The objective of this article is to forecast stock prices and earnings. It involves the independent collection of stock data, the establishment of a mathematical model, the consideration of multiple factors’ combined influence, the analysis of their impact on future stock development, and the calculation of the development trend and potential stock trajectories within a specified time frame profit and loss. First, the historical stock price data of BMW Motor Company was collected, and the missing values in the data were filled using linear interpolation. Subsequently, the ARIMA time series model was used to analyze the stock price data before April 19, 2023, and predict the price trend of BMW stock after April 20 without the “ice cream incident”, and compare it with the actual situation. Finally, we used Pearson correlation analysis to obtain the time-varying correlation between the two. It was found that the “ice cream incident” had a relatively significant impact on the price changes of BMW stock in a short period of time and had a strong time-varying correlation. However, in the long run, this characteristic has an upper limit.