The COVID-19 pandemic has caused significant disruptions in global air travel demand, presenting new challenges for accurately forecasting passenger volumes. This study analyzes the monthly air passenger demand data from 2010 to 2022 to identify key external factors that influence passenger demand. Our analysis shows that the number of international visitors to Singapore is a critical determinant of passenger demand. Consequently, we propose a SARIMAX (Seasonal AutoRegressive Integrated Moving Average with eXogenous variables) model to forecast monthly air passenger demand at Singapore's Changi Airport, integrating international visitor numbers as an exogenous variable. Through comprehensive model identification and parameter estimation, we select the best SARIMAX configuration. To validate the performance of the model, traditional time series methods such as SARIMA, various exponential smoothing methods, and advanced machine learning methods like LSTM (Long Short-Term Memory) and Prophet were compared for forecasting monthly air passenger demand at Changi Airport in 2023. The results show that the SARIMAX model significantly outperforms all other tested models, achieving the best performance across multiple forecasting metrics, including the Mean Absolute Percentage Error.