Skip to main content
Log in

Enhancement of Neural Networks Model’s Predictions of Currencies Exchange Rates by Phase Space Reconstruction and Harris Hawks’ Optimization

  • Published:
Computational Economics Aims and scope Submit manuscript

Abstract

Predictions of variations in exchange rates of other currencies to a vehicle currency such as the Dollar (USD) are vital in order to reduce the risks for international transactions. In this study, we use a heuristic algorithm of Harris Hawks’ optimization (HHO) along with phase space reconstructions (PSRs) coupled to the ANN (PSR-ANNHHO) to predict the daily data of GBP/USD and CAD/USD exchange rates. In this new hybrid model, unlike the previous ones, the input of the model is based on the two parameters of time delay and the embedding dimension. The HHO algorithm increases the performance of ANN, which has can model non-linear systems in a natural manner. The performance of the PSR-ANNHHO model can be compared with the ANN and the ANN hybridized with metaheuristic Algorithm of Innovative Gunner (AIG) model (ANN-AIG). The Modified Diebold–Mariano test indicates the statistical difference between the accuracy of the models. Based on the statistical measures and graphs, the PSR-ANNHHO model predicts exchange rates considerably better than stand-alone ANN and ANN-AIG model in each case. Hence, implementing PSR along with using the heuristic algorithms could increase the accuracy of the model. This model’s precise performance supports the case for it to be employed to predict future exchange rate variations, in order to decrease transactions risks in the global markets.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Availability of data and materials

The data set analyzed during this study are available in:" https://www.investing.com/currencies/usd-try-historical-data".

References

  • Abarbanel, H. D. I. (1996). Analysis of observed chaotic data (p. 272). Springer.

    Book  Google Scholar 

  • Abdollahi Dehkordi, A., Safaa Sadiq, A., Mirjalali, S., & Ghafoor, K. Z. (2021). Non-linear-based chaotic harris hawks optimizer: algorithm and internet of vehicles application. Applied Soft Computing, 109, 107574.

    Article  Google Scholar 

  • Abiodun, O. I., Jantan, A., Omolara, A. E., Dada, K. V., Mohamed, N. A., & Arshad, H. (2018). State-of-the-art in artificial neural network applications: A survey. Heliyon, 4(11), e00938.

    Article  Google Scholar 

  • Adhikari, R., & Agrawal, R. (2014). A combination of artificial neural network and random walk models for financial time series forecasting. Neural Computing and Applications, 24(6), 1441–1449.

    Article  Google Scholar 

  • Altay E., & Satman, M. H. (2005). Stock market forecasting: artificial neural network and linear regression comparison in an emerging market. SSRN Scholarly Paper ID 893741, Social Science Research Network, Rochester.

  • Andreou, A. S., Georgopoulos, E. F., & Likothanassis, S. D. (2002). Exchange-rates forecasting: A hybrid algorithm based on genetically optimized adaptive neural networks. Computational Economics, 20(3), 191–210.

    Article  Google Scholar 

  • Aydin, A. D., & Cevdar, S. C. (2015). Comparison of prediction performances of artificial neural network (ANN) and vector autoregressive (VAR) Models by using the macroeconomic variables of gold prices, Borsa Istanbul (BIST) 100 index and US Dollar-Turkish Lira (USD/TRY) exchange rates. Procedia Economics and Finance, 30, 3–14.

    Article  Google Scholar 

  • Baffour, A. A., Feng, J., & Taylor, E. K. (2019). A hybrid artificial neural network-GJR modeling approach to forecasting currency exchange rate volatility. Neurocomputing, 365, 285–301.

    Article  Google Scholar 

  • Bal, C., & Demir, S. (2017). Forecasting TRY/USD exchange rate with various artificial Neural Network Models. TEM Journal, 6(1), 11.

    Google Scholar 

  • Bao, X., Jia, H., & Lang, C. (2019). A novel hybrid harris hawks optimization for color image multilevel thresholding segmentation. IEEE Access, 7, 76529–576546.

    Article  Google Scholar 

  • Birgul, E., Ozturan, M., & Badur, B. (2003). Stock market prediction using artificial neural networks. In Proceedings of the in the 3rd Hawaii International Conference on Business.

