A fuzzy seasonal ARIMA model for forecasting. (English) Zbl 1003.62081

Summary: This paper proposes a fuzzy seasonal ARIMA (FSARIMA) forecasting model, which combines the advantages of the seasonal time series ARIMA (SARIMA) model and the fuzzy regression model. It is used to forecast two seasonal time series data of the total production value of the Taiwan machinery industry and the soft drink time series. The intention of this paper is to provide business which is affected by diversified management with a new method to conduct short-term forecasting. This model includes both interval models with interval parameters and the possible distribution of future values. Based on the results of practical application, it can be shown that this model makes good forecasts and is realistic. Furthermore, this model makes it possible for decision makers to forecast the best and worst estimates based on fewer observations than the SARIMA model.


62M20 Inference from stochastic processes and prediction
62P30 Applications of statistics in engineering and industry; control charts
62M99 Inference from stochastic processes
Full Text: DOI


[1] Box, G.P.; Jenkins, G.M., Time series analysis: forecasting and control, (1976), Holden-Day San Francisco, CA · Zbl 0363.62069
[2] Chen, S.M., Forecasting enrollments based on fuzzy time series, Fuzzy sets and systems, 81, 3, 311-319, (1996)
[3] Dubois, D.; Prade, H., Operations on fuzzy numbers, Internat. J. systems sci., 9, 613-629, (1978) · Zbl 0383.94045
[4] Dubois, D.; Prade, H., Theory and applications, Fuzzy sets and systems, (1980), Academic Press New York · Zbl 0444.94049
[5] Institute of Mechanical Industry in Industrial Technology Research Institute, 1997, Present Position and Trend Analysis of Mechanical Industry, Research Report in Industrial Technology Research Institute, 1998.
[6] Institution for Economic Research, Taiwan Year Book of Mechanical Industry, Research Report in Institution for Economic Research, 1996.
[7] Ishibuchi, H.; Tanaka, H., Interval regression analysis based on mixed 0-1 integer programming problem, J. Japan soc. industrial engng., 40, 5, 312-319, (1988)
[8] Laarhoven, P.J.M.; Pedrycz, W., A fuzzy extension of Saaty’s priority theory, Fuzzy sets and systems, 11, 229-241, (1983) · Zbl 0528.90054
[9] Montgomery; Johnson, D.C.L.A.; Gardiner, J.S., (), 364
[10] Savic, D.A.; Pedrycz, W., Evaluation of fuzzy linear regression models, Fuzzy sets and systems, 39, 1, 51-63, (1991) · Zbl 0714.62065
[11] Song, Q.; Chissom, B.S., Fuzzy time series and its models, Fuzzy sets and systems, 54, 3, 269-277, (1993) · Zbl 0792.62087
[12] Song, Q.; Chissom, B.S., Forecasting enrollments with fuzzy time series—part I, Fuzzy sets and systems, 54, 1, 1-9, (1993)
[13] Song, Q.; Chissom, B.S., Forecasting enrollments with fuzzy time series—part II, Fuzzy sets and systems, 62, 1, 1-8, (1994)
[14] Tanaka, H., Fuzzy data analysis by possibility linear models, Fuzzy sets and systems, 24, 3, 363-375, (1987) · Zbl 0633.93060
[15] Tanaka, H.; Ishibuchi, H., Possibility regression analysis based on linear programming, fuzzy regression analysis, (), 47-60
[16] Tanaka, H.; Uejima, S.; Asai, K., Linear regression analysis with fuzzy model, IEEE trans. systems, Man cybernet., 12, 6, 903-907, (1982) · Zbl 0501.90060
[17] Tseng, F.M.; Tzeng, G.H.; Yu, H.C.; Yuan, B.J.C., Fuzzy ARIMA model for forecasting the foreign exchange market, Fuzzy sets and systems, 118, 9-19, (2000)
[18] Watada, J., Fuzzy time series analysis and forecasting of sales volume, fuzzy regression analysis, (), 211-227
[19] L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, Parts 1-3, Inform. Sci. 8 (1975) 199-249; 8 (1975) 301-357; 9 (1976) 43-80. · Zbl 0397.68071
[20] Akaike, H., Maximum likelihood identification of Gaussian auto-regressive moving average models, Biometrika, 60, 255-266, (1973)
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