Development and Performance Evaluation of Adaptive Hybrid Higher Order Neural Networks for Exchange Rate Prediction

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Sarat Chandra Nayak 1,*

1. Kommuri Pratap Reddy Institute of technology, Department of Computer Science & Engineering, Ghatkesar, R.R. Dist.-500088, Hyderabad, India

* Corresponding author.


Received: 28 Feb. 2017 / Revised: 17 Mar. 2017 / Accepted: 10 Apr. 2017 / Published: 8 Aug. 2017

Index Terms

Higher Order Neural Network, Jordan Pi-Sigma Neural Network, Radial Basis Function, Pi-Sigma Neural Network, Functional Link Artificial Neural Network, Genetic Algorithm, Particle Swarm Optimization, Exchange Rate Prediction


Higher Order Neural Networks (HONN) are characterized with fast learning abilities, stronger approximation, greater storage capacity, higher fault tolerance capability and powerful mapping of single layer trainable weights. Since higher order terms are introduced, they provide nonlinear decision boundaries, hence offering better classification capability as compared to linear neuron. Nature-inspired optimization algorithms are capable of searching better than gradient descent-based search techniques. This paper develops some hybrid models by considering four HONNs such as Pi-Sigma, Sigma-Pi, Jordan Pi-Sigma neural network and Functional link artificial neural network as the base model. The optimal parameters of these neural nets are searched by a Particle swarm optimization, and a Genetic Algorithm. The models are employed to capture the extreme volatility, nonlinearity and uncertainty associated with stock data. Performance of these hybrid models is evaluated through prediction of one-step-ahead exchange rates of some real stock market. The efficiency of the models is compared with that of a Radial basis functional neural network, a multilayer perceptron, and a multi linear regression method and established their superiority. Friedman’s test and Nemenyi post-hoc test are conducted for statistical significance of the results.

Cite This Paper

Sarat Chandra Nayak, "Development and Performance Evaluation of Adaptive Hybrid Higher Order Neural Networks for Exchange Rate Prediction", International Journal of Intelligent Systems and Applications(IJISA), Vol.9, No.8, pp.71-85, 2017. DOI:10.5815/ijisa.2017.08.08


