Skip to main content
SpringerLink
Log in

Forecasting nonstationary time series based on Hilbert-Huang transform and machine learning

  • Data Analysis
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

We propose a modification of the adaptive approach to time series forecasting. On the first stage, the original signal is decomposed with respect to a special empirical adaptive orthogonal basis, and the Hilbert’s integral transform is applied. On the second stage, the resulting orthogonal functions and their instantaneous amplitudes are used as input variables for the machine learning unit that employs a hybrid genetic algorithm to train an artificial neural network and a regressive model based on support vector machines. The efficiency of the proposed approach is demonstrated on real data coming from Nord Pool Spot and Australian National Energy Market.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Brockwell, P.J. and Davis, R.A., Introduction to Time Series and Forecasting, Springer Texts in Statistics, New York: Springer-Verlag, 2002.

    Book  MATH  Google Scholar 

  2. Fan, J. and Yao, Q., Nonlinear Time Series: Nonparametric and Parametric Methods, New York: Springer-Verlag, 2003.

    Book  Google Scholar 

  3. Khaikin, S., Neironnye seti (Neural Networks), Moscow: Wil’yams, 2006.

    Google Scholar 

  4. Osovskii, S., Neironnye seti dlya obrabotki informatsii (Neural Networks for Information Processing), Moscow: Finansy i Statistika, 2004.

    Google Scholar 

  5. Zhang, G.P., Patuwo, B.E., and Hu, M.Y., Forecasting with Artificial Neural Networks: The State of the Art, Int. J. Forecast., 1998, vol. 14, no. 5, pp. 35–62.

    Article  Google Scholar 

  6. Breiman, H., Random Forests, J. Machine Learning, 2001, vol. 45, pp. 5–32.

    Article  MATH  Google Scholar 

  7. Areekul, P., Senjyu, T., Toyama, H., and Yona, A., A Hybrid ARIMA and Neural Network Model for Short-Term Price Forecasting in Deregulated Market, IEEE Trans. Power Syst., 2010, vol. 25, no. 1, pp. 524–530.

    Article  Google Scholar 

  8. Adya, M. and Collopy, F., How Effective are Neural Networks at Forecasting and Prediction? A Review and Evaluation, Int. J. Forecast., 1998, vol. 17, nos. 5–6, pp. 481–495.

    Article  Google Scholar 

  9. Callen, L.J., Kwan, C.C., Yip, C.P., and Yuan, Y., Neural Network Forecasting of Quarterly Accounting Earnings, Int. J. Forecast., 1996, vol. 12, no. 4, pp. 475–482.

    Article  Google Scholar 

  10. Heravi, S., Osborn, D.R., and Birchenhall, C.R., Linear Versus Neural Network Forecasts for European Industrial Production Series, Int. J. Forecast., 2004, vol. 20, no. 3, pp. 435–446.

    Article  Google Scholar 

  11. Yan, W., Toward Automatic Time-Series Forecasting Using Neural Networks, IEEE Trans. Neural Networks Learning Syst., 2012, vol. 23, no. 7, pp. 1028–1039.

    Article  Google Scholar 

  12. Vapnik, V.N. and Lerner, A.Ya., Pattern Recognition Using Generalized Portraits, Autom. Remote Control, 1963, vol. 24, no. 6, pp. 709–715.

    Google Scholar 

  13. Vapnik, V.N., Vosstanovlenie zavisimostei po empiricheskim dannym (Reconstructing Dependencies by Empirical Data), Moscow: Nauka, 1979.

    Google Scholar 

  14. Vapnik, V.N. and Chervonenkis, A.Ya., Teoriya raspoznavaniya obrazov (Pattern Recognition Theory), Moscow: Nauka, 1974.

    MATH  Google Scholar 

  15. Vasil’ev, I.L. and Sidorov, D.N., An Application of Cluster Analysis to Automated Defect Recognition, Probl. Upravlen., 2007, no. 4, pp. 36–42.

    Google Scholar 

  16. Cover, T., Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition, IEEE Trans. Electron. Comput., 1965, vol. 14, pp. 326–334.

    Article  MATH  Google Scholar 

  17. Huang, N.E., Zheng, S., Long, S.R., et al., The Empirical Mode Decomposition and the Hilbert Spectrum for Non-Linear and Non-Stationary Time Series Analysis, Proc. Royal Soc. London, Ser. A: Math., Phys. Eng. Sci., 1971, vol. 454, pp. 903–995.

    Article  MathSciNet  Google Scholar 

  18. Gorban’, A.N., Dunin-Barkovskii, V.L., and Mirkes, E.M., Neiroinformatika (Neuroinformatics), Novosibirsk: Nauka, 1998.

    Google Scholar 

  19. Gerikh, V.P., Kolosok, I.N., Kurbatsky, V.G., and Tomin, N.V., Application of Neural Network Technologies for Price Forecasting in the Liberalized Electricity Market, Power Electr. Eng., Sci. J. Riga Techn. Univ., 2009, no. 5, pp. 91–96.

