Operational Research

, Volume 6, Issue 2, pp 103–127 | Cite as

Financial forecasting through unsupervised clustering and neural networks

  • N. G. Pavlidis
  • V. P. Plagianakos
  • D. K. Tasoulis
  • M. N. Vrahatis


In this paper, we review our work on a time series forecasting methodology based on the combination of unsupervised clustering and artificial neural networks. To address noise and non-stationarity, a common approach is to combine a method for the partitioning of the input space into a number of subspaces with a local approximation scheme for each subspace. Unsupervised clustering algorithms have the desirable property of deciding on the number of partitions required to accurately segment the input space during the clustering process, thus relieving the user from making this ad hoc choice. Artificial neural networks, on the other hand, are powerful computational models that have proved their capabilities on numerous hard real-world problems. The time series that we consider are all daily spot foreign exchange rates of major currencies. The experimental results reported suggest that predictability varies across different regions of the input space, irrespective of clustering algorithm. In all cases, there are regions that are associated with a particularly high forecasting performance. Evaluating the performance of the proposed methodology with respect to its profit generating capability indicates that it compares favorably with that of two other established approaches. Moving from the task of one-step-ahead to multiple-step-ahead prediction, performance deteriorates rapidly.


Time Series Modeling and Prediction Unsupervised Clustering Neural Networks 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alevizos P., Boutsinas B., Tasoulis D.K., Vrahatis M.N. (2002). Improving the orthogonal range searchk-windows clustering algorithm. Proceedings of the 14th IEEE International Conference on Tools with Artificial Intelligence, 239–245.Google Scholar
  2. Alevizos P.,Tasoulis D.K., Vrahatis M.N. (2004). Parallelizing the unsupervisedk-windows clustering algorithm. Parallel Processing and Applied Mathematics (eds. R. Wyrzykowski, J. Dongarra, M. Paprzycki, and J. Wasniewski), Springer-Verlag, Lecture Notes in Computer Science vol. 3019, 225–232.Google Scholar
  3. Allen F., Karjalainen R. (1999). Using genetic algorithms to find technical trading rules. Journal of Financial Economics vol. 51, 245–271.CrossRefGoogle Scholar
  4. Bakker R., Schouten J.C., Giles C.L., Takens F., van den Bleek C.M. (2000). Learning of chaotic attractors by neural networks. Neural Computation vol. 12, 2355–2383.CrossRefGoogle Scholar
  5. Bezdek J.C. (1981). Pattern recognition with fuzzy objective function algorithms, Kluwer Academic Publishers.Google Scholar
  6. Cao L. (2003). Support vector machines experts for time series forecasting. Neurocomputing vol. 51, 321–329.CrossRefGoogle Scholar
  7. Clerc M., Kennedy J. (2002). The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation vol. 6, 58–73.CrossRefGoogle Scholar
  8. de Bodt E., Rynkiewicz J., and Cottrell M. (2001). Some known facts about financial data. Proceedings of European Symposium on Artificial Neural Networks (ESANN’2001), 223–236.Google Scholar
  9. Diks C., van Zwet W.R., Takens F., DeGoede J. (1996). Detecting differences between delay vector distributions. Physical Review E vol. 53, 2169–2176.CrossRefGoogle Scholar
  10. Eberhart R.C., Simpson P., Dobbins R. (1996). Computational intelligence PC tools. Academic Press.Google Scholar
  11. Ester M., Kriegel H.P., Sander J., Xu X. (1996). A density-based algorithm for discovering clusters in large spatial databases with noise. Proceedings of the 2nd Int. Conf. on Knowledge Discovery and Data Mining, 226–231.Google Scholar
  12. Farmer J.D., Sidorowich J.J. (1987). Predicting chaotic time series. Physical Review Letters vol. 59, 845–848.CrossRefGoogle Scholar
  13. Frankel J.A., Rose A.K. (1995). Empirical research on nominal exchange rates. Handbook of International Economics (eds. G. Grossman and K. Rogoff), Amsterdam, North-Holland, vol. 3, 1689–1729.Google Scholar
