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Drought is regarded as one of the most intangible and creeping natural disasters, which occurs in almost all climates, and its characteristics vary from region to region. The present study aims to investigate the effect of differentiation operations on improving the static and modeling accuracy of the drought index time series and after selecting the best selected model, evaluate drought severity and duration, as well as predict future drought behavior, in Semnan city. During this process, the effect of time series on modeling different monthly scales of drought index was analyzed, as well as the effect of differencing approach on stationarity improvement and prediction accuracy of the models. First, the stationarity of time series data related to a one-month drought index is investigated. By using seasonal, non-seasonal, and hybrid differencing, new time series are created to examine the improvement of the stationarity of these series through analyzing the ACF diagram and generalized Dickey–Fuller test. Based on the results, hybrid differencing indicates the best degree of stability. Then, the type and number of states required to evaluate the models are determined, and finally, the best prediction model is selected by applying assessment criteria. In the following, the same stages are analyzed for the drought index time series data derived from 6-month rainfall data. The results reveal that the SARIMA (2,0,2) (1,1,1) 6  model with calibration assessment criteria of MAE = 0.510, RMSE = 0.752, and R = 0.218 is the best model for one-month data from seasonal differencing series. In addition to identifying and introducing the best time series model related to the six-month drought index data (SARIMA (3,0,5) (1,1,1) 6  seasonal model with assessment criteria of MAE = 0.430, RMSE = 0.588, and R = 0.812), the results highlight the increased prediction accuracy of the six-month time series model by 4 times the correlation coefficient in the calibration section and 8 times that in the validation section, respectively, relative to the one-month state. After modeling and comparing the results of the drought index between the selected model and the reality of the event, the severity and duration of the drought were also examined, and the results indicated a high agreement. Finally by applying the best six-month drought index model, a predicted series of the SPI drought index for the next 24 months is created.

Evaluation of Time Series Models in Simulating Different Monthly Scales of Drought Index for Improving Their Forecast Accuracy