International Journal of Mathematics and Computational Science
Articles Information
International Journal of Mathematics and Computational Science, Vol.4, No.2, Jun. 2018, Pub. Date: May 28, 2018
A Hybrid SARIMA-NARX Nonlinear Dynamics Model for Predicting Solar Radiation in Makurdi
Pages: 35-47 Views: 405 Downloads: 174
Authors
[01] Emmanuel Vezua Tikyaa, Department of Physics, Federal University Dutsin-Ma, Katsina State, Nigeria.
[02] Matthias Idugba Echi, Department of Physics, University of Agriculture Makurdi, Benue State, Nigeria.
[03] Bernadette Chidomnso Isikwue, Department of Physics, University of Agriculture Makurdi, Benue State, Nigeria.
[04] Alexander Nwabueze Amah, Department of Physics, University of Agriculture Makurdi, Benue State, Nigeria.
Abstract
In this paper a hybrid SARIMA-NARX neural network model was successfully developed, trained using 16 years data obtained from the Nigerian Meteorological Agency (NIMET) and tested by forecasting daily solar radiation time series in Makurdi. The intrinsic parameters of the model was optimized using the predetermined nonlinear dynamics of the meteorological data in order to get the right neural network configuration, save time and ensure accurate forecasts. The results of the model testing showed that, the model performed better and faster using the Levenberg-Marquardt training function with daily solar radiation successfully forecasted using minimum temperature and maximum temperature as exogenous variables. The daily solar radiation in Makurdi for the year 2016 was successfully predicted to validate the model using the hybrid model generating a RMSE value of 1.6475, correlation coefficient of 0.8782, MAE of 1.2042 and MAPE of 5.9695%. After validation, forecasts of daily solar radiation were then made for 2016 and 2017 with quite good accuracy recorded. It was also observed that the data trends were accurately predicted as a result of the SARIMA model adopted while the NARX model generated the nonlinear part of the time series with relatively fair but acceptable RMSE values which could be as a result of the poor correlation of the meteorological variables emanating from the presence of missing data and noise in the meteorological data used.
Keywords
NARX, SARIMA, Neural Network, Chaos Theory, Forecasting
References
[01] Lorenz, E. N. (1963). Deterministic Non-periodic Flow. Journal of the Atmospheric Sciences, 20 (2): 130-141.
[02] IPCC (2017). Working Group I: The Physical Science Basis. Fourth Assessment. Report of the Intergovernmental Panel on Climate Change (AR4): Summary of Policymakers, Geneva.
[03] Masqood, I., Khan, R. M. and Abraham, A. (2004). An Ensemble of Neural Networks for Weather Forecasting. Neural Computing and Application, 13: 112-122. DOI: 10.1007/s00521-004-0413-4.
[04] Diaz-Robles, L. A., Ortega, J. C., Fu, J. S., Reed, G. D., Chow, J. C., Watson, J. G. and Moncada-Herrera, J. A. (2008). A Hybrid ARIMA and Artificial Neural Networks Model to Forecast Particulate Matter in Urban Areas: The case of Temuco, Chile. Atmosphere environment, 42: 8337.
[05] Unsihuay-Vila, C., Zambroni de Souza, A. C., Marangon-Lima, J. W. and Balestrassi, P. P. (2009). Electricity Demand and Spot Price Forecasting using Evolutionary Computation Combined with Chaos Nonlinear Dynamics Model. Elsevier: Electrical Power and Energy Systems, 32: 112.
[06] Caiado, J. (2010). Performance of combined double seasonal univariate time series models for forecasting water demand. Journal of Hydrologic Engineering, 15 (3): 8.
[07] Di Piazza, A., Di Piazza, M. C. and Vitale, G. (2014). Estimation and Forecast of Wind Power Generation by FTDNN and NARX-net based Models for Energy Management Purpose in Smart Grids,” Proceedings of the International Conference on Renewable Energies and Power Quality, ICREPQ ’14, Vol. 12, 8th-12th April, 2014.
