A UNIFIED BENCHMARK OF STATISTICAL, MACHINE LEARNING, AND DEEP LEARNING APPROACHES FOR S&P 500 INDEX FORECASTING

Abstract

Financial time series forecasting remains one of the most challenging problems in quantitative finance due to the highly volatile, noisy, and non-stationary nature of financial markets. Accurate prediction of stock market indices plays a crucial role in investment decision-making, portfolio optimization, and risk management. In recent years, machine learning and deep learning techniques have gained increasing attention for financial forecasting tasks. However, the comparative effectiveness of traditional statistical models, classical machine learning algorithms, and deep learning architectures under a unified experimental framework remains insufficiently explored.

This study presents a comprehensive empirical evaluation of statistical, machine learning, and deep learning approaches for forecasting the S&P 500 stock market index. Using a dataset consisting of 25 years of daily historical data (2000–2024) including Open, High, Low, Close, and Volume (OHLCV) features, we benchmark eight forecasting models across three methodological categories. The evaluated models include ARIMA as a statistical baseline; logistic regression and support vector machines as classical machine learning methods; random forest and XGBoost as ensemble learning approaches; and deep learning architectures including Long Short-Term Memory (LSTM), Convolutional Neural Networks (CNN), and a hybrid CNN–LSTM model.

To ensure a fair comparison, all models are implemented within a unified experimental pipeline incorporating consistent preprocessing, feature normalization, rolling window segmentation, and chronological train–validation–test splitting to prevent data leakage. Model performance is evaluated using two complementary metrics: Root Mean Squared Error (RMSE) for regression forecasting and directional accuracy for classification-based prediction of market movements.

Experimental results reveal that simpler models can outperform more complex architectures in financial time series forecasting under constrained feature spaces. In particular, logistic regression achieved the highest directional accuracy of 81.96%, significantly outperforming several machine learning and deep learning models. Deep learning architectures such as LSTM and CNN–LSTM demonstrated susceptibility to overfitting and limited generalization capability when trained solely on price-based inputs. Furthermore, feature importance analysis indicates that price-related variables, particularly opening and closing prices, contribute more significantly to predictive performance than trading volume.

The findings challenge the common assumption that deep learning models consistently outperform traditional approaches in financial forecasting tasks. Instead, they highlight the importance of model simplicity, robust validation protocols, and appropriate feature selection when dealing with noisy financial data. This study provides a reproducible benchmarking framework for evaluating forecasting models and offers practical insights for researchers and practitioners developing predictive systems for financial markets. Future research may benefit from incorporating external information sources such as macroeconomic indicators, sentiment analysis, and attention-based architectures to enhance predictive capability.