  • Chen, H., Wan, Q., & Wang, Y. (2014). Refined Diebold–Mariano test methods for the evaluation of wind power forecasting models. Energies, 7, 4185–4198. https://doi.org/10.3390/en7074185

    Article  Google Scholar 

  • Cheung, Y. W., Chinn, M. D., Pascual, A. G., & Zhang, Y. (2018). Exchange rate prediction redux: New models, new data, new currencies. Journal of International Money and Finance. https://doi.org/10.1016/j.jimonfin.2018.03.010

    Article  Google Scholar 

  • Dash, R. (2018). Performance analysis of a higher order neural network with an improved shuffled frog leaping algorithm for currency exchange rate prediction. Applied Soft Computing, 67, 215–231.

    Article  Google Scholar 

  • Dehghani, R., & Poudeh, H. T. (2021). Application of novel hybrid artificial intelligence algorithms to groundwater simulation. International Journal of Environmental Science and Technology. https://doi.org/10.1007/s13762-021-03596-5

    Article  Google Scholar 

  • Dhamija, A. K., & Bhalla, V. K. (2010). Financial time series forecasting: Comparison of neural networks and ARCH models. International Research Journal of Finance and Economics, 49, 194–212.

    Google Scholar 

  • El Shazly, M. R., & El Shazly, H. E. (1999). Forecasting currency prices using a genetically evolved neural network architecture. International Review of Financial Analysis, 8(1), 67–82.

    Article  Google Scholar 

  • Elgamal, Z. M., Yasin, N. B. M., Tubishat, M., Alswaitti, M., & Mirjalili, S. (2020). An improved harris hawks optimization algorithm with simulated annealing for feature selection in the medical field. IEEE Access, 8, 186638–186652.

    Article  Google Scholar 

  • Elshorbagy, A., Simonovic, S. P., & Panu, U. S. (2002). Estimation of missing streamflow data using principles of chaos theory. Journal of Hydrology, 255, 123–133. https://doi.org/10.1016/S0022-1694(01)00513-3

    Article  Google Scholar 

  • Fahimifard, S. M., Homayounifar, M., Sabouhi, M., & Moghaddamnia, A. R. (2009). Comparison of ANFIS, ANN, GARCH and ARIMA techniques to exchange rate forecasting. Journal of Applied Sciences, 9, 3641–3651.

    Article  Google Scholar 

  • Fernando, S., Morán, R., Rossi, R., & Oñate, E. (2013). Analysis of the discharge capacity of radial-gated spillways using CFD and ANN–Oliana Dam case study. Journal of Hydraulic Research, 51(3), 244–252. https://doi.org/10.1080/00221686.2012

    Article  Google Scholar 

  • Fraser, A. M., & Swinney, H. L. (1986). Independent coordinates for strange attractors from mutual information. Physical Review A, 33(2), 1134.

    Article  Google Scholar 

  • Galeshchuk, S. (2016). Neural networks performance in exchange rate prediction. Neurocomputing, 172, 446–452.

    Article  Google Scholar 

  • Gezici, H., & Livatyali, H. (2022). Chaotic Harris hawks algorithm. Journal of Computational Design and Engineering, 9(1), 216–245.

    Article  Google Scholar 

  • Ghorbani, M. A., Khatibi, R., Mehr, A. D., & Asadi, H. (2018). Chaos-based multigene genetic programming: A new hybrid strategy for river flow forecasting. J. Hydrology., 562, 455–467.

    Article  Google Scholar 

  • Golilarz, N. A., Addeh, A., Gao, H., et al. (2019). A new automatic method for control chart patterns recognition based on ConvNet and harris hawks meta heuristic optimization algorithm. IEEE Access. https://doi.org/10.1109/ACCESS.2019.2945596

    Article  Google Scholar 

  • Guresen, E., Kayakutlu, G., & Daim, T. U. (2011). Using artificial neural network models in stock market index prediction. Expert Systems with Applications, 38(8), 10389–10397.

    Article  Google Scholar 

  • Hajizadeh, E., Mahootchi, M., Esfahanipour, A., & Kh, M. M. (2019). A new NN-PSO hybrid model for forecasting Euro/Dollar exchange rate volatility. Neural Computing and Applications, 31(7), 2063–2071.

