The purpose of this paper is to investigate the impact of the Olympic Games on economic growth, with a particular focus on changes in gross domestic product (GDP) in China and the United States. By applying the ARIMA model, the GDP trends of the two countries during the period when they do not host the Olympic Games are predicted. The construction of the ARIMA model involves three core steps when dealing with time series data. First, the collected data are analyzed in depth and reasonable assumptions are made on this basis. Next, in view of the characteristic volatility of time series data, the difference method is used to eliminate non-stationarity and ensure the smoothness of the data series. Finally, by combining the observations with the lagged observations of the moving average model residuals, to ensure that the model can accurately capture the characteristics of the time series data. After completing the model construction, this paper further compares the changes in GDP and tourism indicators of the two countries before and after the Olympic Games. Through the comparative analysis, it is confirmed that hosting the Olympic Games has a positive contribution to the economic growth of the two countries. These conclusions not only provide valuable references for policy makers, but also provide strong support for the economic impact assessment of cities hosting the Olympic Games in the future.