Effective prediction of air quality is an essential measure in order to reduce the effects of health suffering that arises from the currently growing menace in the urban areas. The present work uses Time Series Extrinsic Regression (TSER) to estimate the daily air quality index for PM10 in Beijing through weather conditions and pollutants concentration. TSER distinguishes from classical forecasting by capturing multivariate temporal dynamics and interdependencies, providing a richer understanding of drivers of air quality. ROCKET and Multi-ROCKET are advanced feature extraction techniques to produce high dimensional features that encompass localized and frequency based patterns. These features allow both traditional as well as ensemble models like XGBoost, Random Forest and Gradient Boosting to detect both short-term oscillations and longer terms trends. The models are hyperparameter optimized via methods including Random Search CV and Grid Search CV to refine model configuration minimizing overfitting and find optimal balance between computational efficiency and accuracy. This results indicate that TSER performs well in multivariate time series applications, and yields both higher accuracy and improved generalizability. This study offers a robust framework for generating accurate and useful PM10- environment relationships, and through this in identifying robust PM10-environment relationships.