Statistical and Machine Learning Models for Stock Price and Return Forecasting: An Out-of-Sample Comparison

This study compares classical statistical and tree-based machine learning models for one-step-ahead forecasting of S&P 500 prices and returns. The analysis considers ARIMA, ARMA–GARCH, Random Forest, and XGBoost under a common chronological out-of-sample design, with a random-walk benchmark for prices and a zero-return benchmark for returns. Particular attention is given to the distinction between forecasting price levels and forecasting returns, since the two targets exhibit different statistical behavior and may lead to different conclusions about model performance. In the main 2025 holdout period, ARIMA produced price forecasts close to those of the random walk, while Random Forest and XGBoost performed substantially worse when the index moved beyond price levels represented in the training sample. For return forecasting, ARMA–GARCH, Random Forest, and XGBoost produced modest differences in forecast accuracy, but none significantly outperformed the zero-return benchmark. A robustness analysis using separate annual holdouts from 2022 to 2025 produced similar conclusions: the random walk remained highly competitive for price forecasting, while no model showed a stable advantage for daily return prediction. The findings indicate that greater model complexity does not necessarily translate into improved short-horizon financial forecasts and emphasize the importance of appropriate benchmarks, target specification, and repeated out-of-sample evaluation.