The forecasting of exchange rates has become a challenging area of research that has attracted many researchers over recent years. This work presents a sliding-window metaheuristic optimization-based forecast system for one-step ahead forecasting. The proposed system is a graphical user interface, which is developed in the MATLAB environment and functions as a stand-alone application. The system integrates the novel firefly algorithm (FA), metaheuristic (Meta) intelligence, and least squares support vector regression (LSSVR), namely MetaFA-LSSVR. The MetaFA automatically tunes the hyperparameters of the LSSVR to construct an optimal LSSVR prediction model. The optimization effectiveness of the MetaFA is verified using ten benchmark functions. Two case studies on the daily Canadian dollar-USD exchange rate (CAN/USD) and the four-hour closing EUR-USD rates (EUR/USD) were used to confirm the performance of the system, in which the mean absolute percentage errors are 0.2532% and 0.169%, respectively. The MetaFA-LSSVR has an 89.8-99.7% greater predictive accuracy than prior work when applied to the currency pair CAN/USD. With respect to the EUR/USD exchange rate, the error rates obtained using the proposed system were up to 23.9% better than those obtained by the LSSVR system. Therefore, the sliding-window metaheuristic system is potentially useful for decision-makers in financial markets.

1. Korol, T., A fuzzy logic model for forecasting exchange rates. Knowledge-Based
Systems, 2014. 67: p. 49-60.
2. Lin, S.-Y., C.-H. Chen, and C.-C. Lo, Currency Exchange Rates Prediction based on
Linear Regression Analysis Using Cloud Computing. International Journal of Grid and
Distributed Computing, 2013. 6: p. 10.
3. Hadavandi, E., H. Shavandi, and A. Ghanbari, Integration of genetic fuzzy systems and
artificial neural networks for stock price forecasting. Knowledge-Based Systems, 2010.
23(8): p. 800-808.
4. Jiang, H. and W. He, Grey relational grade in local support vector regression for
financial time series prediction. Expert Systems with Applications, 2012. 39(3): p. 2256-
2262.
5. Box, G. and G. Jenkins, Time series analysis, forecasting and control. 1970, San
Francisco: CA: Holden-Day.
6. Zhang, G.P., Time series forecasting using a hybrid ARIMA and neural network model.
Neurocomputing, 2003. 50: p. 159-175.
7. Abdoos, A., M. Hemmati, and A.A. Abdoos, Short term load forecasting using a hybrid
intelligent method. Knowledge-Based Systems, 2015. 76: p. 139-147.
8. Kecman, V., Learning and Soft Computing, Support Vector Machines, Neural Networks,
and Fuzzy Logic Models. 2001: MIT Press, Cambridge, MA.
9. Hansen, J.V. and R.D. Nelson, Neural Networks and Traditional Time Series Methods:
A Synergistic Combination in State Economic Forecasts. IEEE TRANSACTIONS ON
NEURAL NETWORKS, 1997. 8: p. 863-873.
10. Yeh, C.-Y., C.-W. Huang, and S.-J. Lee, A multiple-kernel support vector regression
approach for stock market price forecasting. Expert Systems with Applications, 2011.
38(3): p. 2177-2186.
11. Kazem, A., et al., Support vector regression with chaos-based firefly algorithm for stock
market price forecasting. Applied Soft Computing, 2013. 13(2): p. 947-958.
12. Taskaya-Temizel, T. and M.C. Casey, A comparative study of autoregressive neural
network hybrids. Neural Networks, 2005. 18(5–6): p. 781-789.
13. Hann, T.H. and E. Steurer, Much ado about nothing? Exchange rate forecasting: neural
networks vs. linearmodels usingmonthly and weekly data. Neurocomputing, 1996. 10: p.
323-339.
14. Denton, J.W., How good are neural networks for causal forecasting? . The Journal of
Business Forecasting 1995. 18(2): p. 17-20.
15. Vapnik, V.N., The nature of statistical learning theory. 1995, New York: Springer-
Verlag.
16. Suykens, J.A.K., et al., Least squares support vector machines. 2002, Singapore: World
Scientific.
17. Vapnik, V.N., The Nature of Statistical Learning Theory. 2000, New York: Springer.
18. Vapnik, V.N. An overview of statistical learning theory. in IEEE Transactions on Neural
Networks 1999. IEEE.
