The impact assessments of the ACF shape on time series forecasting by the ANFIS model

Time series modelling and control of hydrological parameters are the most critical issues in water resources management. The subject matter of this study is finding the significant relationship between natural properties of time series like correlogram and selecting the best combination set of inputs for the fuzzy-neural adaptive network model. In this regard, two different types of the ACF, including sinusoidal and descending shapes, are considered in different climate. Selecting model inputs from the stability range of the ACF diagram for any shape types and model fine tuning lead to inferior results in testing stage. The best R-value of the original temperature and groundwater time series in stability range is 0.2 (|SI|= 1.23, RMSE = 11.91) and 0.2 (SI = 0.14, RMSE = 3.32), respectively. When they choose from the non-stationary range of the ACF, the powerful results for sinusoidal and descending ACF shapes would be achieved. In case, the R-value is more than 94% (|SI|< 0.57, 2.57 < RMSE < 5.5]) and 78% (SI = 0.03 and RMSE = 0.71), respectively. Whether they are picked up from the absolute maximum of ρ value in the ACF diagram, the best model results would have appeared. By applying the inverse of standardization and reforming the shape of the descending ACF to sinusoidal form, R-value is upgraded about 18%, from 78 to 96% the case. Finally, using preprocessing, in particular, standardization on time series does not always lead to improve forecasting model accuracy, but it depends on the shape of the ACF diagram. If it has the sine periodic shape, applying this action leads to poor results. In opposite, by descending ACF shape, using the inverse of standardization can improve the model accuracy in case. Finally, choosing ANFIS model inputs using the ACF diagram and appropriate input sets are more effective than using the model tuning and different fuzzy generators.