  14. Fraser A.M. (1989). Information and entropy in strange attractors. IEEE Transactions on Information Theory vol. 35, 245–262.CrossRefGoogle Scholar
  15. Fritzke B. (1995). A growing neural gas network learns topologies. Advances in Neural Information Processing Systems (eds. G. Tesauro, D.S. Touretzky, and T.K. Leen), MIT Press, Cambridge MA, 625–632.Google Scholar
  16. Giles L.C., Lawrence S., Tsoi A.H. (2001). Noisy time series prediction using a recurrent neural network and grammatical inference. Machine Learning vol. 44, 161–183.CrossRefGoogle Scholar
  17. Hartigan J.A., Wong M.A. (1979). Ak-means clustering algorithm. Applied Statistics vol. 28, 100–108.CrossRefGoogle Scholar
  18. Hastie T., Tibshirani R., Friedman J. (2001). The elements of statistical learning. Springer-Verlag.Google Scholar
  19. Haykin S. (1999). Neural networks: A comprehensive foundation. New York: Macmillan College Publishing Company.Google Scholar
  20. Igel C., Husken M. (2000). Improving the Rprop learning algorithm. Proceedings of the Second International ICSC Symposium on Neural Computation (NC 2000) (H. Bothe and R. Rojas, eds.), ICSC Academic Press, 115–121.Google Scholar
  21. Kennel M.B., Brown R., Abarbanel H.D. (1992). Determining embedding dimension for phase—space reconstruction using a geometrical construction. Physical Review A vol. 45, 3403–3411.CrossRefGoogle Scholar
  22. Keogh E, and Folias T. (2002). The UCR time series data mining archive.Google Scholar
  23. Kohonen T. (1997). Self-organized maps. Berlin: Springer.Google Scholar
  24. Magoulas G.D., Plagianakos V.P., Vrahatis M.N. (2001). Adaptive stepsize algorithms for on-line training of neural networks. Nonlinear Analysis: Theory Methods and Applications A vol. 47, 3425–3430.CrossRefGoogle Scholar
  25. Meese R.A., Rogoff K. (1983). Empirical exchange rate models of the seventies: do they fit out-of-sample? Journal of International Economics vol. 14, 3–24.CrossRefGoogle Scholar
  26. Meese R.A., Rogoff K. (1986). Was it real? the exchange rate-interest differential relation over the modern floating-rate period. The Journal of Finance vol. 43, 933–948.CrossRefGoogle Scholar
  27. Milidiu R.L., Machado R.J., Renteria R.~P. (1999). Time-series forecasting through wavelets transformation and a mixture of expert models. Neurocomputing vol. 28 145–156.CrossRefGoogle Scholar
  28. Moller M. (1993). A scaled conjugate gradient algorithm for fast supervised learning. Neural Networks vol. 6, 525–533.CrossRefGoogle Scholar
  29. Bank of International Settlements. (2001). Central bank survey of foreign exchange and derivative market activity in April 2001. Bank of International Settlements.Google Scholar
  30. Parsopoulos K.E., Vrahatis M.N. (2002). Recent approaches to global optimization problems through particle swarm optimization. Natural Computing vol. 1235–1306.Google Scholar
  31. Pavlidis N.G., Tasoulis D.K., Plagianakos V.P., Siriopoulos C., Vrahatis M.N. (2005). Computational intelligence methods for financial forecasting. Proceedings of the International Conference of Computational Methods in Sciences and Engineering (ICCMSE 2005) (ed. T.E. Simos), Lecture Series on Computer and Computational Sciences vol. 4, 1416–1419.Google Scholar
  32. Pavlidis N.G., Tasoulis D.K., Plagianakos V.P., Vrahatis M.N. (2005). Time series forecasting methodology for multiple-step-ahead prediction. Proceedings of IASTED International Conference on Computational Intelligence (CI2005), 456–461.Google Scholar
  33. Pavlidis N.G., Tasoulis D.K., Plagianakos V.P., Vrahatis M.N. Computational intelligence methods for financial time series modeling. International Journal of Bifurcation and Chaos (in press).Google Scholar
  34. Pinkus A. (1999). Approximation theory of the MLP model in neural networks. Acta Numerica, 143–195.Google Scholar
  35. Plagianakos V.P., Magoulas G.D., Vrahatis M.N. (2000). Global learning rate adaptation in on-line neural network training. Proceedings of the Second International ICSC Symposium on Neural Computation (NC 2000).Google Scholar