19. Lu, C.-J., T.-S. Lee, and C.-C. Chiu, Financial time series forecasting using independent
component analysis and support vector regression. Decision Support Systems, 2009.
47(2): p. 115-125.
20. Khemchandani, R., Jayadeva, and S. Chandra, Regularized least squares fuzzy support
vector regression for financial time series forecasting. Expert Systems with
Applications, 2009. 36(1): p. 132-138.
21. Wang, H. and D. Hu. Comparison of SVM and LS-SVM for regression. in International
Conference on Neural Networks and Brain. 2005. IEEE.
47
22. Chapelle, O., et al., Choosing Multiple Parameters for Support Vector Machines.
Machine Learning, 2002. 46(1): p. 131-159.
23. Duan, K., S.S. Keerthi, and A.N. Poo, Evaluation of simple performance measures for
tuning SVM hyperparameters. Neurocomputing, 2003. 51: p. 41-59.
24. Yang, X.-S., Firefly algorithm. 2008, Bristol, U.K: Luniver Press.
25. Yang, X.-S., Firefly algorithm, stochastic test functions and design optimisation.
International Journal of Bio-Inspired Computation, 2010. 2(2): p. 78-84.
26. Yang, X.-S., Chaos-enhanced firefly algorithm with automatic parameter tuning. Int. J.
Swarm Intell. Res 2011. 2(4): p. 1-11.
27. Yang, X.-S., Multiobjective firefly algorithm for continuous optimization. Engineering
with Computers, 2013. 29(2): p. 175–184.
28. Pal, S.K., C.S. Rai, and A.P. Singh, Comparative Study of Firefly Algorithm and Particle
Swarm Optimization for Noisy Non-Linear Optimization Problems. International Journal
of Intelligent Systems and Applications, 2012. 4(10): p. 50-57.
29. Fister, I., et al., A comprehensive review of firefly algorithms. Swarm and Evolutionary
Computation, 2013. 13: p. 34-46.
30. Chou, J.-S. and A.-D. Pham, Smart Artificial Firefly Colony Algorithm-Based Support
Vector Regression for Enhanced Forecasting in Civil Engineering. Computer-Aided
Civil and Infrastructure Engineering, 2015. 30(9): p. 715–732.
31. Chou, J.-S., N.-T. Ngo, and A.-D. Pham, Shear Strength Prediction in Reinforced
Concrete Deep Beams Using Nature-Inspired Metaheuristic Support Vector Regression.
Journal of Computing in Civil Engineering, 2015.
32. Chou, J.-S., W.K. Chong, and D.-K. Bui, Nature-Inspired Metaheuristic Regression
System: Programming and Implementation for Civil Engineering Applications. Journal
of Computing in Civil Engineering, 2016.
33. Chou, J.-S. and J.P.P. Thedja, Metaheuristic optimization within machine learning-based
classification system for early warnings related to geotechnical problems. Automation
in Construction, 2016. 68: p. 65-80.
34. Tay, F.E.H. and L. Cao, Application of support vector machines in financial time series
forecasting. Omega, 2001. 29(4): p. 309-317.
35. Cao, D.-Z., S.-l. Pang, and Y.-H. Bai. Forecasting exchange rate using support vector
machines. in The Fourth International Conference on Machine Learning and
Cybernetics. 2005. Guangzhou, China.
36. Bao, Y., Y. Lu, and J. Zhang, Forecasting Stock Price by SVMs Regression, in Artificial
Intelligence: Methodology, Systems, and Applications. 2004, Springer Berlin
Heidelberg. p. 295-303.
37. Cao, L.J. and F.E.H. Tay, Support Vector Machine With Adaptive Parameters in
Financial Time Series Forecasting. IEEE Transactions on Neural Networks, 2003. 14(6):
p. 1506-1518
38. Trafalis, T.B. and H. Ince. Support vector machine for regression and applications to
financial forecasting. in Proceedings of the IEEE-INNS-ENNS International Joint
Conference on Neural Networks. 2000. Como: IEEE.
39. Kim, K.-j., Financial time series forecasting using support vector machines.
Neurocomputing, 2003. 55(1–2): p. 307-319.
