A Fuzzy Time Series Forecasting Model for Multi-Variate Forecasting Analysis with Fuzzy C-Means Clustering
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.
[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.
[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.
@article{"International Journal of Information, Control and Computer Sciences:63980", author = "Emrah Bulut and Okan Duru and Shigeru Yoshida", title = "A Fuzzy Time Series Forecasting Model for Multi-Variate Forecasting Analysis with Fuzzy C-Means Clustering", 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", volume = "6", number = "3", pages = "417-7", }