[08] Cadenas, E., Rivera, W., Campos-Amezcua, R. and Heard, C. (2016). Wind Speed Prediction Using a Univariate ARIMA Model and a Multivariate NARX Model. Energies, 2016 (9), 109.
[09] Haykin, S. (2009). Neural Networks and Learning Machines, 3rd edition, Pearson Education Inc., New Jersey, P. 37.
[10] Beale, M. H., Hagan, M. T. and Demuth, B. H. (2014). Neural Network ToolboxTM User’s Guide (R2014b), MathWorks Inc., Pp. 23-34.
[11] Menezes-Jnr, J. M. and Barreto, G. A. (2007). Long-Term Time Series Prediction with the NARX Network: An Empirical Evaluation. Preprint submitted to Elsevier Science, Department of Teleinformatics Engineering, Fortaleza, Cear´a, Brazil, P. 15.
[12] Diaconescu, E. (2008). The Use of NARX Neural Networks to Predict Chaotic Time Series. WSEAS Transactions on Computer Research, 3 (3): 189.
[13] Menezes-Jnr, J. M. and Barreto, G. M. (2007). Multistep-Ahead Prediction of Rainfall Precipitation Using the NARX Network. Department of Teleinformatics Engineering, Fortaleza, Cear´a, Brazil, P. 12.
[14] Box, G. E. P., Jenkins, G. M. and Reinsel, G. C. (1994). Time Series Analysis: Forecasting and Control, 3rd edition, Englewood Cliffs, New Jersey, Pp. 34-51.
[15] Nau, R. (2014). Introduction to ARIMA models. Lecture notes on forecasting, Duke University. http://people.duke.edu/~rnau/forecasting.html
[16] Iwok, A. I. (2017). Handling Seasonal Autoregressive Integrated Moving Average Model with Correlated Residuals. American Journal of Mathematics and Statistics, 7 (1): 1-6. DOI: 10.5923/j.ajms.20170701.01.
[17] Telgarsky, R. (2013). Dominant Frequency Extraction. arXiv 1 (2013): 1-12.
[18] NOAA (2016). Nigeria: Climatic Normals from 1961-1990. National Oceanic and Atmospheric Administration. http://www.ncdc.noaa.gov/wdcmet/data-access-search-viewer-tools/nigeria-climate-normals-1961-1990.
[19] Kiusalaas, J. (2010). Numerical Methods in Engineering with MATLAB, 2nd edition. Cambridge University Press, London, 2010, Pp. 116-119.
[20] Cellucci, C., Albano, A. and Rapp, P. (2003). Comparative Study of Embedding Methods. Physical Review E, 67 (6): 1-13.
[21] Takens, F. (1980). Detecting Strange Attractors in Turbulence. Lecture Notes in Mathematics, 898: 366.
[22] Kennel, M. B., Brown, R. and Abarbanel, H. D. (1992). Determining Embedding Dimension for Phase-Space Reconstruction using a Geometrical Construction. Physical Review A, 45 (6): 3403-3411.
[23] Baghirli, O. (2015). Comparison of Lavenberg-Marquardt, Scaled Conjugate Gradient and Bayesian Regularization Backpropagation Algorithms for Multistep Ahead Wind Speed Forecasting Using Multilayer Perceptron Feedforward Neural Network,” Published M.Sc. Thesis in Energy Technology With Focus on Wind Power, Dept. of Earth Sciences, Uppsala University, Pp: 21-35.
[24] Ljung, G. and Box, G. E. P. (1978). On a Measure of Lack of Fit in Time Series Models. Biometrika, 66: 67-72.
[25] Zhongxian, M., Eugene, Y., Fue-sang, L., Zhiling, Y., and Yongquian, L. (2014). Ensemble Nonlinear Autoregressive Artificial Neural Networks for Short-term Wind Speed and Power Forecasting, International Scholarly Research Notices, 6: 1-16. http://dx.doi.org/10.1155/2014/972580.
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