40. Huang, W., Y. Nakamori, and S.-Y. Wang, Forecasting stock market movement
direction with support vector machine. Computers & Operations Research, 2005. 32(10):
p. 2513-2522.
41. Yang, H., et al., Localized support vector regression for time series prediction.
Neurocomputing, 2009. 72(10–12): p. 2659-2669.
42. Huang, S.-C., et al., Chaos-based support vector regressions for exchange rate
forecasting. Expert Systems with Applications, 2010. 37(12): p. 8590-8598.
43. Lin, C.-S., S.-H. Chiu, and T.-Y. Lin, Empirical mode decomposition–based least
squares support vector regression for foreign exchange rate forecasting. Economic
Modelling, 2012. 29: p. 2583-2590.
44. Pai, P.-F. and W.-C. Hong, Support vector machines with simulated annealing
algorithms in electricity load forecasting. Energy Conversion and Management, 2005.
46(17): p. 2669-2688.
45. Oliveira, J.F.L.d. and T.B. Ludermir, A Hybrid Evolutionary System for Parameter
Optimization and Lag selection in Time Series Forecasting, in Brazilian Conference on
Intelligent Systems. 2014: Brazil. p. 73-78.
46. Hong, W.-C., Hybrid evolutionary algorithms in a SVR-based electric load forecasting
model. International Journal of Electrical Power & Energy Systems, 2009. 31(7–8): p.
409-417.
47. Min, S.-H., J. Lee, and I. Han, Hybrid genetic algorithms and support vector machines
for bankruptcy prediction. Expert Systems with Applications, 2006. 31(3): p. 652-660.
48. Wu, C.-H., et al., A real-valued genetic algorithm to optimize the parameters of support
vector machine for predicting bankruptcy. Expert Systems with Applications, 2007.
32(2): p. 397-408.
49. Hsieh, H.-I., T.-P. Lee, and T.-S. Lee, A Hybrid Particle Swarm Optimization and
Support Vector Regression Model for Financial Time Series Forecasting. International
Journal of Business Administration, 2011. 2: p. 48-56.
50. Hong, W.-C., Application of chaotic ant swarm optimization in electric load forecasting.
Energy Policy, 2010. 38(10): p. 5830-5839.
51. Hong, W.-C., Electric load forecasting by seasonal recurrent SVR (support vector
regression) with chaotic artificial bee colony algorithm. Energy, 2011. 36(9): p. 5568-
5578.
52. Wang, J., et al., Swarm Intelligence-Based Hybrid Models for Short-Term Power Load
Prediction. Mathematical Problems in Engineering, 2014.
53. Banati, H. and M. Bajaj, Fire Fly Based Feature Selection Approach. International
Journal of Computer Science Issues, 2011. 8(4): p. 473-479.
54. Kavousi-Fard, A., H. Samet, and F. Marzbani, A new hybrid Modified Firefly Algorithm
and Support Vector Regression model for accurate Short Term Load Forecasting. Expert
Systems with Applications, 2014. 41(13): p. 6047-6056.
55. Xiong, T., Y. Bao, and Z. Hu, Multiple-output support vector regression with a firefly
algorithm for interval-valued stock price index forecasting. Knowledge-Based Systems,
2014. 55: p. 87-100.
56. Chou, J.-S., et al., Evolutionary metaheuristic intelligence to simulate tensile loads in
reinforcement for geosynthetic-reinforced soil structures. Computers and Geotechnics,
2015. 66: p. 1-15.
57. Chou, J.-S. and N.-T. Ngo, Smart grid data analytics framework for increasing energy
savings in residential buildings. Automation in Construction, 2016.
58. Oliveira, J.F.L.d. and T.B. Ludermir, A Distributed PSO-ARIMA-SVR Hybrid System for
Time Series Forecasting, in IEEE International Conference on Systems, Man, and
Cybernetics. 2014: San Diego, CA, USA.
59. Shengchao, S., Z. Wei, and Z. Shuguang. Online fault prediction for nonlinear system
based on sliding ARMA combined with online LS-SVR. in Proceedings of the 33rd
Chinese Control Conference. 2014. Nanjing, China.
60. Singh, P. and B. Borah, High-order fuzzy-neuro expert system for time series forecasting.
Knowledge-Based Systems, 2013. 46: p. 12-21.