    Article  Google Scholar 

  • He, K., Wang, L., Zou, Y., & Lai, K. K. (2014). Exchange rate forecasting using entropy optimized multivariate wavelet denoising model. Mathematical Problems in Engineering. https://doi.org/10.1155/2014/389598

    Article  Google Scholar 

  • Heidari, A. A., Mirjalili, S., Faris, H., Aljarah, I., Mafarja, M., & Chen, H. (2019). Harris Hawks optimization: Algorithm and applications. Future Generation Computer Systems, 97, 849–872.

    Article  Google Scholar 

  • Henríquez, J., & Kristjanpoller, W. (2019). A combined independent component analysis–neural network model for forecasting exchange rate variation. Applied Soft Computing, 83, 105654.

    Article  Google Scholar 

  • Holzfuss, J., & Mayer-Kress, G. (1986). An approach to error-estimation in the application of dimension algorithms. In Dimensions and entropies in chaotic systems (pp. 114–122). Berlin: Springer.

  • 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.

    Article  Google Scholar 

  • Huang, W., Lai, K. K., Nakamori, Y., & Wang, S. (2004). Forecasting foreign exchange rates with artificial neural networks: A review. International Journal of Information Technology & Decision Making, 3(01), 145–165.

    Article  Google Scholar 

  • Ince, H., Cebeci, A. F., & Imamoglu, S. Z. (2019). An artificial neural network-based approach to the monetary model of exchange rate. Computational Economics, 53(2), 817–831.

    Article  Google Scholar 

  • Ismael, O. M., Qasim, O. S., & Algamal, Z. Y. (2020). Improving Harris Hawks optimization algorithm for hyperparameters estimation and feature selection in v-support vector regression based on opposition-based learning. Journal of Chemometrics, 34(11), e3311.

    Article  Google Scholar 

  • Jia, H., Lang, C., Oliva, D., Song, W., & Peng, X. (2019). Dynamic Harris Hawks optimization with mutation mechanism for satellite image segmentation. Remote Sensing, 11(12), 1421.

    Article  Google Scholar 

  • Jiménez-Rodríguez, R., & Morales-Zumaquero, A. (2020). BRICS: How important is the exchange rate pass-through? The World Economy, 43(3), 781–793.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Khan, H.A. (2021). AI, Deep machine learning via neuro-fuzzy models: Complexities of international financial economics of crises. International Journal of Computation and Neural Engineering, 7(3), 122–134. https://doi.org/10.19070/2572-7389-2100016

    Article  Google Scholar 

  • Khashei, M., & Bijari, M. (2014). Fuzzy artificial neural network model for incomplete financial time series forecasting. Journal of Intelligent & Fuzzy Systems, 26(2), 831–845.

    Article  Google Scholar 

  • Khatibi, R., Sivakumar, B., Ghorbani, M. A., Kisi, O., Koçak, K., & Farsadi Zadeh, D. (2012). Investigating chaos in river stage and discharge time series. Journal of Hydrology, 414–415, 108–117. https://doi.org/10.1016/j.jhydrol.2011.10.026

    Article  Google Scholar 

  • Kimoto, T., Asakawa, K., Yoda, M., & Takeoka, M. (1990). Stock market prediction system with modular neural networks. In Proceedings of the 1990 International Joint Conference on Neural Networks (IJCNN '90), (Vol. 1, pp. 1–6), Washington, DC

  • Koçak, K., Şaylan, L., & Eitzinger, J. (2004). Nonlinear prediction of near-surface temperature via univariate and multivariate time series embedding. Ecol. Modell., 173, 1–7. https://doi.org/10.1016/S0304-3800(03)00249-7

    Article  Google Scholar 

  • Kristjanpoller, W., & Minutolo, M. C. (2018). A hybrid volatility forecasting framework integrating GARCH, artificial neural network, technical analysis and principal components analysis. Expert Systems with Applications, 109, 1–11.

    Article  Google Scholar 

  • Kashani, M.H., Inyurt, S., Golabi, M.R., AmirRahmani, M., & Band, S. Sh. (2022). Estimation of solar radiation by joint application of phase space reconstruction and a hybrid neural network. Theoretical and Applied Climatology, 147, 1725–1742.

    Article  Google Scholar 

  • Lahmiri, S., & Bekiros, S. (2019). Cryptocurrency forecasting with deep learning chaotic neural networks. Chaos, Solitons & Fractals, 118, 35–40.

