Forecasting Apple Inc. Stock prices: A comparative analysis of ARIMA, LSTM, and ARIMA-LSTM models

Stock price fluctuation and prediction is a problem that has attracted much attention. There exist many mathematical and statistical problems behind it. In essence, the key to solving this problem lies in capturing the linear and nonlinear characteristics in the time series to predict future price movements. This study investigates the predictive capabilities of two distinct methodologiesLong Short-Term Memory (LSTM) networks and Autoregressive Integrated Moving Average (ARIMA) modelsusing Apple Inc. (AAPL) stock price data spanning 2016 to 2024. By synthesizing theoretical frameworks with empirical analysis, the research evaluates how each model captures linear trends and nonlinear fluctuations, ultimately proposing a hybrid ARIMA-LSTM architecture to enhance forecasting accuracy. Finally, according to the principal characteristics of the two models, the ARIMA-LSTM hybrid model is constructed. The results show that the hybrid model significantly outperforms single models in terms of RMSE and directional accuracy. Combined with error distribution visualization and volatility analysis, the hybrid model demonstrates efficient performance in achieving prediction optimization through the decomposition of linear and nonlinear components. It provides a new methodological perspective for financial time series modeling.