Predicting stock prices: an empirical study using ARIMA and LSTM with model evaluation

This study employs the Autoregressive Integrated Moving Average (ARIMA) model and Long Short-Term Memory (LSTM) neural networks to forecast Google stock prices. The ARIMA methodology, implemented in MATLAB, involves managing time-stamped data, tuning model parameters including the Degree of Integration, Autoregressive Order, and Moving Average Order, transforming data to achieve stationarity, and conducting goodness-of-fit checks using AIC and BIC. The LSTM model, built with Keras, incorporates data preprocessing, feature scaling, structuring data for LSTM input, model building with LSTM and Dropout layers, and training with callbacks to prevent overfitting. The models are evaluated using metrics such as Root Mean Squared Error (RMSE) and Mean Squared Error (MSE). The LSTM model achieved an MSE of 0.0429 and an RMSE of 0.2070 on the training data, and an MSE of 0.6213 and an RMSE of 0.7883 for future predictions. In comparison, the ARIMA(2,1,2) model resulted in an MSE of 1.1434 and an RMSE of 2.9136. The results demonstrate the models’ ability to fit training data, with the LSTM model showing superior performance on the training set, and the challenges in predicting future values, highlighting the importance of data preprocessing, model selection, and out-of-sample testing for effective stock price forecasting.