A Novel ARMA Type Possibilistic Fuzzy Forecasting Functions Based on Grey-Wolf Optimizer (ARMA-PFFs)

This study proposes a new time series forecasting method that employs possibilistic fuzzy c-means, an autoregressive moving average model (ARMA), and a grey wolf optimizer (GWO) in type-1 fuzzy functions. Type-1 fuzzy functions (T1FFs) were used to forecast functions using an autoregressive model. However, rather than relying solely on past values of the forecast variable in a regression, the inclusion of past forecast errors improves forecasting ability. In this sense, the moving average model also employed in the proposed method. The inputs therefore are a combination of the past values of the time series and the past errors. The main idea of T1FFs is to include a new variable (or variables) that provides more information about the time series. The fuzzy c-means clustering (FCM) algorithm was used to quantify the values of this new variable. The degrees of memberships were obtained for each observation in each cluster and these membership grades were used as a new variable in the input matrix. Studies in the literature, however, have shown certain restrictions for FCM, such as sensitive noise and coincidence cluster centers. Consequently, possibilistic FCM is employed in T1FFs to overcome the aforementioned limitations. Because of the non-derivative objective function of ARMA type possibilistic fuzzy forecasting functions, the GWO was adapted in order to obtain coefficients for the model. The performance of the proposed ARMA type-1 fuzzy possibilistic functions was validated using 16 practical time-series.