Journal of Mathematics and Statistics

A Hybrid Approach based on Winter's Model and Weighted Fuzzy Time Series for Forecasting Trend and Seasonal Data

Suhartono and Muhammad Hisyam Lee

DOI : 10.3844/jmssp.2011.177.183

Journal of Mathematics and Statistics

Volume 7, Issue 3

Pages 177-183


Problem statement: In the literature, the most studied of fuzzy time series for the purpose of forecasting is the first order fuzzy time series model. In this model, only the first lagged variable is used when constructing the first order fuzzy time series model. Therefore, such approaches fail to analyze accurately trend and seasonal time series which is an important class in time series models. Approach: In this paper, a hybrid approach is proposed in order to analyze trend and seasonal fuzzy time series. The proposed hybrid approach is based on Winter’s model and weighted fuzzy time series. The Winter’s model and the WFTS model are used jointly, aiming to capture different forms of pattern in the time series data. The order of this model is determined by utilizing graphical order fuzzy relationship. A real time series about tourist arrivals data is analyzed with this method to show the efficiency of the proposed hybrid method. Results: The results obtained from the proposed method are compared with the other methods, i.e., Decomposition, Winter’s and ARIMA models. As a result, it is observed that more accurate results are obtained from the proposed hybrid method. Conclusion: The empirical results with tourist arrivals data clearly suggest that the hybrid model is able to outperform each component model used in isolation the pattern of time series data. Moreover, these empirical evidences suggest that by using dissimilar models or models that disagree each other strongly, the hybrid model will have lower generalization variance or error. Additionally, because of the possible unstable or changing patterns in the data, using the hybrid method can reduce the model uncertainty which typically occurred in statistical inference and time series forecasting.


© 2011 Suhartono and Muhammad Hisyam Lee. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.