Residual analysis using Fourier series transform in Fuzzy time series model

Document Type: Research Paper

Author

Department of Management Sciences, Tamkang University, No.151, Yingzhuan Rd., Tamsui Dist., New Taipei City 25137, Taiwan, R.O.C.

Abstract

In this paper, we propose a new residual analysis method using Fourier series transform into fuzzy time series model for improving the forecasting performance. This hybrid model takes advantage of the high predictable power of fuzzy time series model and Fourier series transform to fit the estimated residuals into frequency spectra, select the low-frequency terms, filter out high-frequency terms, and then have well forecasting performance.
Two numerical examples are given to show that our proposed model can be applied with the best forecasting performance than the other models.

Keywords


bibitem{1} S. M. Chen, {it Forecasting enrollments based on fuzzy time series}, Fuzzy Sets and Systems, {bf 81}textbf{(3)}(1996), 311--319.
bibitem{2} T. L. Chen, C. H. Cheng and H. J. Teoh, {it High-order fuzzy time-series based on multi-period adaptation model for forecasting stock markets}, Physica A, {bf 387}textbf{(4)} (2008), 876--888.
bibitem{3} C. H. Cheng, T. L. Chen, H. J. Teoh and C. H. Chiang, {it Fuzzy time-series based on adaptive expectation model for TAIEX forecasting}, Expert System with Applications, {bf 34}textbf{(2)} (2008), 1126--1132.
bibitem{4} C. H. Cheng, G. W. Cheng and J. W. Wang, {it Multi-attribute fuzzy time series method based on fuzzy clustering}, Expert Systems with Applications, {bf 34}textbf{(2)} (2008), 1235--1242.
bibitem{5} K. H. Huarng, {it Effective lengths of intervals to improve forecasting in fuzzy time series}, Fuzzy Sets and Systems, {bf 123}textbf{(3)} (2001), 387--394.
bibitem{6} K. Huarng and T. H. K. Yu, {it The application of neural networks to forecast fuzzy time series}, Physica A, {bf 336}textbf{(2)} (2006), 481--491.
bibitem{7} M. Khashei, M. Bijari and S. R. Hejazi, {it An extended fuzzy artificial neural networks model for time series forecasting}, Iranian Journal of Fuzzy Systems, {bf 8}textbf{(3)} (2011), 45--66.
bibitem{8} I. H. Kuo, S. J. Horng, T. W. Kao, T. L. Lin, C. L. Lee and Y. Pan, {it An improved method for forecasting enrollments based on fuzzy time series and particle swarm optimization}, Expert Systems with Applications, {bf 36}textbf{(3)} (2009), 6108--6117.
bibitem{9} I. H. Kuo, S. J. Horng, Y. H. Chen, R. S. Run, T. W. Kao, R. J. Chen, J. L. Lai and T. L. Lin, {it Forecasting TAIFEX based on fuzzy time series and particle swarm optimization}, Expert Systems with Applications, {bf 37}textbf{(2)} (2010), 1494--1502.
bibitem{10} L. W. Lee, L. H. Wang and S. M. Chen, {it Temperature prediction and TAIFEX forecasting based on fuzzy logical relationships and genetic algorithms}, Expert Systems with Applications, {bf 33}textbf{(3)} (2007), 539--550.
bibitem{11} Y. H. Lin and P. C. Lee, {it Novel high-precision grey forecasting model}, Automation in Contruction, textbf{16}textbf{(6)} (2007), 771--777.
bibitem{12} B. Moller and U. Reuter, {it Prediction of uncertain structural responses using fuzzy time series}, Computers and Structures, {bf 86}textbf{(10)} (2008), 1123--1139.
bibitem{13} S. R. Singh, {it A robust method of forecasting based on fuzzy time series}, Applied Mathematics and Computation, {bf 188}textbf{(1)} (2007), 472-484.
bibitem{14} Q. Song and B. S. Chissom, {it Forecasting enrollments with fuzzy time series --- part I}, Fuzzy Sets and Systems, {bf 54}textbf{(1)} (1993), 1--9.
bibitem{15} Q. Song and B. S. Chissom, {it Fuzzy time series and its models}, Fuzzy Sets and Systems, {bf 54}textbf{(3)} (1993), 269--277.
bibitem{16} Q. Song and B. S. Chissom, {it Forecasting enrollments with fuzzy time series --- part II}, Fuzzy Sets and Systems, {bf 62}textbf{(1)} (1994), 1--8.
%bibitem{17} R. C. Tsaur, J. C. O. Yang and H. F. Wang, {it Fuzzy relation analysis in fuzzy time series model}, Computers and Mathematics with Application, {bf 49}textbf{(4)}(2005), 539--548.
bibitem{18} C. H. Wang, {it Predicting tourism demand using fuzzy time series and hybrid grey theory}, Tourism Management, {bf 25}textbf{(3)} (2004), 367--374.
bibitem{19} N. Y. Wang and S. M. Chen, {it Temperature prediction and TAIFEX forecasting based on automatic clustering techniques and two-factor high-order fuzzy time series}, Expert Systems with Applications, {bf 36}textbf{(2)} (2007), 2143--2154.
bibitem{20} H. L. Wong, Y. H. Tu and C. C. Wang, {it Application of fuzzy time series models for forecasting the amount of Taiwan export}, Expert Systems with Applications, {bf 37}textbf{(2)} (2010), 1465--1470.
bibitem{21} H. K. Yu, {it Weighted fuzzy time series model for TAIEX forecasting}, Physica A, {bf 349}textbf{(3-4)} (2005), 609--624.