A Fuzzy Time Series Forecasting Model for Multi-Variate Forecasting Analysis with Fuzzy C-Means Clustering

Authors: Emrah Bulut, Okan Duru, Shigeru Yoshida

Abstract:

In this study, a fuzzy integrated logical forecasting method (FILF) is extended for multi-variate systems by using a vector autoregressive model. Fuzzy time series forecasting (FTSF) method was recently introduced by Song and Chissom [1]-[2] after that Chen improved the FTSF method. Rather than the existing literature, the proposed model is not only compared with the previous FTS models, but also with the conventional time series methods such as the classical vector autoregressive model. The cluster optimization is based on the C-means clustering method. An empirical study is performed for the prediction of the chartering rates of a group of dry bulk cargo ships. The root mean squared error (RMSE) metric is used for the comparing of results of methods and the proposed method has superiority than both traditional FTS methods and also the classical time series methods.

Keywords: C-means clustering, Fuzzy time series, Multi-variate design

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1084161

References:

[1] Q. Song and B. S. Chissom, "Forecasting enrollments with fuzzy time series - Part I," Fuzzy Sets and Systems, vol. 54, pp. 1-9, 1993.
[2] Q. Song and B. S. Chissom, "Forecasting enrollments with fuzzy time series -- Part II," Fuzzy Sets and Systems, vol. 62, pp. 1-8, 1994.
[3] S. M. Chen, "Forecasting enrollments based on fuzzy time series," Fuzzy Sets and Systems, vol. 81, pp. 311-319, 1996.
[4] K. Huarng, "Heuristic models of fuzzy time series for forecasting," Fuzzy Sets and Systems, vol. 123, pp. 369-386, 2001.
[5] O. Duru, "A fuzzy integrated logical forecasting model for dry bulk shipping index forecasting: An improved fuzzy time series approach," Expert Systems with Applications, vol. 37, pp. 5372-5380, 2010.
[6] K. Huarng and H.-K. Yu, "A Type 2 fuzzy time series model for stock index forecasting," Physica A: Statistical Mechanics and its Applications, vol. 353, pp. 445-462, 2005.
[7] J. R. Hwang, C. Shyi-Ming, and L. Chia-Hoang, "Handling forecasting problems using fuzzy time series," Fuzzy Sets and Systems, vol. 100, pp. 217-228, 1998.
[8] S. M. Chen and J. R. Hwang, "Temperature prediction using fuzzy time series," IEEE Transaction on Systems, Man and Cybernetics, vol. 30, pp. 263-275, 2000.
[9] K. Huarng, "Effective lengths of intervals to improve forecasting in fuzzy time series," Fuzzy Sets and Systems, vol. 123, pp. 387-394, 2001.
[10] S. M. Chen, "Forecasting enrollments based on high-order fuzzy time series," Cybernetics and Systems: An International Journal, vol. 33, pp. 1 - 16, 2002.
[11] S. M. Chen and C. C. Hsu, "A new method to forecast enrollments using fuzzy time series," International Journal of Applied Science and Engineering, vol. 2, pp. 234-244, 2004 2004.
[12] K. Huarng and T. H.-K. Yu, "The application of neural networks to forecast fuzzy time series," Physica A: Statistical Mechanics and its Applications, vol. 363, pp. 481-491, 2006.
[13] Q. Song, "A note on fuzzy time series model selection with sample autocorrelation with sample functions," Cybernetics and Systems: An International Journal, vol. 34, pp. 93- 07, 2003.
[14] J. Tinbergen, "Tonnage and Freight," De Nederlandsche Conjunctuur, pp. 23-35, reprinted in J. H. Klassen, L. M. Koyck and H. J. Wittenveen (eds) Jan TinbergenÔÇöSelected Papers (North Holland(1959)). 1934.
[15] W. Charemza and M. Gronicki, "An econometric model of world shipping and shipbuilding," Maritime Policy & Management, vol. 8, pp. 21-30, 1981.
[16] M. Beenstock, "A theory of ship prices," Maritime Policy & Management, vol. 12, pp. 215-225, 1985.