    Article  Google Scholar 

  • Leung, M. T., Chen, A. S., & Daouk, H. (2000). Forecasting exchange rates using general regression neural networks. Computers & Operations Research, 27(11–12), 1093–1110.

    Article  Google Scholar 

  • Liebert, W., & Schuster, H. G. (1989). Proper choice of the time delay for the analysis of chaotic time series. Physics Letters A, 142(2–3), 107–111.

    Article  Google Scholar 

  • Lin, Y., Lin, Z. X., Liao, Y., Li, Y. Z., Xu, J. L., & Yan, Y. (2022a). Forecasting the realized volatility of stock price index: A hybrid model integrating CEEMDAN and LSTM. Expert Systems with Applications, 206, 117736.

    Article  Google Scholar 

  • Lin, Y., Lu, Q., Tan, B., & Yu, Y. (2022b). Forecasting energy prices using a novel hybrid model with variational mode decomposition. Energy, 246, 123366.

    Article  Google Scholar 

  • Mafarja, M., Qasem, A., Heidari, A. A., Aljarah, I., Faris, H., & Mirjalili, S. (2020). Efficient hybrid nature-inspired binary optimizers for feature selection. Cognitive Computation, 12(1), 150–175.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Menesy, A. S., Sultan, H. M., Selim, A., Ashmawy, M. G., & Kamel, S. (2019). Developing and applying chaotic Harris hawks optimization technique for extracting parameters of several proton exchange membrane fuel cell stacks. IEEE Access, 8, 1146–1159.

    Article  Google Scholar 

  • Ng, W. W., Panu, U. S., & Lennox, W. C. (2007). Chaos based analytical techniques for daily extreme hydrological observations. Journal of Hydrology, 342, 17–41. https://doi.org/10.1016/j.jhydrol.2007.04.023

    Article  Google Scholar 

  • Pacelli, V., Bevilacqua, V., & Azzollini, M. (2011). An artificial neural network model to forecast exchange rates. Journal of Intelligent Learning Systems and Applications, 3(02), 57.

    Article  Google Scholar 

  • Panda, M. M., Panda, S. N., & Pattnaik, P. K. (2021). Multi-currency exchange rate prediction using convolutional neural network. Materials Today Proceedings. https://doi.org/10.1016/j.matpr.2020.11.317

    Article  Google Scholar 

  • Perwej, Y., & Perwej, A. (2012). Prediction of the Bombay Stock Exchange (BSE) market returns using artificial neural network and genetic algorithm.

  • Pham, Q. V., Huynh-The, T., Alazab, M., Zhao, J., & Hwang, W. J. (2020). Sum-rate maximization for UAV-assisted visible light communications using NOMA: Swarm intelligence meets machine learning. IEEE Internet of Eings Journal, 7(10), 10375–87.

    Article  Google Scholar 

  • Pijarski, P., & Kacejko, P. (2019). A new metaheuristic optimization method: The algorithm of the innovative gunner (AIG). Engineering Optimization, 51(12), 2049–2068.

    Article  Google Scholar 

  • Piotrowski, A. P., & Napiorkowski, J. J. (2011). Optimizing neural networks for river flow forecasting–Evolutionary Computation methods versus the Levenberg–Marquardt approach. Journal of Hydrology, 407(1–4), 12–27.

    Article  Google Scholar 

  • Polat, K., & Tsang, K. P. (2021). Forecasting exchange rates with elliptically symmetric principal components. International Journal of Forecasting. https://doi.org/10.1016/j.ijforecast.2020.11.007

    Article  Google Scholar 

  • Pradeepkumar, D., & Ravi, V. (2017). Forecasting financial time series volatility using particle swarm optimization trained quantile regression neural network. Applied Soft Computing, 58, 35–52.

    Article  Google Scholar 

  • Ramadan, A., Kamel, S., Korashy, A., Almalaq, A., & Duminguez-Garcia, J. L. (2022). An enhanced Harris Hawks optimization algorithm for parameter estimation of single, double, and triple diode photovoltaic models. Soft Computing, 26, 7233–7257.

    Article  Google Scholar 

  • Samma, H., & Bin Sama, A. S. (2022). Rulles embedded Harris Hawks optimizer for large-scale optimization problems. Neural Computing and Applications, 34, 13599–13624.

