Machine learning models and ensemble methods for stock index return forecasting

Aivaras Bielskis; Igoris Belovas; Aivaras Bielskis; Igoris Belovas

doi:10.3934/nhm.2026035

Networks and Heterogeneous Media

2026, Volume 21, Issue 3: 848-864. doi: 10.3934/nhm.2026035

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Research article Special Issues

Machine learning models and ensemble methods for stock index return forecasting

Aivaras Bielskis ^,,
Igoris Belovas

Institute of Data Science and Digital Technologies, Vilnius University, Akademijos str. 4, Vilnius, LT-08412, Lithuania

Received: 12 February 2026 Revised: 29 March 2026 Accepted: 03 April 2026 Published: 06 May 2026

Reliable prediction of financial market movements remains a challenging task due to high volatility, complex interdependencies, and sensitivity to external shocks. This study assessed the performance of advanced machine learning models, including long short-term memory (LSTM), gated recurrent unit (GRU), transformer networks, extreme gradient boosting (XGBoost), and deep multi-layer perceptron (DMLP), as well as proposes their ensemble combinations, in forecasting daily closing prices of five major stock indices (S&P 500, NASDAQ-100, Dow Jones Industrial Average, FTSE 100, and DAX). Results indicate that although all models achieved high predictive accuracy, profitability outcomes varied substantially across models and markets. Among single-model approaches, LSTM generally exhibited more stable positive returns in several indices, while other models showed pronounced variability depending on market conditions. Meanwhile ensemble strategies frequently ranked among the top-performing configurations, often matching or exceeding the performance of adaptive weighting schemes. Performance was strongly index-dependent, with S&P 500 and NASDAQ-100 exhibiting comparatively stronger profitability, whereas FTSE and Dow Jones showed weaker and less differentiated results. These findings emphasize that statistical accuracy (e.g., RMSE, $R^2$ metrics) alone is insufficient for profitable trading, underscoring the importance of financial performance metrics, such as total return, drawdown, and risk-adjusted measures, when evaluating predictive models.
- returns forecasting,
- machine learning,
- deep learning,
- ensemble methods,
- stock indices,
- trading
Citation: Aivaras Bielskis, Igoris Belovas. Machine learning models and ensemble methods for stock index return forecasting[J]. Networks and Heterogeneous Media, 2026, 21(3): 848-864. doi: 10.3934/nhm.2026035

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Abstract

Reliable prediction of financial market movements remains a challenging task due to high volatility, complex interdependencies, and sensitivity to external shocks. This study assessed the performance of advanced machine learning models, including long short-term memory (LSTM), gated recurrent unit (GRU), transformer networks, extreme gradient boosting (XGBoost), and deep multi-layer perceptron (DMLP), as well as proposes their ensemble combinations, in forecasting daily closing prices of five major stock indices (S&P 500, NASDAQ-100, Dow Jones Industrial Average, FTSE 100, and DAX). Results indicate that although all models achieved high predictive accuracy, profitability outcomes varied substantially across models and markets. Among single-model approaches, LSTM generally exhibited more stable positive returns in several indices, while other models showed pronounced variability depending on market conditions. Meanwhile ensemble strategies frequently ranked among the top-performing configurations, often matching or exceeding the performance of adaptive weighting schemes. Performance was strongly index-dependent, with S&P 500 and NASDAQ-100 exhibiting comparatively stronger profitability, whereas FTSE and Dow Jones showed weaker and less differentiated results. These findings emphasize that statistical accuracy (e.g., RMSE, $R^2$ metrics) alone is insufficient for profitable trading, underscoring the importance of financial performance metrics, such as total return, drawdown, and risk-adjusted measures, when evaluating predictive models.

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