A New High Order Fuzzy ARMA Time Series Forecasting Method by Using Neural Networks to Define Fuzzy Relations

Abstract

Linear time series methods are researched under 3 topics, namely, AR (autoregressive), MA (moving averages), and ARMA (autoregressive moving averages) models. On the other hand, the univariate fuzzy time series forecasting methods proposed in the literature are based on fuzzy lagged (autoregressive (AR)) variables, having not used the error lagged (moving average (MA)) variables except for only two studies in the fuzzy time series literature. Not using MA variables could cause the model specification error in solutions of fuzzy time series. For this reason, this model specification error should be eliminated. In this study, a solution algorithm based on artificial neural networks has been proposed by defining a new high order fuzzy ARMA time series forecasting model that contains fuzzy MA variables along with fuzzy AR variables. It has been pointed out by the applications that the forecasting performance could have been increased by the proposed method in accordance with the fuzzy AR models in the literature since the proposed method is a high order model and also utilizes artificial neural networks to identify the fuzzy relation.