A New Approach for Parameter Estimation of Autoregressive Models Using Adaptive Network-Based Fuzzy Inference System (ANFIS)

Abstract

Time series modeling plays an important role in different fields of science and engineering such as hydrology and water resources management. The proper estimation of the parameters in time series models is one of the essential steps of modeling. Yule–Walker, least square, Burge and forward–backward approaches are known, and common methods of parameter estimation are used in many time series studies. Recently, intelligent techniques such as adaptive network-based fuzzy inference system (ANFIS) have been used for time series modeling. Review of previous researches, especially in the field of hydrological time series, shows that these systems are often used as intelligent forecasting systems; indeed, they were considered as a black box. In this study, using ANFIS and its basic concepts, a new approach is devised for parameter estimation of autoregressive (AR) models. Performance of this approach is evaluated through the Akaike information criterion; also its application has been surveyed in time series forecasting by naturalized inflow of the Zayandehrud dam located in central Iran. Results show that the proposed approach has a good and effective performance for parameter estimation of AR models which can be depicted as a new “intelligent approach.” In addition, this capability of ANFIS in parameter estimation is a new application of ANFIS that was not addressed in the past. Also, the new driven method from ANFIS shows that this system can be employed as a parameter estimator for time series models such as AR models.