Assessing the Improvement of Stability and Precision of Predicting the Time Series Models of River Flow under the influence of Differential Approach (Case study: Dez River)

The purpose of this study was to investigate the effect of seasonal, non-seasonal and combined differentiations on the time series stability of Dez River’s monthly discharge for 60 years. Also, the effect of the stability level on the performance of SARIMA models in the prediction of the time series is investigated from different aspects. Out of 720 data, 80% are taken into account for the calibration and the rest for the validation period. First, the stability of the variance of time series was investigated and the necessary transformations were applied to stabilize the variance. Then, with the help of seasonal Mann-Kendall test, the average stability was evaluated and its results have been used to assess the existence of the process and the need for differentiation. Using seasonal, non-seasonal and combined differentiations, three new series have been created, whose stability with the original series have been investigated by analyzing the ACF graph and the generalized Dickey-Fuller test. In the following, the type and number of parameters required in the models are determined for each scenario.  The results indicate that when using combined differentiation, the number of models needed for review is severely reduced so that for modeling of series with seasonal differentiation, 196 and for modeling of combined differentiation series, only 16 models need to be investigated. While the outcomes of the best model of both types of differentiated series were almost the same, the best model of the seasonal differencing series, with the criteria of the assessment of MAE= 92.4, RMSE = 154.4 and R = 0.61 showed its superiority over the other models. Finally, the selected model namely SARIMA (4, 0, 4) (1, 1, 1)12 has been used to predict the river flow in the next 24 months.