Water scarcity and climate change are two of the biggest worldwide concerns.  A complicated and sometimes underappreciated occurrence, drought has an impact on many facets of human existence.  Early drought forecasts are therefore essential for water resource management and strategic planning.  In order to improve the accuracy of drought prediction, this work presents a unique hybrid model that combines the Autoregressive Moving Average (ARMA), Holt-Winters (Exponential Smoothing) model, Autoregressive Integrated Moving Average (ARIMA), and Random Forest Regressor model. We do a thorough analysis of the Dhaka Division, Bangladesh, daily precipitation data from January 1981 to March 2025. In contrast to other research that only examined standalone machine learning algorithms or conventional statistical models, our study combines the two and offers a comparative performance analysis of hybrid models in the context of drought prediction using SPI.  Furthermore, the study uses these models in the understudied setting of Dhaka, Bangladesh, a place where little previous research has been done on drought forecasting. When examined side by side, our hybrid model Holt-Winters with LSTM model outperforms the hybrid approach. For SPI daily predictions, significant statistical parameters like Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) are especially crucial. This noteworthy enhancement highlights how much more accurate the innovative model is in forecasting droughts in Bangladesh's Dhaka Division. Our findings highlight the hybrid model's vital importance in tackling the problems caused by drought in the larger framework of climate change and water resource management.