Non - stationary short - term time series forecasting is crucial for decision - making across multiple fields. However, traditional machine learning models’ linear assumptions and deep learning models’ high computational complexity and strong data dependence hamper their application in this area. Additionally, uniform noise reduction strategies can’t well balance noise resistance and generalization. This paper proposes AW - SARIMA, a lightweight hybrid framework. It uses DWT to decompose original signals and an adaptive dynamic thresholding mechanism for noise energy feedback adjustment, suppressing interference and retaining valid signals. SARIMA then models the denoised signals to improve prediction accuracy. Cross - domain experiments reveal that AW - SARIMA reduces RMSE by 37% compared to SARIMA in ATL airport passenger flow prediction and MAPE by 11% compared to ESARIMA in NCDC cholera case prediction. In few - sample prediction, it performs similarly to Time - LLM but with a 55% reduction in computation time, providing an effective solution for low - latency, data - limited, and noise - interfered scenarios.