Modeling fitting-function-based fuzzy time series patterns for evolving stock index forecasting

Fuzzy time series models that have been developed have been widely applied to many applications of forecasting future stock prices or weighted indexes in the financial field. Three interesting problems have been identified in relation to the associated time series methods, as follows: (1) conventional time series models that consider single variables on associated problems only, (2) fuzzy time series models that determine the interval length of the linguistic values subjectively, and (3) selected variables that depend on personal experience and opinion subjectively. In light of the above limitations, this study constitutes a hybrid seven-step procedure that proposes three integrated fuzzy time series models that are based on fitting functions to forecast weighted indexes of the stock market. First, the proposed models employ Pearson correlation coefficients to objectively select important technical indicators. Second, this study utilizes an objective algorithm to determine the lower bound and upper bound of the universe of discourse automatically. Third, the proposed models use the spread-partition algorithm to automatically determine linguistic intervals. Finally, they combine the transformed variables to build three fuzzy time series models using the criterion of the minimal root mean square error (RMSE). Furthermore, this study provides all of the necessary justifying information for using a linear process to select the inputs for the given non-linear data. To further evaluate the performance of the proposed models, the transaction records of TAIEX (Taiwan Stock Exchange Capitalization Weighted Stock Index) and HSI (Hang Seng Indexes) from 1998/01/03 to 2006/12/31 are used to illustrate the methodology with two experimental data sets. Chen’s (Fuzzy Sets Syst. 81:311–319, 1996) model, Yu’s (Physica A 349:609–624, 2005) model, support vector regression (SVR), and partial least square regression (PLSR) are used as models to be compared with the proposed model when given the same data sets. The analytical results show that the proposed models outperform the listed models under the evaluation criteria of the RMSE (in contrast to the forecasting accuracy) for forecasting a weighted stock index in both the Taiwan and Hong Kong stock markets.