Abstract
Financial time series forecasting has been a challenge for time series analysts and researchers because it is noisy, nonstationary and chaotic. To overcome this limitation, this study uses empirical mode decomposition (EMD) and phase space reconstruction (PSR) to assist in the task of financial time series forecasting. In addition, we propose an approach that combines these two data preprocessing methods with extreme learning machine (ELM). The approach contains four steps as follows. (1) EMD is used to decompose the dynamics of the exchange rate time series into several components of intrinsic mode function (IMF) and one residual component. (2) The IMF and residual time series phase space is reconstructed to reveal its unseen dynamics according to the optimum time delay \(\tau \) and embedding dimension m. (3) The reconstructed time series datasets are divided into two datasets: training and testing, in which the training datasets are used to build ELM models. (4) A regression forecast model is set up for each IMF as well as the residual component by using ELM. The final prediction results are obtained by compositing the prediction values. To verify the effectiveness of the proposed approach, four exchange rates are chosen as the forecasting targets. Compared with some existing state-of-the-art models, the proposed approach yields superior results. Academically, we demonstrated the validity and superiority of the proposed approach that integrates EMD, PSR, and ELM. Corporations or individuals can apply the results of this study to acquire accurate exchange rate information and reduce exchange rate expenses.
Similar content being viewed by others
References
Adhikari, R., & Agrawal, R. K. (2013). A combination of artificial neural network and random walk models for financial time series forecasting. Neural Computing and Applications, 24(6), 1441–1449.
Babovic, V., Keijzer, M., & Bundzel, M. (2000). From global to local modelling: A case study in error correction of deterministic models. In Proceedings of Fourth International Conference on Hydroinformatics, Iowa City, USA: CD-ROM, IAHR
Bao, Y. K., Xiong, T., & Hu, Z. Y. (2012). Forecasting air passenger traffic by support vector machines with ensemble empirical mode decomposition and slope-based method. Discrete Dynamics in Nature and Society, 2012
Barkoulas, J., & Travos, N. (1998). Chaos in an emerging capital market? The case of Athens stock exchange. Applied Financial Economics, 8, 231–243.
Chen, C. F., Lai, M. C., & Yeh, C. C. (2012). Forecasting tourism demand based on empirical mode decomposition and neural network. Knowledge-Based Systems, 26, 281–287. doi:10.1016/j.knosys.2011.09.002.
Chen, F. L., & Ou, T. Y. (2011). Sales forecasting system based on Gray extreme learning machine with Taguchi method in retail industry. Expert Systems with Applications, 38(3), 1336–1345. doi:10.1016/j.eswa.2010.07.014.
Chen, K. L., Yeh, C. C., & Lu, T. L. (2012). A hybrid demand forecasting model based on empirical mode decomposition and neural network in TFT-LCD industry. Cybernetics and Systems, 43(5), 426–441.
Deng, S. K., Yoshiyama, K., Mitsubuchi, T., & Sakurai, A. (2015). Hybrid method mf Multiple kernel learning and genetic algorithm for forecasting short-term foreign exchange rates. Computational Economics, 45(1), 49–89. doi:10.1007/s10614-013-9407-6.
GEP, B., & GM, J. (1970). Time Series Analysis Forecasting and Control (3rd ed.). CA: Holden-Day.
Gimore, C. G. (2001). An examination of nonlinear dependence in exchange rates, using recent methods from chaos theory. Global Finance Journal, 12, 139–151.
Hadavandi, E., Shavandi, H., & Ghanbari, A. (2010). Integration of genetic fuzzy systems and artificial neural networks for stock price forecasting. Knowledge-Based System, 23(8), 800–808.
Huang, G. B., Chen, L., & Siew, C. K. (2006a). Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Transactions on Neural Networks, 17(4), 879–892. doi:10.1109/TNN.2006.875977.
Huang, G. B., Zhu, Q. Y., & Siew, C. K. (2006b). Extreme learning machine: Theory and applications. Neurocomputing, 70(1–3), 489–501. doi:10.1016/j.neucom.2005.12.126.
Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., et al. (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society A, 454(1971), 903–995.
Huang, N. E., Wu, M. L. C., Long, S. R., Shen, S. S. P., Qu, W., Gloersen, P., et al. (2003). A confidence limit for the empirical mode decomposition and Hilbert spectral analysis. Proceedings of the Royal Society A, 459(2037), 2317–2345.
Huang, S. C., Chuang, P. J., Wu, C. F., & Lai, H. J. (2010). Chaos-based support vector regressions for exchange rate forecasting. Expert Systems with Applications, 37(12), 8590–8598. doi:10.1016/j.eswa.2010.06.001.
Jaeger, H., & Haas, H. (2004). Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication. Science, 304(5667), 78–80.
Kazem, A., Sharifi, E., Hussain, F. K., Saberi, M., & Hussain, O. K. (2013). Support vector regression with chaos-based firefly algorithm for stock market price forecasting. Applied Soft Somputing, 13(2), 947–958. doi:10.1016/j.asoc.2012.09.024.
