007/s11227-019-03064-5

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