Computational Economics

, Volume 47, Issue 2, pp 219–253 | Cite as

Financial Time Series Modeling and Prediction Using Postfix-GP

  • Vipul K. Dabhi
  • Sanjay Chaudhary


Financial time series prediction is considered as a challenging task. The task becomes difficult due to inherent nonlinear and non-stationary characteristics of financial time series. This article proposes a combination of wavelet and Postfix-GP, a postfix notation based genetic programming system, for financial time series prediction. The discrete wavelet transform approach is used to smoothen the time series by separating the fluctuations from the trend of the series. Postx-GP is then employed to evolve models for the smoothen series. The out-of-sample prediction capability of evolved solutions is tested on two stocks price and two stock indexes series. The results are compared with those obtained using ECJ, a Java based evolutionary framework. The nonparametric statistical tests are applied to evaluate the significance of the obtained results.


Financial time series prediction Postfix genetic programming One-step prediction Multi-step prediction 


  1. Abarbanel, H. D., Brown, R., Sidorowich, J. J., & Tsimring, L. S. (1993). The analysis of observed chaotic data in physical systems. Reviews of modern physics, 65(4), 1331.CrossRefGoogle Scholar
  2. Abarbanel, H. D., & Gollub, J. P. (1996). Analysis of observed chaotic data. Physics Today, 49, 86.CrossRefGoogle Scholar
  3. Ahalpara, D., & Parikh, J. (2008). Genetic programming based approach for modeling time series data of real systems. International Journal of Modern Physics C, 19(01), 63–91.CrossRefGoogle Scholar
  4. Atsalakis, G. S., & Valavanis, K. P. (2009). Forecasting stock market short-term trends using a neuro-fuzzy based methodology. Expert Systems with Applications, 36(7), 10 696–10 707.CrossRefGoogle Scholar
  5. Beran, J., Shumeyko, Y., et al. (2012). On asymptotically optimal wavelet estimation of trend functions under long-range dependence. Bernoulli, 18(1), 137–176.CrossRefGoogle Scholar
  6. Brabazon, A., O’Neill, M., & Dempsey, I. (2008). An introduction to evolutionary computation in finance. Computational Intelligence Magazine, IEEE, 3(4), 42–55.CrossRefGoogle Scholar
  7. Chang, P.-C., & Fan, C.-Y. (2008). A hybrid system integrating a wavelet and tsk fuzzy rules for stock price forecasting. Systems, Man, and Cybernetics, Part C: Applications and Reviews, IEEE Transactions on, 38(6), 802–815.CrossRefGoogle Scholar
  8. Chatfield, C. (2003). The analysis of time series: An introduction. Boca Raton: CRC Press.Google Scholar
  9. Cheng, H. (2004). Self-similar, chaos and fractal matlab toolbox.
  10. Dabhi, V., & Chaudhary, S. (2013). Semantic sub-tree crossover operator for postfix genetic programming. In J. C. Bansal, P. K. Singh, K. Deep, M. Pant, & A. K. Nagar (Eds.), Proceedings of seventh international conference on bio-inspired computing: Theories and applications (BIC-TA 2012) (Vol. 201, pp. 391–402). Advances in intelligent systems and computing. Springer.Google Scholar
  11. Dabhi, V., & Vij, S. (2011). Empirical modeling using symbolic regression via postfix genetic programming. In Image Information Processing (ICIIP), 2011 International Conference on (pp. 1–6).Google Scholar
  12. Daubechies, I. (1992). Ten lectures on wavelets. Philadelphia: SIAM.CrossRefGoogle Scholar
  13. Ferreira, C. (2001). Gene expression programming: A new adaptive algorithm for solving problems. Complex Systems, 13(2), 87–129.Google Scholar
  14. García, S., Molina, D., Lozano, M., & Herrera, F. (2009). A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: A case study on the cec’2005 special session on real parameter optimization. Journal of Heuristics, 15(6), 617–644.CrossRefGoogle Scholar
  15. Grosan, C., & Abraham, A. (2006). Stock market modeling using genetic programming ensembles. Genetic systems programming (pp. 131–146). Berlin: Springer.CrossRefGoogle Scholar