  36. Plagianakos V.P., Vrahatis M.N. (2002). Parallel evolutionary training algorithms for “hardware-friendly” neural networks. Natural Computing vol. 1, 307–322.CrossRefGoogle Scholar
  37. Principe J.C., Wang L., Motter M.A. (1998). Local dynamic modeling with self-organizing maps and applications to nonlinear system identification and control. Proceedings of the IEEE vol. 86, 2240–2258.CrossRefGoogle Scholar
  38. Refenes A.N., Holt W.T. (2004). Forecasting volatility with neural regression: A contribution to model adequacy. IEEE Transactions on Neural Networks vol. 12, 850–864.CrossRefGoogle Scholar
  39. Riedmiller M., Braun H. (1993). A direct adaptive method for faster backpropagation learning: The Rprop algorithm. Proceedings of the IEEE International Conference on Neural Networks, San Francisco, CA, 586–591.Google Scholar
  40. Sandberg I.W., Xu L. (1997). Uniform approximation and gamma networks. Neural Networks vol. 10, 781–784.CrossRefGoogle Scholar
  41. Sandberg I.W., Xu L. (1997). Uniform approximation of multidimensional myopic maps. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications vol. 44, 477–485.CrossRefGoogle Scholar
  42. Sander J., Ester M., Kriegel H.-P., Xu X. (1998). Density-based clustering in spatial databases: The algorithm gdbscan and its applications. Data Mining and Knowledge Discovery vol. 2, 169–194.CrossRefGoogle Scholar
  43. Sfetsos A., Siriopoulos C. (2004). Time series forecasting with a hybrid clustering scheme and pattern recognition. IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans vol. 34, 399–405.CrossRefGoogle Scholar
  44. Storn R., Price K. (1997). Differential evolution — a simple and efficient adaptive scheme for global optimization over continuous spaces. Journal of Global Optimization vol. 11, 341–359.CrossRefGoogle Scholar
  45. Sutton R.S., Whitehead S.D. (1993). Online learning with random representations. Proceedings of the Tenth International Conference on Machine Learning, Morgan Kaufmann, 314–321.Google Scholar
  46. Takens F. (1981). Detecting strange attractors in turbulence. Dynamical Systems and Turbulence (eds. D.A. Rand and L.S. Young), Lecture Notes in Mathematics, vol. 898, Springer, 366–381.Google Scholar
  47. Tasoulis D.K., Vrahatis M.N. (2004). Unsupervised distributed clustering. IASTED International Conference on Parallel and Distributed Computing and Networks, 347–351.Google Scholar
  48. Tasoulis D.K., Vrahatis M.N. (2005). Unsupervised clustering on dynamic databases. Pattern Recognition Letters vol. 26, 2116–2127.CrossRefGoogle Scholar
  49. Vrahatis M.N., Boutsinas B., Alevizos P., Pavlides G. (2002). The newk-windows algorithm for improving thek-means clustering algorithm. Journal of Complexity vol. 18, 375–391.CrossRefGoogle Scholar
  50. Walczak S., (2001). An empirical analysis of data requirements for financial forecasting with neural networks. Journal of Management Information Systems vol. 17, 203–222.Google Scholar
  51. Weigend A.S., Mangeas M., Srivastava A.N. (1995). Nonlinear gated experts for time series: Discovering regimes and avoiding overfitting. International Journal of Neural Systems vol. 6, 373–399.CrossRefGoogle Scholar
  52. White H. (1990). Connectionist nonparametric regression: Multilayer feedforward networks can learn arbitrary mappings. Neural Networks vol. 3, 535–549.CrossRefGoogle Scholar
  53. Wilson D.R., Martinez T.R. (1997). Improved heterogeneous distance functions. Journal of Artificial Intelligence Research vol. 6, 1–34.Google Scholar
  54. Yao J., Tan C.L. (2000). A case study on using neural networks to perform technical forecasting of forex. Neurocomputing vol. 34, 79–98.CrossRefGoogle Scholar

Copyright information

© Hellenic Operational Research Society 2006

Authors and Affiliations

  • N. G. Pavlidis
    • 1
    • 2
  • V. P. Plagianakos
    • 1
    • 2
  • D. K. Tasoulis
    • 1
    • 2
  • M. N. Vrahatis
    • 1
    • 2
  1. 1.Computational Intelligence Laboratory (CI Lab), Department of MathematicsUniversity of PatrasGreece
  2. 2.University of Patras Artificial Intelligence Research Center (UPAIRC)PatrasGreece

Personalised recommendations