In the context of global warming, the increasing frequency of drought events has caused negative impacts on agricultural productivity and societal activities. However, the drought occurrences have not been well predicted by any single model, and precipitation may show nonstationary behavior. In this study, 60 years of monthly precipitation data from 1960 to 2019 for the Ningxia Hui Autonomous Region were analyzed. The standard precipitation index (SPI) was used to classify drought events. This study combined the strengths of autoregressive integrated moving average (ARIMA) and complementary ensemble empirical mode decomposition (CEEMD) to predict drought. First, based on the precipitation dataset, the SPI at timescales of 1, 3, 6, 9, 12, and 24 months was calculated. Then, each of these SPI time series was predicted using the ARIMA model and the CEEMD–ARIMA combined model. Finally, the models′ performance was compared using statistical metrics, namely, root-mean-square error (RMSE), mean absolute error (MAE), Kling–Gupta efficiency (KGE), Willmott index (WI), and Nash–Sutcliffe efficiency (NSE). The results show that the following: (1) Compared with the ARIMA forecast value, the prediction results of the CEEMD–ARIMA model were in good agreement with the SPI values, indicating that the combined model outperformed the single model. (2) Two different models obtained the lowest accuracy for the SPI1 prediction and the highest accuracy for the SPI24 prediction. (3) The CEEMD–ARIMA model achieved higher prediction accuracy than the ARIMA model at each time scale. The most precise model during the test phase was the CEEMD–ARIMA model at SPI24 at Xiji Station, with error measures of MAE = 0.076, RMSE = 0.100, NSE = 0.994, KGE = 0.993, and WI = 0.999. Such findings will be essential for government to make decisions.