[1]Haykin, S., Neural Networks and Learning Machine, PHI, ISBN -978-81-203-4000-8, 2010.
[2]Rajasekaran, S. and Vijayalakshmi Pai, G. A., Neural Networks, Fuzzy Logic and Genetic Algorithms Synthesis and Application, PHI, ISBN-978-81-203-2186-1, 2007.
[3]Wang, Z., Fang, J., and Liu, X., ‘Global stability of stochastic high-order neural networks with discrete and distributed delays’, Chaos, Solutions and Fractals, Vol. 36, No. 2, pp.388–396, 2008.
[4]Shin, Y. and Ghosh, J., ‘Efficient higher-order neural networks for classification and function approximation’, International Journal on Neural Systems, Vol. 3, pp. 323–350, 1992.
[5]Ghazali, R., Hussain, A., and El-Deredy, W., “Application of ridge polynomial neural networks to financial time series prediction”, International Joint Conference on Neural Networks, Sheraton Vancouver Wall Centre Hotel, Vancouver, BC, Canada, pp. 913–920, (July, 2006).
[6]Knowles, A., Hussain, A., El Deredy, W., Lisboa, P. G., and Dunis, C. L., “Higher order neural networks with Bayesian confidence measure for the prediction of the EUR/USD exchange rate” In Artificial higher order neural networks for economics and business (pp. 48-59), IGI Global , 2009.
[7]Shin, Y., and Ghosh, J., “Efficient higher-order neural networks for classification and function approximation”, International Journal on Neural Systems, Vol. 3(4), pp. 323–350, 1992.
[8]Nayak, S. C., Misra, B. B., and Behera, H. S. , “A Pi-Sigma Higher Order Neural Network for Stock Index Forecasting”, . In Computational Intelligence in Data Mining, Vol. 2, pp 311-319, Springer India, (2015).
[9]Nayak, S. C., Misra, B. B., and Behera, H. S., “Fluctuation prediction of stock market index by adaptive evolutionary higher order neural networks”, International Journal of Swarm Intelligence, Vol. 2(2-4), pp. 229-253, Inderscience, (2016).
[10]Nayak, J., Naik, B., and Behera, H. S., “A novel Chemical Reaction Optimization based Higher order Neural Network (CRO-HONN) for nonlinear classification”, Ain Shams Engineering Journal, Vol. 6(3), pp. 1069-1091, (2015).
[11]Perantonis, S., Ampazis, N., Varoufakis S., and Antoniou, G. (1998) ‘Constrained learning in neural networks: Application to stable factorization of 2-d polynomials’, Neural Processing Letter, Vol.7, No. 1, pp. 5–14.
[12]Huang, D. S., Ip, H. H. S., Law K. C. K., and Chi, Z. (2005) ‘Zeroing polynomials using modified constrained neural network approach’, IEEE Transactions on Neural Networks, Vol. 16, No. 3, pp. 721–732.
[13]Epitropakis, M. G., Plagianakos, V. P. and Vrahatis, M. N. (2010), ‘Hardwarefriendly higher-order neural network training using distributed evolutionary algorithms’, Appl Soft Comput, Vol. 10, pp.398–408.
[14]Ghazali, R., Hussain, A. J. and Liatsis, P. (2011) ‘Dynamic Ridge Polynomial Neural Network: Forecasting the univariate non-stationary and stationary trading signals’, Expert Systems with Applications, Vol. 38, pp. 3765-3776.
[15]Ghazali, R., Husaini, N. A., Ismail, L. H. and Samsuddin, N. A. (2012) ‘An Application of Jordan Pi-Sigma Neural Network for the Prediction of Temperature Time Series Signal’, Recurrent Neural Networks and Soft Computing, Dr. Mahmoud ElHefnawi (Ed.), ISBN: 978-953-51-0409-4.
[16]Yong, N., Wei, D. (2008) ‘A hybrid genetic learning algorithm for Pi–Sigma neural network and the analysis of its convergence’, In: IEEE fourth international conference on natural computation, pp. 19–23.
[17]Fallahnezhad, M., Moradi, M. H., Zaferanlouei, S. (2011), ‘A hybrid higher order neural classifier for handling classification problems’, Expert Systems with Appl., Vol. 38, pp.386–393.
[18]Zhang, M., Xu, S., and Fulcher, J. (2002), ‘Neuron-Adaptive Higher Order Neural-Network Models for Automated Financial Data Modeling’, IEEE Transactions on neural networks, Vol. 13, No. 1.
[19]Majhi B., Rout M., Majhi R., Panda G. and Fleming P. J. (2012), ‘New robust forecasting models for exchange rates prediction’, Expert Systems with Applications, Vol. 39, pp.12658–12670.
[20]Sahu K. K., Biswal G.R., Sahu P.K., Sahu S.R., and Behera H. S. (2014) ‘A CRO based FLANN for Forecasting Foreign Exchange Rates’, 2014 International Conference on Computational Intelligence in Data Mining (ICCIDM), Smart Innovation, System and Technology, Vol. 31, pp. 647-664.
[21]Yu. Lean, Wang S. and Lai K. K. (2005), ‘A novel nonlinear ensemble forecasting model incorporating GLAR and ANN for foreign exchange rates’, Computers and Operations Research 32, Elsevier, 2523-2541.
[22]Jordan, M. I. (1986). Attractor Dynamics and Parallelism in a Connectionist Sequential Machine. Paper presented at the Proceedings of the Eighth Conference of the Cognitive Science Society, New Jersey, USA.
[23]Husaini, N.A., Ghazali, R., Nawi, N.M. and Ismail, L.H., 2011, April. Jordan pi-sigma neural network for temperature prediction. In International Conference on Ubiquitous Computing and Multimedia Applications (pp. 547-558). Springer Berlin Heidelberg.
[24]Husaini, N. A., Ghazali, R., Ismail, L. H., & Herawan, T. (2014). A jordan pi-sigma neural network for temperature forecasting in batu pahat region. InRecent Advances on Soft Computing and Data Mining (pp. 11-24). Springer International Publishing.
