Comparative Study of Wavelet-SARIMA and EMD-SARIMA for Forecasting Daily Temperature Series

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DOI: https://doi.org/10.28924/2291-8639-20-2022-17
Published: Mar 18, 2022
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Luwam Ghide, Siyuan Wei, Yiming Ding, Comparative Study of Wavelet-SARIMA and EMD-SARIMA for Forecasting Daily Temperature Series, Int. J. Anal. Appl., 20 (2022), 17.

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Luwam Ghide, Siyuan Wei, Yiming Ding

Abstract

This paper aims to find a forecasting model based on the comparative study of wavelet- ARIMA and EMD-ARIMA models and residual-based model selection technique for temperature time series. Time series analysis is essential in studying temperature data for investigating the variation and predicting the future trend, in which we can control the changes and make good decisions. And most important is to understand the trend in the series with time. This study applied hybridized models of wavelet transform and empirical mode decomposition with seasonal autoregressive integrated moving average (SARIMA), which combines two models to get better accuracy, for forecasting daily average temperature time series data in the central region of Eritrea, Asmara. Daily data was collected for 30 years, from January 1, 1991, to December 31, 2020. The study compares WT-SARIMA and EMD-SARIMA models to find a well fit and better forecasting model. Model selection techniques are essential for time series analysis to determine which model best fits our data. AIC and BIC are the most used methods in model selection. This paper uses an additional method based on the residual series. In estimating accurate parameters, the structure of the residual sequence had a lot of connection, in which a stationary residual depict an accurate estimation. From this perspective, a nonstationarity measurement of the residual series is used for model selection. The relative performance is based on the predictive capability of sample forecasts assessed. The results indicate that the hybridized wavelet-SARIMA model is more effective than the other models, and MATLAB soft-wire is used for this analysis.

