This research addresses the escalating concern of air pollution, primarily due to fine particulate matter (PM2.5) and coarse particulate matter (PM10), in Siliguri city, West Bengal, India. Using a comprehensive dataset of daily 24-h average concentrations from February 2018 to February 2023, procured from the Central Pollution Control Board, six advanced computational models i.e., Artificial Neural Networks (ANN), Autoregressive Integrated Moving Averages (ARIMA), Extreme Learning Machine (ELM), Exponential Smoothing State Space Models (ETS), Naïve, and Trigonometric Seasonality, Box-Cox Transformation, ARMA Errors, Trend, and Seasonality (TBATS) were rigorously tested for predicting particulate matter concentrations. Daily data from 2018 to 2021 was used for training and the remaining for testing. The models in the testing phase were evaluated using Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE) along with R2. In the testing phase, the TBATS model emerged as the most accurate with the lowest RMSE values of 8.11 for PM2.5 and 12.33 for PM10, followed by the ARIMA model with an RMSE of 10.72 for PM2.5 and 18.10 for PM10. The ETS model also demonstrated reliable performance. In addition, by using the advantages of the most effective models, namely ARIMA and TBATS, the research makes forecasts for PM2.5 and PM10 levels from 2023 to 2025, on a monthly basis. These findings are helpful for air quality management in Siliguri and underscore the importance of using advanced computational models for pollution forecasting, encouraging further research on hybrid models with meteorological parameters.