  16. Gustafson, S., Burke, E., & Krasnogor, N. (2005). On improving genetic programming for symbolic regression. In Evolutionary computation, 2005. The 2005 IEEE congress on (Vol. 1, pp. 912–919). IEEE.Google Scholar
  17. Hansen, J. V., & Nelson, R. D. (1997). Neural networks and traditional time series methods: A synergistic combination in state economic forecasts. Neural Networks, IEEE Transactions on, 8(4), 863–873.CrossRefGoogle Scholar
  18. Holland, J. H. (1992). Adaptation in natural and artificial Systems: An introductory analysis with applications to biology, control and artificial intelligence. Cambridge, USA: MIT Press.Google Scholar
  19. Hong Tan, B. (1995). Neural network model for stock forecasting, Ph.D. dissertation, Texas Tech University.Google Scholar
  20. Hsieh, T.-J., Hsiao, H.-F., & Yeh, W.-C. (2011). Forecasting stock markets using wavelet transforms and recurrent neural networks: An integrated system based on artificial bee colony algorithm. Applied Soft Computing, 11(2), 2510–2525.CrossRefGoogle Scholar
  21. Huang, S.-C., & Wu, T.-K. (2010). Integrating recurrent SOM with wavelet-based kernel partial least square regressions for financial forecasting. Expert Systems with Applications, 37(8), 5698–5705.CrossRefGoogle Scholar
  22. Huang, S.-C. (2011). Forecasting stock indices with wavelet domain kernel partial least square regressions. Applied Soft Computing, 11(8), 5433–5443.CrossRefGoogle Scholar
  23. Iba, H., & Sasaki, T. (1999). Using genetic programming to predict financial data. In Evolutionary computation, 1999. CEC 99. Proceedings of the 1999 congress on (Vol. 1, pp. 244–251).Google Scholar
  24. Kaboudan, M. A. (2000). Genetic programming prediction of stock prices. Computational Economics, 16(3), 207–236.CrossRefGoogle Scholar
  25. Kampouridis, M., & Tsang, E. (2010). Eddie for investment opportunities forecasting: Extending the search space of the gp. In Evolutionary computation (CEC). IEEE congress on, 2010 (pp. 1–8).Google Scholar
  26. Kantz, H., & Schreiber, T. (1997). Nonlinear time series analysis. Cambridge nonlinear science series. Cambridge: Cambridge University Press.Google Scholar
  27. Kara, Y., Acar Boyacioglu, M., & Baykan, O. K. (2011). Predicting direction of stock price index movement using artificial neural networks and support vector machines: The sample of the istanbul stock exchange. Expert Systems with Applications, 38(5), 5311–5319.CrossRefGoogle Scholar
  28. Kazem, A., Sharifi, E., Hussain, F. K., Saberi, M., & Hussain, O. K. (2012). Support vector regression with chaos-based firefly algorithm for stock market price forecasting. Applied Soft Computing, 13, 947–958.CrossRefGoogle Scholar
  29. Keith, M. J., & Martin, M. C. (1994). Genetic programming in c++: Implementation issues. Advances in Genetic Programming, 1, 285–310.Google Scholar
  30. Kennel, M., Brown, R., & Abarbanel, H. D. I. (1992). Determining embedding dimension for phase-space reconstruction using a geometrical construction. Physical Review A, 45, 3403–3411.CrossRefGoogle Scholar
  31. Kim, K.-J. (2003). Financial time series forecasting using support vector machines. Neurocomputing, 55(1), 307–319.CrossRefGoogle Scholar
  32. Koza, J. R. (1992). Genetic programming: On the programming of computers by means of natural selection. Cambridge: MIT Press.Google Scholar
  33. Laumanns, M., Thiele, L., Zitzler, E., & Deb, K. (2002). Archiving with guaranteed convergence and diversity in multi-objective optimization. In Proceedings of the genetic and evolutionary computation conference (GECCO) (pp. 439–447), GECCO ’02. San Francisco, CA, USA: Morgan Kaufmann Publishers Inc.Google Scholar
  34. Li, J., & Taiwo, S. ( 2006). Enhancing financial decision making using multi-objective financial genetic programming. In Evolutionary computation, 2006. CEC 2006. IEEE congress on(pp. 2171–2178). IEEE.Google Scholar
  35. Li, J., Shi, Z., & Li, X. (2006). Genetic programming with wavelet-based indicators for financial forecasting. Transactions of the Institute of Measurement and Control, 28(3), 285–297.CrossRefGoogle Scholar
