This study is based on the investigation of the performance of the band similarity (BS) method, which is quite new in the literature, in the prediction of flow and in determining the memory properties of the flow phenomenon. For this purpose, flow prediction models for the monthly flow data of the Sarız station, located in the Seyhan Basin in Türkiye, were produced first with the particle swarm optimization (PSO) algorithm. Second, these models were used in the BS method to create the BSPSO approach. Then, flow prediction was made for the same data set with support vector regression (SVR). In the test period, the standalone PSO, BSPSO, and SVR models achieved the most successful Nash–Sutcliffe efficiency (NSE) values of 0.516, 0.691, and 0.659, respectively. As a result, it was seen that BS increased the success of PSO by approximately 35%.