    Google Scholar 

  20. Friedman, J.H., Stochastic Gradient Boosting, Comput. Statist. Data Anal., 2002, vol. 38, pp. 367–378.

    Article  MATH  MathSciNet  Google Scholar 

  21. Yun, Z., RBF Neural Network and ANFIS-Based Short-Term Load Forecasting Approach in Real-Time Price Environment, IEEE Trans. Power Syst., 2008, vol. 23, no. 3, pp. 853–858.

    Article  Google Scholar 

  22. Neironnye seti. STATISTICA Neural Networks: Metodologiya i tekhnologii sovremennogo analiza dannykh (Neural Networks. STATISTICA Neural Networks: Methodology and Technology of Modern Data Mining), Borovikov, V.P., Ed., Moscow: Goryachaya Liniya-Telekom, 2008.

    Google Scholar 

  23. Zhu, C., Byrd, C.V., Lu, P., and Nocedal, J., Algorithm 778: L-BFGS-B, Fortran Subroutines for Large Scale Bound Constrained Optimization, ACM Trans. Math. Softw., 1997, vol. 23, no. 4, pp. 550–560.

    Article  MATH  MathSciNet  Google Scholar 

  24. Aizerman, M.A., Braverman, E.M., and Rozonoer, L.I., Metod potentsial’nykh funktsii v teorii obucheniya mashin (Method of Potential Functions in Machine Learning Theory), Moscow: Nauka, 1970.

    Google Scholar 

  25. Tikhonov, A.N. and Arsenin, V.Ya., Metody resheniya nekorrektnykh zadach (Methods for Solving Ill-Posed Problems), Moscow: Nauka, 1979.

    MATH  Google Scholar 

  26. Morozov, V.A., Methods for Solving Incorrectly Posed Problems, New York: Springer, 1984.

    Book  Google Scholar 

  27. Nesterov, Yu.E., Vvedenie v vypukluyu optimizatsiyu (Introduction to Convex Optimization), Polyak, B. and Nazin, S., Eds., Moscow: Mosk. Tsentr Nepreryvn. Mat. Obrazov., 2010.

  28. Hornik, K., Stinchcombe, M., and White, H., Multilayer Feedforward Networks are Universal Approximators, Neural Networks, 1989, vol. 2, pp. 359–366.

    Article  Google Scholar 

  29. Flandrin, P., Rilling, G., and Goncalves, P., On Empirical Mode Decomposition and Its Algorithms, IEEE Signal Proc. Lett., 2004, vol. 11, no. 2, pp. 112–114.

    Article  Google Scholar 

  30. Czerny, V., Thermodynamical Approach to the Traveling Salesman Problem: An Efficient Simulation Algorithm, J. Optim. Theory Appl., 1985, vol. 45, pp. 41–51.

    Article  MathSciNet  Google Scholar 

  31. Shumkov, D.S., Development and Study of Forecasting Methods Based on SVM Models, Cand. Sci. (Tech.) Dissertation, St. Petersburg: State Univ. of Information Technologies, Mechanics, and Optics, 2009.

    Google Scholar 

  32. Kurbatsky, V.G. and Tomin, N.V., Using PVK “ANAPRO” for Analysis and Forecasting of Mode Parameters and Technological Characteristics in Electical Energy Systems, in Tr. XIII Baikal. Vseross. Konf. “Informatsionnye i matematicheskie tekhnologii v nauke i upravlenii” (Proc. XIII Baikal All-Russian Conf. “Informational and Mathematical Technologies in Science and Management”), Irkutsk: Inst. Sist. Energet. Sib. Otd. Ross. Akad. Nauk, 2008, part I.

    Google Scholar 

  33. Andreev, A.V., Livshits, G.N., Mashanskii, A.M., et al., A Hierarchical System for Automated Control over Frequency and Overflows in Active Power of EES Russia, Elektrich. Stantsii, 2010, no. 3, pp. 43–51.

    Google Scholar 

  34. Kalman, R.E. and Bucy, R.S., New Results in Linear Filtering and Prediction Theory, Trans. ASME, Ser. D, J. Basic Eng., 1961, vol. 83, pp. 95–108.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Melentiev Energy Systems Institute, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia

    V. G. Kurbatsky, D. N. Sidorov, V. A. Spiryaev & N. V. Tomin

Authors
  1. V. G. Kurbatsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. N. Sidorov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. A. Spiryaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. N. V. Tomin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. G. Kurbatsky.

Additional information

Original Russian Text © V.G. Kurbatsky, D.N. Sidorov, V.A. Spiryaev, N.V. Tomin, 2014, published in Avtomatika i Telemekhanika, 2014, No. 5, pp. 143–158.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kurbatsky, V.G., Sidorov, D.N., Spiryaev, V.A. et al. Forecasting nonstationary time series based on Hilbert-Huang transform and machine learning. Autom Remote Control 75, 922–934 (2014). https://doi.org/10.1134/S0005117914050105

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117914050105

Keywords

Search

Navigation