Comparative analysis of traditional statistical methods and the lstm neural network model

Abstract

This paper presents a comparative analysis of traditional statistical methods (ARIMA, SARIMA) and a modern deep learning approach (LSTM) for financial time series forecasting. The study focuses on evaluating the efficiency of each model in predicting the closing price of Apple Inc. (NASDAQ: AAPL) stock. These models were selected due to their widespread use in financial analysis: ARIMA is suitable for stationary time series, SARIMA accounts for sea-sonal variations, and LSTM excels at capturing nonlinear dependencies and long-term trends. The study is based on historical closing price data of AAPL stock from January 1, 2023, to January 20, 2025, obtained via the yfinance service. The experimental modeling aimed to compare the forecasting accuracy of each method using key performance metrics such as Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE). The results indicate that the LSTM model outperforms ARIMA and SARIMA in forecast-ing accuracy due to its ability to efficiently model complex patterns in time series. SARIMA also demonstrated strong predictive capabilities, particularly for data with distinct seasonal components, surpassing ARIMA in accuracy. However, ARIMA yielded the lowest accuracy due to its limitations in capturing seasonality and nonlinear dependencies. These findings provide valuable insights for analysts, investors, and researchers in-volved in financial forecasting. The study offers practical recommendations on model selec-tion based on data characteristics and forecasting requirements, as well as an overview of the strengths and limitations of each approach.