Cognitive Computation

, Volume 10, Issue 2, pp 187–200 | Cite as

An Online Sequential Learning Non-parametric Value-at-Risk Model for High-Dimensional Time Series

  • Heng-Guo Zhang
  • Libo Wu
  • Yan Song
  • Chi-Wei Su
  • Qingping Wang
  • Fei Su


Online Value-at-Risk (VaR) analysis in high-dimensional space remains a challenge in the era of big data. In this paper, we propose an online sequential learning non-parametric VaR model called OS-GELM which is an autonomous cognitive system. This model uses a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) process and an online sequential extreme learning machine (OS-ELM) to cognitively calculate VaR, which can be used for online risk analysis. The proposed model not only learns the data one-by-one or chunk-by-chunk but also calculates VaR in real time by extending OS-ELM from machine learning to the non-parametric GARCH process. The GARCH process is also extended to one-by-one and chunk-by-chunk mode. In OS-GELM, the parameters of hidden nodes are randomly selected. The output weights are analytically determined based on the sequentially arriving data. In addition, the generalization performance of the OS-GELM model attains a small training error and generates the smallest norm of weights. Experimentally obtained VaRs are compared with those given by GARCH-type models and conventional OS-ELM. The computational results demonstrate that the OS-GELM model obtains more accurate results and is better at forecasting the online VaR. OS-GELM model is an autonomous cognitive system to dynamically calculate Value-at-Risk, which can be used for online financial risk assessment about human being’s behavior. The OS-GELM model can calculate VaR in real time, which can be used as a tool for online risk management. OS-GELM can handle any bounded, non-constant, piecewise-continuous membership function to realize real-time VaR monitoring.


OS-ELM GARCH models Value-at-Risk High-dimensional space Time series 



This research is supported by China Postdoctoral Science Foundation funded project, the National Social Science Foundation (15BJY155) and the National High Technology Research and Development Program of China (863 Program) (2015AA050203).

Compliance with Ethical Standards

Ethical Approval

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.


