A Multivariate and Multi-step Ahead Machine Learning Approach to Traditional and Cryptocurrencies Volatility Forecasting

  • Jacopo De StefaniEmail author
  • Olivier Caelen
  • Dalila Hattab
  • Yann-Aël Le Borgne
  • Gianluca Bontempi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11054)


Multivariate time series forecasting involves the learning of historical multivariate information in order to predict the future values of several quantities of interests, accounting for interdependencies among them. In finance, several of this quantities of interests (stock valuations, return, volatility) have been shown to be mutually influencing each other, making the prediction of such quantities a difficult task, especially while dealing with an high number of variables and multiple horizons in the future. Here we propose a machine learning based framework, the DFML, based on the Dynamic Factor Model, to first perform a dimensionality reduction and then perform a multiple step ahead forecasting of a reduced number of components. Finally, the components are transformed again into an high dimensional space, providing the desired forecast. Our results, comparing the DFML with several state of the art techniques from different domanins (PLS, RNN, LSTM, DFM), on both traditional stock markets and cryptocurrencies market and for different families of volatility proxies show that the DFML outperforms the concurrent methods, especially for longer horizons. We conclude by explaining how we wish to further improve the performances of the framework, both in terms of accuracy and computational efficiency.


Multivariate time series forecasting Volatility forecasting Multi-step ahead forecast Dynamic factor models 


