Forecasting trend data using a hybrid simple moving average-weighted fuzzy time series model

Abstract

First order fuzzy time series (1st order FTS) is one of popular time series forecasting models. Since employing the first lag variable and using fuzzy logical relationship to derive the forecasting value, 1st order FTS is often unsuccessful in analyzing trend time series. On the other hand, moving averages can be used to quickly identify the direction of trend by smoothing the data. However, moving averages are lagging indicators that will always be a step behind and give late signals. Therefore, It had better not use moving averages alone as a forecasting model. This paper proposed a hybrid approach based on moving averages and weighted fuzzy time series (WFTS) model to analyze and forecast the trend time series data. By using both models jointly, it is expected that the different forms of pattern in time series data can be captured. This hybrid model takes advantage of moving averages in identifying trend direction and WFTS to model the stationary residuals series after removing trend effect using moving averages. The proposed moving averages and WFTS hybrid approach is applied to historical enrollment data for the University of Alabama and maize production data for Indonesia. Comparisons with other previous methods proposed in the literature show that combination of moving averages and WFTS model yields the smallest root mean square error (RMSE).