  1. 1.
    Youssef M, Belkacem L, Mokni K. Value-at-risk estimation of energy commodities: a long-memory GARCH–EVT approach. Energy Econ. 2015;51:99–110.CrossRefGoogle Scholar
  2. 2.
    Kim M, Lee S. Nonlinear expectile regression with application to value-at-risk and expected shortfall estimation. Comput Stat Data Anal. 2016;94:1–19.CrossRefGoogle Scholar
  3. 3.
    Liang N-Y, Huang G-B, Saratchandran P, Sundararajan N. A fast and accurate online sequential learning algorithm for feedforward networks. Neural Netw IEEE Trans. 2006;17(6):1411–23.CrossRefGoogle Scholar
  4. 4.
    Platt J. A resource-allocating network for function interpolation. Neural Comput. 1991;3(2):213–25.CrossRefGoogle Scholar
  5. 5.
    Bildirici M, Ersin ÖÖ. Improving forecasts of garch family models with the artificial neural networks: an application to the daily returns in istanbul stock exchange. Expert Syst Appl. 2009;36(4):7355–62.CrossRefGoogle Scholar
  6. 6.
    Ghorbel A, Trabelsi A. Energy portfolio risk management using time-varying extreme value copula methods. Econ Model. 2014;38:470–85.CrossRefGoogle Scholar
  7. 7.
    Berman JJ, Principles of big data: preparing, sharing, and analyzing complex information, Newnes, 2013.Google Scholar
  8. 8.
    Li G, Liu M, Dong M. A new online learning algorithm for structure adjustable extreme learning machine. Comput Math Appl. 2010;60(3):377–89.CrossRefGoogle Scholar
  9. 9.
    Grossberg S. Nonlinear neural networks: principles, mechanisms, and architectures. Neural Netw. 1988;1(1):17–61.CrossRefGoogle Scholar
  10. 10.
    LeCun YA, Bottou L, Orr GB, Müller K-R, Efficient backprop, in: Neural Networks: Tricks of the Trade, Springer, 2012:9–48.Google Scholar
  11. 11.
    Huang G-B, Saratchandran P, Sundararajan N. An efficient sequential learning algorithm for growing and pruning RBF (GAP-RBF) networks. Syst Man Cybern Part B: Cybern IEEE Trans. 2004;34(6):2284–92.CrossRefGoogle Scholar
  12. 12.
    Zou H, Jiang H, Lu X, Xie L, An online sequential extreme learning machine approach to WiFi based indoor positioning, in: Internet of Things (WF-IoT), 2014 I.E. World Forum on, IEEE, 2014:111–116.Google Scholar
  13. 13.
    Huang G-B, Zhu Q-Y, Siew C-K. Extreme learning machine: theoryand applications. Neurocomputing. 2006;70(1):489–501.CrossRefGoogle Scholar
  14. 14.
    Golub GH, Van Loan CF, Matrix computations, 3rd (2012).Google Scholar
  15. 15.
    Huang G-B, Zhou H, Ding X, Zhang R. Extreme learning machine for regression and multiclass classification. Syst Man Cybern Part B: Cybern IEEE Trans. 2012;42(2):513–29.CrossRefGoogle Scholar
  16. 16.
    Tamura S, Tateishi M. Capabilities of a four-layered feedforward neuralnetwork: four layers versus three. Neural Netw IEEE Trans. 1997;8(2):251–5.CrossRefGoogle Scholar
  17. 17.
    Chong EK, Zak SH, An introduction to optimization, Vol. 76, John Wiley & Sons, 2013.Google Scholar
  18. 18.
    Giot P, Laurent S. Modelling daily value-at-risk using realized volatility and arch type models. J Empir Financ. 2004;11(3):379–98.CrossRefGoogle Scholar
  19. 19.
    Kupiec P. Techniques for verifiying the accuracy of risk management models. J Deriv. 1995;3:73–84.CrossRefGoogle Scholar
  20. 20.
    Engle RF, Manganelli S. CAViaR: conditional autoregressive value at risk by regression quantiles. J Bus Econ Stat. 2004;22(4):367–81.CrossRefGoogle Scholar
  21. 21.
    Engle RF, Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation, Econometrica: Journal of the Econometric Society 1982: 987–1007.Google Scholar
  22. 22.
    He K, Lai KK, Yen J. Ensemble forecasting of value at risk via multi resolution analysis based methodology in metals markets. Expert Syst Appl. 2012;39(4):4258–67.CrossRefGoogle Scholar
  23. 23.
    Vong C-M, et al. Imbalanced learning for air pollution by meta-cognitive online sequential extreme learning machine. Cogn Comput. 2015;7(3):381–91.CrossRefGoogle Scholar
  24. 24.
    Savitha R, Suresh S, Kim HJ. A meta-cognitive learning algorithm for an extreme learning machine classifier. Cogn Comput. 2014;6(2):253–63.CrossRefGoogle Scholar
  25. 25.
    Cao K, et al. Classification of uncertain data streams based on extreme learning machine. Cogn Comput. 2015;7(1):150–60.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Heng-Guo Zhang
    • 1
  • Libo Wu
    • 2
  • Yan Song
    • 3
  • Chi-Wei Su
    • 4
  • Qingping Wang
    • 5
  • Fei Su
    • 6
  1. 1.School of Data ScienceFudan UniversityShanghaiChina
  2. 2.School of Economics & School of Data ScienceFudan UniversityShanghaiChina
  3. 3.College of Information Science and EngineeringOcean University of ChinaQingdaoChina
  4. 4.Department of FinanceOcean University of ChinaQingdaoChina
  5. 5.School of Mathematical SciencesOcean University of ChinaQingdaoChina
  6. 6.Finance Discipline Group, UTS Business SchoolUniversity of TechnologySydneyAustralia

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