Abstract
Grey forecasting based on GM (1,1) has become an important methodology in time series analysis. But due to the limitation of predicting non-stationary time series, an improved grey forecasting GM (1,1) model with wavelet transform was proposed. The time series data was first decomposed to different scales by wavelet transform with à trous algorithm previous of Mallat algorithm in the parallel movement of time series, and then the decomposed time series were forecasted by GM (1,1) model to obtain forecasting results of the original time series. Time series prediction capability of GM (1,1) combined with wavelet transform was compared with that of traditional GM (1,1) model and autoregressive integrated moving average (ARIMA) model to energy source consumption and production forecasting in China. To effectiveness of these methods, eighteen years of time series records (1985 to 2002) for energy source consumption and production were used. The forecasting result from GM (1,1) model with wavelet transform for the data from 2000 to 2002 presented highest precision of three models. It shows that the GM (1,1) model with wavelet transform is more accurate and performs better than traditional GM (1,1) and ARIMA model.
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References
Tang, Y.M., Feng, M.G.: Data Processing System for Practical Statistics. Science Publishing Company Press, Beijing (2002)
Wu, B., Chen, M.H.: Use of Fuzzy Statistical Technique in Change Periods Detection of Nonlinear Time Series. Applied Mathematics and Computation 99(2-3), 241–254 (1999)
He, Y., Zhang, Y., Xiang, L.G.: Study of Application Model on BP Neural Network Optimized by Fuzzy Clustering. In: Gelbukh, A., de Albornoz, Á., Terashima-Marín, H. (eds.) MICAI 2005. LNCS (LNAI), vol. 3789, pp. 712–720. Springer, Heidelberg (2005)
Deng, J.L.: Control Problems of Grey System, pp. 1–2. Huazhong University of Science and Technology Press, Wuhan (1990)
Deng, J.L.: Grey Forecasting and Decision Making. Huazhong University of Science and Technology Press, Wuhan (1985)
Bao, Y.D., Wu, Y.P., He, Y.: A New Forecasting Model Based on the Combination of GM (1,1) Model and Linear Regression. Systems Engineering (Theory and Practice) 24(3), 95–98 (2004)
Tien, T.L.: A Research on the Prediction of Machining Accuracy by the Deterministic Grey Dynamic Model DGDM (1,1,1). Applied Mathematics and Computation 161(3), 923–945 (2005)
He, Y., Huang, M.: A Grey_Markov Forecasting Model for the Electric Power Requirement in China. In: Gelbukh, A., de Albornoz, Á., Terashima-Marín, H. (eds.) MICAI 2005. LNCS (LNAI), vol. 3789, pp. 574–582. Springer, Heidelberg (2005)
Liu, P.L., Shyr, W.J.: Another Sufficient Condition for the Stability of Grey Discrete-time Systems. Journal of the Franklin Institute 342(1), 15–23 (2005)
Box, G.E.P., Jenkins, G.M.: Time Series Analysis. Forecasting and Control, p. 575. Holden-Day, San Francisco (1976)
Li, X.B., Li, H.Q., Wang, F.Q., Ding, J.: A Remark on the Mallat Pyramidal Algorithm of Wavelet Analysis. Communications in Nonlinear Science and Numerical Simulation 2(4), 240–243 (1997)
Wickerhauser, M.V.: Adapted Wavelet Analysis from Theory to Software, pp. 213–235. Wellesley, Massachusetts (1994)
Sun, Z.M., Jiang, X.W., Wang, X.F.: Application of à Trous Wavelet to Satellite Telemetry Data Recursive Prediction. Journal of Nanjing University of Science and Technology 28(6), 606–611 (2004)
National Bureau of Statistic of China: China Statistical Year Book. China Statistics Press, Beijing (2004)
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Cen, H., Bao, Y., Huang, M., He, Y. (2006). Time Series Analysis of Grey Forecasting Based on Wavelet Transform and Its Prediction Applications. In: Yeung, DY., Kwok, J.T., Fred, A., Roli, F., de Ridder, D. (eds) Structural, Syntactic, and Statistical Pattern Recognition. SSPR /SPR 2006. Lecture Notes in Computer Science, vol 4109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11815921_38
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DOI: https://doi.org/10.1007/11815921_38
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