Urban growth forecasting is a critical component of sustainable city development, enabling policymakers to make informed decisions about land use and infrastructure planning. This study presents a comparative analysis of two prominent forecasting models, Auto ARIMA and Prophet, applied to time series data derived from the Landsat Normalized Difference Built-up Index (NDBI) for the Bhubaneswar-Cuttack twin city region. The dataset spans from January 1, 2000, to January 1, 2024, providing a comprehensive view of urban expansion over nearly two and a half decades. The Auto ARIMA model, known for its robustness in time series forecasting, was first employed to predict future urban growth patterns. Subsequently, the Prophet model, a decomposable time series model that accommodates seasonal fluctuations was applied to the same dataset. The performance of both models was evaluated based on their prediction accuracy and computational efficiency. Results indicate that the Prophet model outperformed Auto ARIMA in forecasting urban growth in the Bhubaneswar-Cuttack region. The findings serve as a foundation for further exploration into the integration of remote sensing data and predictive modeling for urban planning and management.