A study for second-order modeling of fuzzy time series

A formulation is proposed for the modeling of second-order fuzzy time series. The method of fuzzy time series has been proved an effective tool for a variety of forecasting problems. When the historical data on hand are linguistic values, the traditional time series methodologies fail to work. Due to this situation, the fuzzy time series model has been developed and applied. Although many applications of the fuzzy time series method can be found in the literature, they are based on the first-order fuzzy time series and the accuracy of forecast is quite limited. In order to enhance the accuracy of forecasting results and to keep the simplicity of high-order fuzzy time series models, a new formulation is developed. By taking advantage of the current model, the historical records of population in the Taiwan area are tested. The results are compared with those of the traditional regression method and those of the first-order fuzzy time series. It is found that the accuracy of the second-order model is the best.