Recurrent type-1 functions approach for time series forecasting

Abstract

Forecasting future values of a time series is a widespread problem for researchers. There are a lot of methods for thesekindsof problems. While some of these are probabilistic, some of them are non-probabilistic methods. For probabilistic methods, autoregressive integrated moving average and exponential smoothing methods are commonly used. For non-probabilistic methods, Artificial Neural Networks (ANN) and fuzzy systems have been commonly used. There are numerous fuzzy systems methods. While most of these methods are rule-based, there are a few methods which do not require rules, such as type-1 fuzzy functionsapproach. While it is possible to encounter with a model suchasAR model integrated to T1FF, there has not been proposed any model including type-1 fuzzy functionsand moving average model in one algorithm. Our intuition is to get better forecasting results taking into account the disturbance terms. The input data set is organized with the following variables. First, lagged values of the time series are used for the AR(p) part. Second, FCM algorithm is used to cluster the inputs. The degree of memberships and centers are stored. Third, for the MA(q) part, fuzzy functions'residuals are used. So, AR(p), MA(q), and degree of memberships of the objects are restored inthe input data set. Since the function we have is not a derivative function, particle swarm optimization algorithm is preferred to obtain estimations of the coefficients. Australian beer consumption (ABC) data set, Istanbul stock exchange (BIST100) data sets from 2009 to 2013, and Taiwan stock exchange (TAIEX) data sets from 1999 to 2004 are used to evaluate the performance of the proposed method. The outcomes show that the proposed method outperforms the other methods for 12 real-world time series data sets.