    Article  Google Scholar 

  • Sammen, S. S., Ghorbani, M. A., Malik, A., Tikhamarine, Y., AmirRahmani, M., Al-Ansari, N., & Chau, K. W. (2020). Enhanced artificial neural network with Harris Hawks optimization for predicting scour depth downstream of ski-jump spillway. Applied Sciences, 10(15), 5160.

    Article  Google Scholar 

  • Shabani, E., Hayati, B., Pishbahar, E., Ghorbani, M. A., & Ghahremanzadeh, M. (2021). A novel approach to predict CO2 emission in the agriculture sector of Iran based Inclusive Multiple Model. Journal of Cleaner Production. https://doi.org/10.1016/j.jclepro.2020.123708

    Article  Google Scholar 

  • Shen, F., Chao, J., & Zhao, J. (2015). Forecasting exchange rate using deep belief networks and conjugate gradient method. Neurocomputing, 167, 243–253.

    Article  Google Scholar 

  • Singh, T. (2020). A chaotic sequence-guided Harris hawks optimizer for data clustering. Neural Computing & Applications, 32(23), 789–817.

    Article  Google Scholar 

  • Sivakumar, B., & Jayawardena, A. W. (2002). An investigation of the presence of low-dimensional chaotic behaviour in the sediment transport phenomenon. Hydrological Sciences Journal, 47, 405–416. https://doi.org/10.1080/02626660209492943

    Article  Google Scholar 

  • Takens, F. (1981). Detecting strange attractors in turbulence. In D. A. Rand, L. S. Young (Eds.), Lectures notes in mathematics, (Vol. 898, pp. 366–381). New York: Springer-Verlag.

  • Tripathy, B. K., Reddy Maddikunta, P. K., Pham, Q. V., Gadekallu, T. R., Dev, K., Pandya, S., & ElHalawany, B. M. (2022). Harris hawk optimization: A survey on variants and applications. Computational Intelligence and Neuroscience. https://doi.org/10.1155/2022/2218594

    Article  Google Scholar 

  • Uyumaz, A., Danandeh Mehr, A., Kahya, E., & Erdem, H. (2014). Rectangular side weirs discharge coefficient estimation in circular channels using linear genetic programming approach. Journal of Hydroinformatics, 16, 1318–1330. https://doi.org/10.2166/hydro.2014.112

    Article  Google Scholar 

  • Wu, S. I., & Lu, R. P. (1993). Combining artificial neural networks and statistics for stock-market forecasting. In Proceedings of the 21st Annual ACM Computer Science Conference, (pp. 257–264). New York.

  • Yong, Y. L., Lee, Y., Gu, X., Angelov, P. P., Ling Ngo, DCh., & Shafipour, E. (2018). Foreign currency exchange rate prediction using neuro-fuzzy systems. Procedia Computer Science, 144, 232–238.

    Article  Google Scholar 

  • Yu, J., Kim, C. H., & Rhee, S. B. (2020). The comparison of lately proposed Harris Hawks Optimization and Jaya optimization in solving directional overcurrent relays coordination problem. Complexity. https://doi.org/10.1155/2020/3807653

    Article  Google Scholar 

  • Zheng, J., Fu, X., & Zhang, G. (2019). Research on exchange rate forecasting based on deep belief network. Neural Computing and Applications, 31(1), 573–582.

    Article  Google Scholar 

  • Zhou, J., Li, H., & Zhong, W. (2021). A modified Diebold–Mariano test for equal forecast accuracy with clustered dependence. Economics Letters, 207, 110029.

    Article  Google Scholar 

Download references

Funding

No funds, grants, or other support was received.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Elham Shabani or Shahab S. Band.

Ethics declarations

Conflict of interest

The authors declare that they have no competing interests.

Ethics approval

Not applicable.

Consent to participate

Not applicable.

Consent for publication

Not applicable.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khan, H.A., Ghorbani, S., Shabani, E. et al. Enhancement of Neural Networks Model’s Predictions of Currencies Exchange Rates by Phase Space Reconstruction and Harris Hawks’ Optimization. Comput Econ 63, 835–860 (2024). https://doi.org/10.1007/s10614-023-10361-y

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10614-023-10361-y

Keywords

Navigation