a b s t r a c tThe study of fuzzy time series has increasingly attracted much attention due to its salient capabilities of tackling uncertainty and vagueness inherent in the data collected. A variety of forecasting models including high-order models have been devoted to improving forecasting accuracy. However, the high-order forecasting approach is accompanied by the crucial problem of determining an appropriate order number. Consequently, such a deficiency was recently solved by Li and Cheng [S.-T. Li, Y.-C. Cheng, Deterministic Fuzzy time series model for forecasting enrollments, Computers and Mathematics with Applications 53 (2007) 1904-1920] using a deterministic forecasting method. In this paper, we propose a novel forecasting model to enhance forecasting functionality and allow processing of two-factor forecasting problems. In addition, this model applies fuzzy cmeans (FCM) clustering to deal with interval partitioning, which takes the nature of data points into account and produces unequal-sized intervals. Furthermore, in order to cope with the randomness of initially assigned membership degrees of FCM clustering, Monte Carlo simulations are used to justify the reliability of the proposed model. The superior accuracy of the proposed model is demonstrated by experiments comparing it to other existing models using real-world empirical data.

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Recently, fuzzy time series have attracted more academic attention than traditional time series due to their capability of dealing with the uncertainty and vagueness inherent in the data collected. The formulation of fuzzy relations is one of the key issues affecting forecasting results. Most of the present works adopt IF-THEN rules for relationship representation, which leads to higher computational overhead and rule redundancy. Sullivan and Woodall proposed a Markov-based formulation and a forecasting model to reduce computational overhead; however, its applicability is limited to handling one-factor problems. In this paper, we propose a novel forecasting model based on the hidden Markov model by enhancing Sullivan and Woodall's work to allow handling of two-factor forecasting problems. Moreover, in order to make the nature of conjecture and randomness of forecasting more realistic, the Monte Carlo method is adopted to estimate the outcome. To test the effectiveness of the resulting stochastic model, we conduct two experiments and compare the results with those from other models. The first experiment consists of forecasting the daily average temperature and cloud density in Taipei, Taiwan, and the second experiment is based on the Taiwan Weighted Stock Index by forecasting the exchange rate of the New Taiwan dollar against the U.S. dollar. In addition to improving forecasting accuracy, the proposed model adheres to the central limit theorem, and thus, the result statistically approximates to the real mean of the target value being forecast.

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