  1. 1.
    Alessandretti, L., ElBahrawy, A., Aiello, L.M., Baronchelli, A.: Machine learning the cryptocurrency market. arXiv preprint arXiv:1805.08550 (2018)
  2. 2.
    Andersen, T.G., Bollerslev, T.: ARCH and GARCH models. Encyclopedia of Statistical Sciences (1998)Google Scholar
  3. 3.
    Bollerslev, T., Patton, A.J., Quaedvlieg, R.: Multivariate leverage effects and realized semicovariance GARCH models (2018).
  4. 4.
    Bontempi, G., Le Borgne, Y.A., De Stefani, J.: A dynamic factor machine learning method for multi-variate and multi-step-ahead forecasting. In: 2017 IEEE International Conference on Data Science and Advanced Analytics (DSAA), pp. 222–231. IEEE (2017)Google Scholar
  5. 5.
    Bontempi, G., Taieb, S.B.: Conditionally dependent strategies for multiple-step-ahead prediction in local learning. Int. J. Forecast. 27(3), 689–699 (2011)CrossRefGoogle Scholar
  6. 6.
    Catania, L., Grassi, S., Ravazzolo, F.: Forecasting cryptocurrencies financial time series. In: CAMP Working Paper Series 3, BI Norwegian Business School (2018)Google Scholar
  7. 7.
    Catania, L., Grassi, S., Ravazzolo, F.: Predicting the volatility of cryptocurrency time-series. In: CAMP Working Paper Series 5, BI Norwegian Business School (2018)Google Scholar
  8. 8.
    De Stefani, J., Caelen, O., Hattab, D., Bontempi, G.: Machine learning for multi-step ahead forecasting of volatility proxies. In: 2nd Workshop on MIning DAta for Financial Applications (MIDAS). CEUR Workshop Proceedings, Aachen, vol. 1941, pp. 17–28 (2017).
  9. 9.
    De Stefani, J., Le Borgne, Y.A., Caelen, O., Hattab, D., Bontempi, G.: Batch and incremental dynamic factor machine learning for multivariate and multi-step-ahead forecasting.
  10. 10.
    Degiannakis, S.: Multiple days ahead realized volatility forecasting: single, combined and average forecasts. Glob. Financ. J. 36, 41–61 (2018)CrossRefGoogle Scholar
  11. 11.
    ElBahrawy, A., Alessandretti, L., Kandler, A., Pastor-Satorras, R., Baronchelli, A.: Evolutionary dynamics of the cryptocurrency market. Roy. Soc. Open Sci. 4(11), 170623 (2017)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Engle III, R.F., Ito, T., Lin, W.L.: Meteor showers or heat waves? Heteroskedastic intra-daily volatility in the foreign exchange market (1988)Google Scholar
  13. 13.
    Fengler, M.R., Herwartz, H., Raters, F.: Multivariate volatility models. In: Härdle, W.K., Hautsch, N., Overbeck, L. (eds.) Applied Quantitative Finance, pp. 25–37. Springer, Heidelberg (2017). Scholar
  14. 14.
    Forni, M., Hallin, M., Lippi, M., Reichlin, L.: The generalized dynamic factor model. J. Am. Stat. Assoc. 100(471), 830–840 (2005). Scholar
  15. 15.
    Franses, P., Legerstee, R.: A unifying view on multi-step forecasting using an autoregression. J. Econ. Surv. 24(3), 389–401 (2010)Google Scholar
  16. 16.
    Garman, M.B., Klass, M.J.: On the estimation of security price volatilities from historical data. J. Bus. 53(1), 67–78 (1980)CrossRefGoogle Scholar
  17. 17.
    Graves, A.: Supervised Sequence Labelling with Recurrent Neural Networks. Springer, Heidelberg (2012). Scholar
  18. 18.
    Hafner, C.M., Herwartz, H.: Structural analysis of portfolio risk using beta impulse response functions. Statistica Neerlandica 52(3), 336–355 (1998)CrossRefGoogle Scholar
  19. 19.
    Hansen, P.R., Lunde, A.: A forecast comparison of volatility models: does anything beat a garch (1, 1)? J. Appl. Econometrics 20(7), 873–889 (2005)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Hochreiter, S., Schmidhuber, J.: Long short-term memory. Neural Comput. 9(8), 1735–1780 (1997)CrossRefGoogle Scholar
  21. 21.
    Kim, H.Y., Won, C.H.: Forecasting the volatility of stock price index: a hybrid model integrating LSTM with multiple GARCH-type models. Expert Syst. Appl. 103, 25–37 (2018)CrossRefGoogle Scholar
  22. 22.
    Kim, J.M., Jung, H.: Time series forecasting using functional partial least square regression with stochastic volatility, GARCH, and exponential smoothing. J. Forecast. 37(3), 269–280 (2018)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Lipton, Z.C., Berkowitz, J., Elkan, C.: A critical review of recurrent neural networks for sequence learning. arXiv preprint arXiv:1506.00019 (2015)
  24. 24.
    Parkinson, M.: The extreme value method for estimating the variance of the rate of return. J. Bus. 53(1), 61–65 (1980)CrossRefGoogle Scholar
  25. 25.
    Peng, Y., Albuquerque, P.H.M., de Sá, J.M.C., Padula, A.J.A., Montenegro, M.R.: The best of two worlds: forecasting high frequency volatility for cryptocurrencies and traditional currencies with support vector regression. Expert Syst. Appl. 97, 177–192 (2018)CrossRefGoogle Scholar
  26. 26.
    Petneházi, G., Gáll, J.: Exploring the predictability of range-based volatility estimators using rnns. arXiv preprint arXiv:1803.07152 (2018)
  27. 27.
    Poon, S.H., Granger, C.W.: Forecasting volatility in financial markets: a review. J. Econ. Lit. 41(2), 478–539 (2003)CrossRefGoogle Scholar
  28. 28.
    Stock, J., Watson, M.: Dynamic factor models. In: Clements, M., Hendry, D. (eds.) Oxford Handbook of Economic Forecasting. Oxford University Press, Oxford (2010)Google Scholar
  29. 29.
    Tashman, L.J.: Out-of-sample tests of forecasting accuracy: an analysis and review. Int. J. Forecast. 16(4), 437–450 (2000). The M3-CompetitionCrossRefGoogle Scholar
  30. 30.
    Tsay, R.S.: Analysis of Financial Time Series, vol. 543. Wiley, Hoboken (2005)CrossRefGoogle Scholar
  31. 31.
    Vincent, P., Larochelle, H., Lajoie, I., Bengio, Y., Manzagol, P.A.: Stacked denoising autoencoders: learning useful representations in a deep network with a local denoising criterion. J. Mach. Learn. Res. 11, 3371–3408 (2010)MathSciNetzbMATHGoogle Scholar
  32. 32.
    Walther, T., Klein, T.: Exogenous drivers of cryptocurrency volatility - a mixed data sampling approach to forecasting (2018).
  33. 33.
    Yu, S.L., Li, Z.: Forecasting stock price index volatility with LSTM deep neural network. In: Tavana, M., Patnaik, S. (eds.) Recent Developments in Data Science and Business Analytics. SPBE, pp. 265–272. Springer, Cham (2018). Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.MLG, Departement d’InformatiqueUniversité Libre de BruxellesBrusselsBelgium
  2. 2.Worldline SA/NV R&DBrusselsBelgium
  3. 3.Equens Worldline R&DLilleFrance

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