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References

  1. M.G. Ghebrezgabher, X. Yang, Spatio-Temporal Assessment of Climate Change in Eritrea Based on Precipitation and Temperature Variables, World Wide J. Multidiscip. Res. Develop. 4 (2018), 1–10.
  2. ]M. Murat, I. Malinowska, M. Gos, J. Krzyszczak, Forecasting Daily Meteorological Time Series Using ARIMA and Regression Models, Int. Agrophys. 32 (2018), 253–264. https://doi.org/10.1515/intag-2017-0007.
  3. D.B. Lobell, A. Sibley, J. Ivan Ortiz-Monasterio, Extreme Heat Effects on Wheat Senescence in India, Nat. Clim. Change. 2 (2012), 186–189. https://doi.org/10.1038/nclimate1356.
  4. M.A. Semenov, P.R. Shewry, Modelling Predicts That Heat Stress, Not Drought, Will Increase Vulnerability of Wheat in Europe, Sci. Rep. 1 (2011), 66. https://doi.org/10.1038/srep00066.
  5. N. Subash, A.K. Sikka, Trend Analysis of Rainfall and Temperature and Its Relationship Over India, Theor. Appl. Climatol. 117 (2014), 449–462. https://doi.org/10.1007/s00704-013-1015-9.
  6. E. El-Mallah, S. Elsharkawy, Time-Series Modeling and Short Term Prediction of Annual Temperature Trend on Coast Libya Using the Box-Jenkins ARIMA Model, Adv. Res. 6 (2016), 1–11. https://doi.org/10.9734/AIR/2016/24175.
  7. K. Anitha Kumari, N. Kumar Boiroju, P.R. Reddy, Forecasting of Monthly Mean of Maximum Surface Air Temperature in India, Int. J. Stat. Math. 9 (2014), 14–19.
  8. P. Chen, A. Niu, D. Liu, W. Jiang, B. Ma, Time Series Forecasting of Temperatures using SARIMA: An Example from Nanjing, IOP Conf. Ser.: Mater. Sci. Eng. 394 (2018), 052024. https://doi.org/10.1088/1757-899X/394/5/052024.
  9. A.H. Nury, K. Hasan, Md.J.B. Alam, Comparative Study of Wavelet-ARIMA and Wavelet-ANN Models for Temperature Time Series Data in Northeastern Bangladesh, J. King Saud Univ. - Sci. 29 (2017), 47–61. https://doi.org/10.1016/j.jksus.2015.12.002.
  10. N.Q.N. Md-Khair, R. Samsudin, A. Shabri, Wavelet Transform and Autoregressive Integrated Moving Average Combination Approach in Crude Oil Prices Forecasting, Int. J. Innov. Comput. 8 (2018), 41-48. https://doi.org/10.11113/ijic.v8n2.177.
  11. A. Ben Mabrouk, N. Ben Abdallah, Z. Dhifaoui, Wavelet Decomposition and Autoregressive Model for Time Series Prediction, Appl. Math. Comput. 199 (2008), 334–340. https://doi.org/10.1016/j.amc.2007.09.067.
  12. T. Kriechbaumer, A. Angus, D. Parsons, M. Rivas Casado, An Improved Wavelet–ARIMA Approach for Forecasting Metal Prices, Resources Policy. 39 (2014), 32–41. https://doi.org/10.1016/j.resourpol.2013.10.005.
  13. S.A.A. Karim, M.T. Ismail, M.K. Hasan, J. Sulaiman, Denoising the Temperature Data Using Wavelet Transform, Appl. Math. Sci. 7 (2013), 5821–5830. https://doi.org/10.12988/ams.2013.38450.
  14. A. Araghi, M. Mousavi Baygi, J. Adamowski, J. Malard, D. Nalley, S.M. Hasheminia, Using Wavelet Transforms to Estimate Surface Temperature Trends and Dominant Periodicities in Iran Based on Gridded Reanalysis Data, Atmospheric Res. 155 (2015), 52–72. https://doi.org/10.1016/j.atmosres.2014.11.016.
  15. K.-M. Lau, H. Weng, Climate Signal Detection Using Wavelet Transform: How to Make a Time Series Sing, Bull. Amer. Meteor. Soc. 76 (1995), 2391–2402.
  16. M. Sifuzzaman, M. Islam, M. Ali, Application of Wavelet Transform and its Advantages Compared to Fourier Transform, J. Phys. Sci. 13 (2009), 121–134.
  17. N. Al Bassam, V. Ramachandran, S. Eratt Parameswaran, Wavelet Theory and Application in Communication and Signal Processing, in: S. Mohammady (Ed.), Wavelet Theory, IntechOpen, 2021. https://doi.org/10.5772/intechopen.95047.
  18. G. Bousaleh, F. Hassoun, T. Ibrahim, Application of Wavelet Transform in the field of Electromagnetic Compatibility and power quality of industrial systems, in: 2009 International Conference on Advances in Computational Tools for Engineering Applications, IEEE, Beirut, Lebanon, 2009: pp. 284–289. https://doi.org/10.1109/ACTEA.2009.5227896.
  19. N.E. Huang, Z. Shen, S.R. Long, M.C. Wu, H.H. Shih, Q. Zheng, N.-C. Yen, C.C. Tung, H.H. Liu, The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis, Proc. R. Soc. Lond. A. 454 (1998), 903–995. https://doi.org/10.1098/rspa.1998.0193.
  20. M. Kedadouche, M. Thomas, A. Tahan, A Comparative Study Between Empirical Wavelet Transforms and Empirical Mode Decomposition Methods: Application to bearing defect diagnosis, Mech. Syst. Signal Process. 81 (2016), 88–107. https://doi.org/10.1016/j.ymssp.2016.02.049.
  21. H. Wang, L. Liu, Z. (Sean) Qian, H. Wei, S. Dong, Empirical Mode Decomposition–Autoregressive Integrated Moving Average: Hybrid Short-Term Traffic Speed Prediction Model, Transport. Res. Record. 2460 (2014), 66–76. https://doi.org/10.3141/2460-08.
  22. Z.Y. Wang, J. Qiu, F.F. Li, Hybrid Models Combining EMD/EEMD and ARIMA for Long-Term Streamflow Forecasting, Water. 10 (2018), 853. https://doi.org/10.3390/w10070853.
  23. Y. Zhou, M. Huang, Lithium-ion batteries remaining useful life prediction based on a mixture of empirical mode decomposition and ARIMA model, Microelectron. Reliab. 65 (2016), 265–273. https://doi.org/10.1016/j.microrel.2016.07.151.
  24. Q. Tan, H. Jiang, Y. Ding, Model Selection Method Based on Maximal Information Coefficient of Residuals, Acta Math. Sci. 34 (2014), 579–592. https://doi.org/10.1016/S0252-9602(14)60031-X.
  25. Z. Zhou, Z. Zhou, L. Wu, Calibration for Parameter Estimation of Signals with Complex Noise via Nonstationarity Measure, Complexity. 2021 (2021), 8840757. https://doi.org/10.1155/2021/8840757.
  26. Y. Ding, W. Fan, Q. Tan, K. Wu, Y. Zou, Nonstationarity Measure of Data Stream (in Chinese), Acta Math. Sci. 30A (2010), 1364–1376.
  27. K. Wu, Nonstationarity of Stock Returns, in: M. Bohner, Y. Ding, O. Došlý (Eds.), Difference Equations, Discrete Dynamical Systems and Applications, Springer International Publishing, Cham, 2015: pp. 153–165. https://doi.org/10.1007/978-3-319-24747-2_12.
  28. Q. Tan, The Nonstationarity Measure of Time Series and Its Application (in Chinese), Ph.D. thesis, University of Chinese Academy of Sciences, Beijing, China, 2013.
  29. J. Lan, Q. Tan, and Q. Dong, Selection of Forecasting Models For Irrigation Water Consumption Based on Nonstationarity Measure (in Chinese), Eng. J. Wuhan Univ. 47 (2014), 721–725.
  30. Q. Tan, L. Wu, B. Li, Decomposition of Noise and Trend Based on EMD and Nonstationarity Measure (in Chinese), Acta Math. Sci. 36A (2016), 783–794.
  31. S. Maheshwari and A. Kumar, Empirical Mode Decomposition: Theory & Applications, Int. J. Electron. Electric. Eng. 7 (2014), 873–878.
  32. B. Yadollah, F. Gharib, B. Ali, A Study and Prediction of Annual Temperature in Shiraz Using ARIMA Model, Geograph. Space, 12 (2012), 127-144.
  33. N. Al Bassam, V. Ramachandran, S. Eratt Parameswaran, Wavelet Theory and Application in Communication and Signal Processing, in: S. Mohammady (Ed.), Wavelet Theory, IntechOpen, 2021. https://doi.org/10.5772/intechopen.95047.
  34. Y. Wei, J. Wang, C. Wang, Network Traffic Prediction Based on Wavelet Transform and Season ARIMA Model, in: D. Liu, H. Zhang, M. Polycarpou, C. Alippi, H. He (Eds.), Advances in Neural Networks – ISNN 2011, Springer Berlin Heidelberg, Berlin, Heidelberg, 2011: pp. 152–159. https://doi.org/10.1007/978-3-642-21111-9_17.