Kennel, M. B., Brown, R., & Abarbanel, H. D. I. (1992). Determining embedding dimension for phase-space reconstruction using a geometrical construction. Physical Review A, 45(6), 3403–3411.
Lemke, C., & Gabrys, B. (2010). Meta-learning for time series forecasting and forecast combination. Neurocomputing, 73(10–12), 2006–2016.
Liong, S. Y., & Sivapragasam, C. (2002). Flood stage forecasting with SVM. Journal of the American Water Resources Association, 38(1), 173–186.
Liu, H., & Wang, J. (2011). Integrating independent component analysis and principal component analysis with neural network to predict chinese stock market. Mathematical Problems in Engineering, 2011, 15.
Lu, C. J. (2010). Integrating independent component analysis-based denoising scheme with neural network for stock price prediction. Expert Systems with Applications, 37(10), 7056–7064.
Lu, C. J., Lee, T. S., & Chiu, C. C. (2009). Financial time series forecasting using independent component analysis and support vector regression. Decision Support Systems, 47(2), 115–125. doi:10.1016/j.dss.2009.02.001.
Lu, C. J., & Shao, Y. E. (2012). Forecasting computer products sales by integrating ensemble empirical mode decomposition and extreme learning machine. Mathematical Problems in Engineering, 2012, 15.
Makridakis, S. (1993). Accuracy measures: Theoretical and practical concerns. International Journal of Forecasting, 9(4), 527–529.
McKenzie, M. D. (2001). Chaotic behavior in national stock market indices: New evidence from the close returns test. Global Finance Journal, 12, 35–53.
Meese, R., & Rogoff, K. (1983). Empirical exchange rate models of the seventies: Do they fit out of sample? Journal of International Economics, 14(1–2), 3–24.
Rao, C. R., & Mitra, S. K. (1971). Generalized inverse of matrices and its applications. New York: Wiley.
Sauer, T., Yorke, J. A., & Casdagli, M. (1991). Embedology. Journal of Statistical Physics, 65(3/4), 579–616.
Sun, Y. (2005). Exchange rate forecasting with an artificial neural network model: Can we beat a random walk model?. New Zealand: Lincoln University.
Takens, F. (1981). Detecting strange attractors in turbulence. Dynamical Systems and Turbulence, 898, 366–381.
Tyree, A., & Long, J. (1995). Forecasting currency exchange rates: neural networks and the random walk model. In Proceedings of the Third International Conference on Artificial Intelligence Applications. New York: Wall Street
Vasilakis, G. A., Theofilatos, K. A., Georgopoulos, E. F., Karathanasopoulos, A., & Likothanassis, S. D. (2013). A genetic programming approach for EUR/USD exchange rate forecasting and trading. Computational Economics, 42(4), 415–431. doi:10.1007/s10614-012-9345-8.
Wang, J. D., & Qi, W. G. (2009). Prediction of river water turbidity based on EMD-SVM. Acta Electronica Sinica, 37(10), 2130–2133.
Wang, J. J., Wang, J. Z., Zhang, Z. G., & Guo, S. P. (2012). Stock index forecasting based on a hybrid model. Omega, 40(6), 758–766. doi:10.1016/j.omega.2011.07.008.
Wu, J. L., & Chang, P. C. (2012). A trend-based segmentation method and the support vector regression for financial time series forecasting. Mathematical Problems in Engineering, 2012, 1–20.
Xia, M., Zhang, Y., Weng, L., & Ye, X. (2012). Fashion retailing forecasting based on extreme learning machine with adaptive metrics of inputs. Knowledge-Based Systems, 36, 253–259. doi:10.1016/j.knosys.2012.07.002.
Xuan, Z. Y., & Yang, G. X. (2008). Application of EMD in the atmosphere time series prediction. Acta Automat Sinica, 34(1), 97–101.
Yang, Y. F., Bao, Y. K., Hu, Z. Y., & Zhang, R. (2010). Crude oil price prediction based on empirical mode decomposition and support vector machines. Chinese Journal of Management, 7(12), 1884–1889.
Ye, L., & Liu, P. (2011). Combined model based on EMD-SVM for short-term wind power prediction. Proceedings of the Chinese Society of Electrical Engineering, 31(31), 102–108.
Zhang, G. P. (2003). Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing, 50, 159–175.
Zhang, Y., & Wu, L. (2009). Stock market prediction of S&P 500 via combination of improved BCO approach and BP neural network. Expert Systems with Applications, 36(5), 8849–8854. doi:10.1016/j.eswa.2008.11.028.
Zhiqiang, G., Huaiqing, W., & Quan, L. (2012). Financial time series forecasting using LPP and SVM optimized by PSO. Soft Computing, 17(5), 805–818.
Zhu, B. Z., & Wei, Y. M. (2013). Carbon price forecasting with a novel hybrid ARIMA and least squares support vector machines methodology. Omega, 41, 517–524.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yang, HL., Lin, HC. Applying the Hybrid Model of EMD, PSR, and ELM to Exchange Rates Forecasting. Comput Econ 49, 99–116 (2017). https://doi.org/10.1007/s10614-015-9549-9
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10614-015-9549-9