Improving stock index forecasts by using a new weighted fuzzy-trend time series method

We propose using new weighted operators in fuzzy time series to forecast the future performance of stock market indices. Based on the chronological sequence of weights associated with the original fuzzy logical relationships, we define both chronological-order and trend-order weights, and incorporate our proposals for the ex-post forecast into the classical modeling approach of fuzzy time series. These modifications for the assignation of weights affect the forecasting process, because we use jumps as technical indicators to predict stock trends, and additionally, they provide a trapezoidal fuzzy number as a forecast of the future performance of the stock index value. Working with trapezoidal fuzzy numbers allows us to analyze both the expected value and the ambiguity of the future behavior of the stock index, using a possibilistic interval-valued mean approach. Therefore, using fuzzy logic more useful information is provided to the decision analyst, which should be appropriate in a financial context. We analyze the effectiveness of our approach with respect to other weighted fuzzy time series methods using trading data sets from the Taiwan Stock Index (TAIEX), the Japanese NIKKEI Index, the German Stock Index (DAX) and the Spanish Stock Index (IBEX35). The comparative results indicate the better accuracy of our procedure for point-wise one-step ahead forecasts.