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The primary purpose of this study was to apply the nonlinear autoregressive neural network to model the long-term records of monthly global price of bananas from January 1990 to November 2020. The development of the optimal architecture for the nonlinear autoregressive neural network requires determination of time delays, the number of hidden neurons, and an efficient training algorithm. Through training of the nonlinear autoregressive neural network models, the prediction performance of the models was evaluated by its mean squared error value, the average squared difference between the observed and predicted values. In this study, the empirical results revealed that the NAR-BR model with 13 neurons in the hidden layer and 6 time delays provided the best performance at its smaller mean squared error value and yielded higher accuracy than the NAR-LM model with 12 neurons in the hidden layer and 4 time delays and NAR-SCG model with 12 neurons in the hidden layer and 6 time delays. Understanding past global price of bananas is important for the analyses of current and future global price of bananas changes. In order to sustain these observations, research programs utilizing the resulting data should be able to improve our understanding and narrow projections of future global price of bananas significantly.
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Beale, Mark Hudson, Hagan, Martin T., & Demuth, Howard B. (2019). Deep Learning ToolboxTM: Getting Started Guide. Natick, MA: The MathWorks, Inc.
Benrhmach, G., Namir, K., Namir, A., and Bouyaghroumni, J. (2020). Nonlinear autoregressive neural network and extended Kalman filters do prediction of financial time series. Journal of Applied Mathematics, Vol. 2020, Article ID 5057801, 1-6.
Eyduran, S. P., Akın, M., Eyduran, E., Çelik, S., Ertürk, Y. E., and Ercişli, S. (2020). Forecasting banana harvest area and production in Turkey using time series analysis. Erwerbs-Obstbau, 62, 281–291.
Fatin, Z. N., Titik, E., and Mulyatno, S. B. (2020). The analysis of price and market integration of banana commodities in Lampung, Indonesia. Russian Journal of Agricultural and Socio-Economic Sciences, 3(99), 2020, 61-68.
Gavin, Henri P. (2020). The Levenberg-Marquardt algorithm for nonlinear least squares curve-fitting problems. Department of Civil and Environmental Engineering Duke University. 19 pages. Retrieved from: http://people.duke.edu/~hpgavin/ce281/lm.pdf
Hamjah, M. A. (2014). Forecasting major fruit crops productions in Bangladesh using Box-Jenkins ARIMA Model. Journal of Economics and Sustainable Development, 5(7), 96-107.
Hossain, M. M., Abdulla, F., and Majumder, A. K. (2016). Forecasting of banana production in Bangladesh. American Journal of Agricultural and Biological Sciences, 11(2), 93-99.
Levenberg, Kenneth (1944). A Method for the Solution of Certain Non-Linear Problems in Least Squares. Quarterly of Applied Mathematics, 2(2): 164–168. doi:10.1090/qam/10666
MacKay, David J. C. (1992). Bayesian Interpolation. Neural Computation, Vol. 4, No. 3, pp. 415–447. https://doi.org/10.1162/neco.19126.96.36.1995
Market Reports World. (2019). Banana market size, share, analysis - segmented by geography - growth, trends, and forecast (2019 - 2024). Global Banana Market Research Report, Market Reports World, 94 pp. Retrieved from: https://www.marketreportsworld.com/banana-market-13487750
Marquardt, Donald W. (1963). An algorithm for least-squares estimation of nonlinear parameters. Journal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 2, pp. 431-441.
Moller, Martin Fodslette. (1993). A scaled conjugate gradient algorithm for fast supervised learning. Neural Networks, Volume 6, Issue 4, pp. 525-533. https://doi.org/10.1016/S0893-6080(05)80056-5
Omar, M. I., Dewan, M. F., and Hoq, M. S. (2014). Analysis of price forecasting and spatial co-integration of banana in Bangladesh. European Journal of Business and Management, 6(7), 244-255.
Rathod, S., Mishra, G. C., and Singh, K. N. (2017). Hybrid time series models for forecasting banana production in Karnataka State, India. Journal of the Indian Society of Agricultural Statistics, 71(3), 193–200.
Rathod, S., and Mishra, G. C. (2018). Statistical models for forecasting mango and banana yield of Karnataka, India. Journal of Agricultural Science and Technology, 20, 803-816.
Rebortera, M. A., and Fajardo, A. C. (2019). An enhanced deep learning approach in forecasting banana harvest yields. International Journal of Advanced Computer Science and Applications, 10(9), 275-280.
Ruiz, A., Fobelets, V., Grosscurt, C., Galgani, P., Lord, R., Hardwicke, R., Tarin, M., P, G., McNeil, D., and Aird, S. (2017). The external costs of banana production: A global study. Research Report Prepared for Fairtrade International, True Price & Trucost. Retrieved from: http://makefruitfair.org/wp-content/uploads/2017/07/170224_Research_Report_External_Cost_of_Bananas_-_final.pdf
Voora, V., Larrea, C., and Bermudez, S. (2020). Global market report: Bananas. Sustainable Commodities Marketplace Series 2019, The International Institute for Sustainable Development, 12 pp. Retrieved from: https://www.iisd.org/system/files/publications/ssi-global-market-report-banana.pdf
Sariev, Eduard, & Germano, Guido. (2020). Bayesian regularized artificial neural networks for the estimation of the probability of default. Quantitative Finance, Vol. 20, No. 2, pp. 311–328. https://doi.org/10.1080/14697688.2019.1633014
Zhang, G. Peter, Patuwo, B. Eddy, and Hu, Michael Y. (1998). Forecasting with artificial neural networks: The state of the art. International Journal of Forecasting, 14, 35-62.
Zhang, G. Peter. (2003). Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing, 50, 159-175.