[17] M. Beenstock and A. Vergottis, "An Econometric Model of the World Tanker Market," Journal of Transport Economics and Policy, vol. 23, pp. 263-280, 1989.
[18] M. Beenstock and A. Vergottis, "An econometric model of the world market for dry cargo freight and shipping," Applied Economics, vol. 21, pp. 339 - 356, 1989.
[19] S. D. Tsolakis, C. Cridland, and H. E. Haralambides, "Econometric Modelling of Second-hand Ship Prices," Maritime Econ Logistics, vol. 5, pp. 347-377, 2003.
[20] S. Engelen, H. Meersman, and E. Van De Voorde, "Using system dynamics in maritime economics: an endogenous decision model for shipowners in the dry bulk sector," Maritime Policy & Management, vol. 33, pp. 141-158, 2006.
[21] J. Randers and U. Göluke, "Forecasting turning points in shipping freight rates: lessons from 30 years of practical effort," vol. 23, ed: John Wiley & Sons, Ltd., 2007, pp. 253-284.
[22] M. G. Kavussanos, "The dynamics of time-varying volatilities in different size second-hand ship prices of the dry-cargo sector," Applied Economics, vol. 29, pp. 433 - 443, 1997.
[23] A. W. Veenstra, "Quantitative Analysis of Shipping Markets," T99/3, TRAIL Thesis Series. Delft University Press: The Netherlands, 1999.
[24] M. G. Kavussanos, "Comparisons of Volatility in the Dry-Cargo Ship Sector: Spot versus Time Charters, and Smaller versus Larger Vessels," Journal of Transport Economics and Policy, vol. 30, pp. 67-82, 1996.
[25] M. G. Kavussanos, "Price risk modelling of different size vessels in the tanker industry," Logistics and Transportation Review, vol. 32, pp. 161- 176, 1996.
[26] J. B. MacQueen, "Some Methods for classification and Analysis of Multivariate Observations," Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, University of California Press., pp. 281-297, 1967.
[27] J. C. Bezdek, "Pattern Recognition with Fuzzy Objective Function Algoritms," 1981.
[28] J. C. Dunn, "A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters," Journal of Cybernetics, vol. 3, pp. 32-57, 1973.
[29] F. Höppner, F. Klawonn, R. Kruse, and T. Runkler, "Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition," Wiley, New York, 2000.
[30] U. Yolcu, E. Egrioglu, V. R. Uslu, M. A. Basaran, and C. H. Aladag, "A new approach for determining the length of intervals for fuzzy time series," Applied Soft Computing, vol. 9, pp. 647-651, 2009.
[31] D. A. Dickey and W. A. Fuller, "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, vol. 49, pp. 1057-1072, 1981.
[32] H. Akaike, "A new look at the statistical model identification," Automatic Control, IEEE Transactions on, vol. 19, pp. 716-723, 1974.
[33] S. Gideon, "Estimating the Dimension of a Model," The Annals of Statistics, vol. 6, pp. 461-464, 1978.
[34] E. J. Hannan and B. G. Quinn, "The Determination of the Order of an Autoregression," Journal of the Royal Statistical Society. Series B (Methodological), vol. 41, pp. 190-195, 1979.
[35] H. White, "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, vol. 48, pp. 817-838, 1980.
[36] T. S. Breusch, "TESTING FOR AUTOCORRELATION IN DYNAMIC LINEAR MODELS*," Australian Economic Papers, vol. 17, pp. 334- 355, 1978.
[37] L. G. Godfrey, "Testing Against General Autoregressive and Moving Average Error Models when the Regressors Include Lagged Dependent Variables," Econometrica, vol. 46, pp. 1293-1301, 1978.
[38] J. Durbin and G. S. Watson, "Testing for Serial Correlation in Least Squares Regression: I," Biometrika, vol. 37, pp. 409-428, 1950.
[39] J. Durbin and G. S. Watson, "TESTING FOR SERIAL CORRELATION IN LEAST SQUARES REGRESSION. II," Biometrika, vol. 38, pp. 159-178, June 1, 1951 1951.
[40] M. Stopford, "Maritime Economics." London: Routledge Publ. , 1997.