  36. Lopes, H. S., & Weinert, W. R. (2004). A gene expression programming system for time series modeling. In Proceedings of XXV Iberian Latin American congress on computational methods in engineering (CILAMCE), Recife (Brazil) (pp. 10–12).Google Scholar
  37. Luke, S., Panait, L., Balan, G., & Et (2007). ECJ 16: A java-based evolutionary computation research system. Accessed 13 Jan 2014.
  38. Majhi, R., Panda, G., & Majhi, B. (2009). Efficient prediction of stock market indices using adaptive bacterial foraging optimization (abfo) and BFO based techniques. Expert Systems with Applications, 36(6), 10 097–10 104.CrossRefGoogle Scholar
  39. Mallat, S. (1999). A wavelet tour of signal processing. Academic Press.Google Scholar
  40. Manimaran, P., Parikh, J., Panigrahi, P., Basu, S., Kishtawal, C., & Porecha, M. (2006). Modelling financial time series. Econophysics of stock and other markets (pp. 183–191). Milan: Springer.CrossRefGoogle Scholar
  41. Porecha, M., Panigrahi, P., Parikh, J., Kishtawal, C., & Basu, S. (2005). Forecasting non-stationary financial time series through genetic algorithm. arXiv:nlin/0507037v1.
  42. Potvin, J.-Y., Soriano, P., & Vallée, M. (2004). Generating trading rules on the stock markets with genetic programming. Computers & Operations Research, 31(7), 1033–1047.CrossRefGoogle Scholar
  43. Saad, E. W., Prokhorov, D. V., & W, D. C, I. I. (1998). Comparative study of stock trend prediction using time delay, recurrent and probabilistic neural networks. IEEE Transactions on Neural Networks, 9(6), 1456–1470.CrossRefGoogle Scholar
  44. Santini, M., & Tettamanzi, A. (2001). Genetic programming for financial time series prediction. In Proceedings of the 4th European Conference on Genetic Programming, ser. EuroGP ’01(pp. 361–370). London, UK: Springer.Google Scholar
  45. Takens, F. (1980). Detecting strange attractors in turbulence. In D. A. Rand & L. S. Young (Eds.), Dynamical systems and turbulence (pp. 366–381). New York: Spinger.Google Scholar
  46. Tan, T. Z., Quek, C., & Ng, G. S. (2005). Brain-inspired genetic complementary learning for stock market prediction. In Congress on evolutionary computation. IEEE (pp. 2653–2660).Google Scholar
  47. Uy, N. Q., Hoai, N. X., & O’Neill, M. (2009). Semantic aware crossover for genetic programming: The case for real-valued function regression. Proceedings of the 12th European conference on genetic programming (pp. 292–302)., EuroGP ’09 Berlin: Springer.Google Scholar
  48. Uy, N. Q., Hoai, N. X., O’Neill, M., Mckay, R. I., & Galván-López, E. (2011). Semantically-based crossover in genetic programming: Application to real-valued symbolic regression. Genetic Programming and Evolvable Machines, 12, 91–119.CrossRefGoogle Scholar
  49. Vapnik, V. (2000). The nature of statistical learning theory. New York: Springer.CrossRefGoogle Scholar
  50. Vasanthi, D., Subha, D., & Nambi, M. S. T. (2011). An empirical study on stock index trend prediction using markov chain analysis. Journal of Banking Financial Services and Insurance Research, 1, 72–91.Google Scholar
  51. Wagner, N., Michalewicz, Z., Khouja, M., & McGregor, R. R. (2007). Time series forecasting for dynamic environments: the dyfor genetic program model. Evolutionary Computation, IEEE Transactions on, 11(4), 433–452.CrossRefGoogle Scholar
  52. Wang, W., & Ding, J. (2003). Wavelet network model and its application to the prediction of hydrology. Nature and Science, 1(1), 67–71.Google Scholar
  53. Yeh, C.-Y., Huang, C.-W., & Lee, S.-J. (2011). A multiple-kernel support vector regression approach for stock market price forecasting. Expert Systems with Applications, 38(3), 2177–2186.CrossRefGoogle Scholar
  54. Zhang, G., & Hu, M. Y. (1998). Neural network forecasting of the british pound/us dollar exchange rate. Omega, 26(4), 495–506.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Information TechnologyDharmsinh Desai UniversityNadiadIndia
  2. 2.Institute of Engineering and TechnologyAhmedabad UniversityAhmadabadIndia

Personalised recommendations