Due to the time-consuming and uneconomical nature of dynamic models, statistical downscaling methods have received increasing attention today. In this study, the performance of the LARS-WG model in downscaling the climatic parameters of the Zarrineh River Basin (located in West Azerbaijan and Kurdistan provinces) was first evaluated. Then, for the first time in this basin, the long-term memory of predicted climatic variables was analyzed using fractal theory and the Hurst exponent. Daily precipitation, minimum temperature, and maximum temperature data from four synoptic stations (Zarrineh, Takab, Saqqez, and Maragheh) during the period 1990–2019 were considered as the baseline period (in accordance with WMO standards and the Sixth IPCC Report). To predict the future climate (2031–2060), the output of the LARS-WG model and two scenarios, SSP2-4.5 (optimistic) and SSP5-8.5 (pessimistic), were used. To reduce uncertainty and increase the accuracy of predictions, the ensemble mean output of three general circulation models, including GFDL-ESM4, HadGEM3-GC31-LL, and IPSL-CM6A-LR, was used. After calibrating and validating the model using R², RMSE, and MAE metrics, the Hurst exponent was calculated for temperature and precipitation time series. The validation results showed that the LARS-WG model is fully reliable for simulating temperature in the Zarrineh River Basin (R² > 0.98), but it is associated with considerable error in simulating precipitation (R² ≈ 0.85), which emphasizes the necessity of using a multi-model ensemble approach. The Hurst exponent analysis showed that in the baseline period, temperature has a strong long-term memory (H ≈ 0.80–0.95) and precipitation has a moderate memory (H ≈ 0.65–0.75). In the future period, this index decreases to approximately 0.51–0.56 for all three variables, indicating the loss of long-term memory and a shift toward random behavior in the model predictions. The projections indicate a temperature increase of 0.3 to 4.6 °C during the period 2031–2060. Annual precipitation will also increase by up to 4% under the optimistic scenario and decrease by up to 21% under the pessimistic scenario. Overall, although the LARS-WG model is reliable for simulating temperature in the Zarrineh River Basin, it performs poorly in simulating precipitation and especially in maintaining the long-term memory of time series. This finding highlights the necessity of using hybrid approaches or dynamic models for future climate studies in this basin.