The prediction of stock prices is a common and crucial problem in trading. Correctly predicting future stock prices enables traders to determine the optimal time to buy and sell stocks, increasing the probability of making profits. This study focuses on predicting the closing price of Goldman Sachs. Initially, an ARIMA (4,1,6) benchmark model was established based on the AIC information criteria for time series prediction. The model was then applied to make forward predictions. Subsequently, a two-layer LSTM model was constructed. The prediction results of both models were visualized, and the regression indicators were calculated for each model. By comparing the prediction results of the two algorithms, it was determined that LSTM model outperforms ARIMA on the dataset used in this paper. Furthermore, this paper highlights some shortcomings of the ARIMA model, including its unsuitability for long-term forecasting and its subjective parameter selection. In contrast, LSTM performs better in predicting turning points in stock prices.