61. Hafezi, R., J. Shahrabi, and E. Hadavandi, A bat-neural network multi-agent system
(BNNMAS) for stock price prediction: Case study of DAX stock price. Applied Soft
Computing, 2015. 29: p. 196-210.
49
62. Feng, H., A.V. Riabov, and D.S. Turaga, Real-time analysis and management of big
time-series data. IBM Journal of Research and Development 2013. 57(3/4): p. 8:1 - 8:12.
63. Song, H., B.Z. Gao, and V.S. Lin, Combining statistical and judgmental forecasts via a
web-based tourism demand forecasting system. International Journal of Forecasting,
2013. 29(2): p. 295-310.
64. Yang, J., H. Rivard, and R. Zmeureanu, On-line building energy prediction using
adaptive artificial neural networks. Energy and Buildings, 2005. 37(12): p. 1250-1259.
65. Braverman, V., R. Ostrovsky, and C. Zaniolo, Optimal sampling from sliding windows.
Journal of Computer and System Sciences, 2012. 78(1): p. 260-272.
66. Akerkar, R., Big data computing. 2013: Chapman and Hall/CRC. 564.
67. Mundani, R.-P., et al., A sliding window technique for interactive high-performance
computing scenarios. Advances in Engineering Software, 2015. 84: p. 21-30.
68. Hoang, N.-D., A.-D. Pham, and M.-T. Cao, A Novel Time Series Prediction Approach
Based on a Hybridization of Least Squares Support Vector Regression and Swarm
Intelligence. Applied Computational Intelligence and Soft Computing, 2014.
69. Min, Z. and T. Huanq, Short Term Load Forecasting with Least Square Support Vector
Regression and PSO, in Communications in Computer and Information Science, J.
Zhang, Editor. 2011, Springer Heidelberg Dordrecht London NewYork. p. 124-132.
70. Chen, T.-T. and S.-J. Lee, A weighted LS-SVM based learning system for time series
forecasting. Information Sciences, 2015. 299: p. 99-116.
71. Suykens, J.A.K. and J. Vandewalle, Least Squares Support Vector Machine Classifiers.
Neural Processing Letters, 1999. 9(3): p. 293-300.
72. Coelho, L.d.S. and V.C. Mariani, Improved firefly algorithm approach applied to chiller
loading for energy conservation. Energy and Buildings, 2013. 59: p. 273-278.
73. Yang, D., G. Li, and G. Cheng, On the efficiency of chaos optimization algorithms for
global optimization. Chaos, Solitons & Fractals, 2007. 34(4): p. 1366-1375.
74. He, D., et al., Chaotic characteristics of a one-dimensional iterative map with infinite
collapses. IEEE Transactions on Circuits and Systems I: Fundamental Theory and
Applications 2001. 48(7): p. 900 - 906.
75. Hong, W.-C., et al., SVR with hybrid chaotic genetic algorithms for tourism demand
forecasting. Applied Soft Computing, 2011. 11(2): p. 1881-1890.
76. Li, Y., S. Deng, and D. Xiao, A novel Hash algorithm construction based on chaotic
neural network. Neural Computing and Applications, 2011. 20(1): p. 133-141.
77. Yang, X.-S. and S. Deb. Cuckoo Search via Lévy Flights. in Proc. of World Congress on
Nature & Biologically Inspired Computing. 2009. India: IEEE.
78. Jamil, M. and X.-S. Yang, A Literature Survey of Benchmark Functions For Global
Optimization Problems. Int. Journal of Mathematical Modelling and Numerical
Optimisation, 2013. 4: p. 150-194.
79. Surjanovic, S. and D. Bingham. Virtual library of simulation experiments: test functions
and datasets. 2013 January 2015 [cited 2016 May 8]; Available from:
http://www.sfu.ca/~ssurjano/optimization.html.
80. Smith, S.T., MATLAB Advanced GUI Development. 2006, USA: Dog Ear Publishing,
LLC. 324.
81. Lahmiri, S., A variational mode decompoisition approach for analysis and forecasting
of economic and financial time series. Expert Systems with Applications, 2016. 55: p.
268-273.
82. Addam, O., et al., Foreign exchange data crawling and analysis for knowledge discovery
leading to informative decision making. Knowledge-Based Systems, 2016. 102: p. 1-19.