Drought analysis is a vital component of water resources planning and management for dam and hydroelectric power plant (HPP) construction, reservoir operation and flood control. In this study, stochastic models were developed to estimate the monthly and annual flows of the Karasu River in the upper section of the Euphrates River valley. A time series model of flows was established based on the Box–Jenkins methodology. An autoregressive (AR) model was selected as the most suitable model. One hundred synthetic series, having the same length as the historical series (40 years), were produced using the AR model. It was also possible to control whether or not the generated time series maintained the statistical characteristics (mean and standard deviation) of the historical time series. After applying specified threshold levels (q = 0.5; q = 0.3; q = 0.1), the historic and synthetic flow series were subjected to runs analysis. Dry period lengths (run sum and run length) of historic and synthetic flow series were determined. Future droughts are estimated using maximum dry period lengths.