[25]Nayak, J., Kanungo, D. P., Naik, B., & Behera, H. S. (2014, December). A higher order evolutionary Jordan Pi-Sigma neural network with gradient descent learning for classification. In High Performance Computing and Applications (ICHPCA), 2014 International Conference on (pp. 1-6). IEEE.
[26]Nenortaite J., Simutis R.(2004), ‘Stocks’ Trading System Based on the Particle Swarm Optimization Algorithm’, Workshop on Computational Methods in Finance and Insurance, Lecture Notes in Computer Science, Springer, vol. 3039/2004.
[27]Zhao L., Yang Y. (2009), ‘Expert systems with applications: PSO-based single multiplicative neuron model for time series prediction’, Expert Systems with Applications, Vol. 36, pp. 2805–2812.
[28]Sermpinis, G., Theofilatos, K., Karathanasopoulos, A., Georgopoulos, E. F., and Dunis, C. L. (2013) ‘Forecasting foreign exchange rates with adaptive neural networks using radial-basis functions and Particle Swarm Optimization’, European Journal of Operational Research, Vol. 225, pp. 528–540.
[29]Chen Y., and Zhang G. (2013), ‘Exchange rates determination based on genetic algorithms using Mendel’s principles: Investigation and estimation under uncertainty’, Information Fusion, Vol. 14, pp. 327–333.
[30]Chang, P.-C., Liu, C.-H., Lin, J.-L., Fan, C.-Y., Ng, Celeste S.P., 2009. A neural network with a case based dynamic window for stock trading prediction. Expert Syst. Appl. 36, 6889–6898.
[31]Atsalakis, G.S., Valavanis, K.P., 2009. Surveying stock market forecasting techniques – part II: soft computing methods. Expert Syst. Appl. 36, 5932–5941.
[32]Venugopal Setty, D., Rangaswamy, T.M., Subramanya, K.N., 2010. A review on data mining applications to the performance of stock marketing. Int. J. Comput. Appl. 1 (3), 33–43.
[33]Kumaran Kumar, J., Kailas, A., 2012. Prediction of future stock close price using proposed hybrid ANN model of functional link fuzzy logic neural model (FLFNM). Int. J. Comput. Appl. Eng. Sci. II (1).
[34]Rout, Minakhi, et al. "Forecasting of currency exchange rates using an adaptive ARMA model with differential evolution based training." Journal of King Saud University-Computer and Information Sciences 26.1 (2014): 7-18.
[35]Jena, Pradyot Ranjan, Ritanjali Majhi, and Babita Majhi. "Development and performance evaluation of a novel knowledge guided artificial neural network (KGANN) model for exchange rate prediction." Journal of King Saud University-Computer and Information Sciences 27.4 (2015): 450-457.
[36]Galeshchuk, Svitlana. "Neural networks performance in exchange rate prediction." Neurocomputing 172 (2016): 446-452.
[37]Nanda, S. K., Tripathy, D. P., Nayak, S. K., & Mohapatra, S. (2013). Prediction of rainfall in India using Artificial Neural Network (ANN) models.International Journal of Intelligent Systems and Applications, 5(12), 1.
[38]Hu, Z., Bodyanskiy, Y. V., Tyshchenko, O. K., & Boiko, O. O. (2016). An Evolving Cascade System Based on A Set Of Neo Fuzzy Nodes. International Journal of Intelligent Systems and Applications, 9, 1-7.
[39]Y. Shin, and J. Ghosh, ‘Efficient higher-order neural networks for classification and function approximation’, International Journal on Neural Systems, Vol. 3, pp. 323–350, 1992.
[40]Hussain, A. J. & Liatsis, P. (2002). Recurrent Pi-Sigma Networks for DPCM Image Coding. Neurocomputing, 55, pp. 363-382.
[41]Pao, Y. H., Takefuji, Y., Functional-link net computing: thory, system architecture, and functionalities. Computer, Vol. 25, 76-79, 1992.
[42]Goldberg, D. E., Genetic algorithms in search, optimization, and machine learning, Addison-Wesley, Reading, MA, USA, 1989.
[43]Kennedy, J., Eberhart, R.C.,. “Particle swarm optimization”, In: Proceedings of the IEEE International Conference on Neural Networks, Perth, Australia, pp. 1942–1948, 1995.
[44]Eberhart, R. C., Simpson, P. and Dobbins, R., "Computational intelligence PC tools," Academic Press, 1996.
[45]Babaei M, A general approach to approximate solutions of nonlinear differential equations using particle swarm optimization. Appl. Soft. Comput 2013(13): 3354-65.
[46]Nayak, S. C., Misra, B. B., and Behera, H. S. (2015), ‘Artificial Chemical Reaction Optimization of Neural Networks for Efficient Prediction of Stock Market Index’, Ain Shams Engineering Journal
[47]Nayak, S. C., Misra, B. B., and Behera, H. S. (2014), ‘Impact of data normalization on stock index forecasting’, International Journal of Computer Information Systems and Industrial Management, Vol. 6, pp. 357-369.
[48]Nayak, S. C., Misra, B. B., and Behera, H. S.,” Evaluation of Normalization Methods on Neuro-Genetic Models for Stock Index Forecasting,” IEEE World Congress on Information and Communication Technologies, (WICT 2012), doi: 10.1109/WICT.2012.6409147.
[49]Demsar, J., “Statistical Comparisons of Classifiers over Multiple Data Sets,” Journal of Machine Learning Research, 7(2006)1–30.
[50]Zar, J. H. (1999). More on dichotomous variables. Biostatistical analysis. 4th ed. Upper Saddle River: Prentice Hall, 516-65.