Volatility Forecasting of Stock Index via GARCH-Family and LSTM Models

DOI: https://doi.org/10.62517/jse.202511607

Author(s)

Zihao Li

Affiliation(s)

School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, China

Abstract

In financial markets, reliable forecasting of stock index volatility constitutes a fundamental component of risk management and strategic investment decisions. Traditional economic models struggle to capture complex financial market relationships. For example, Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models fail to fully account for nonlinear dependencies and long-term memory. As a result, accurate forecasting remains a challenging task. In response to the challenges, the LSTM–GEM hybrid framework is proposed in this study, integrating GARCH-family models with Long Short-Term Memory (LSTM) networks. Conditional volatility predictions from GARCH-family models serve as input features to the LSTM network. This allows the hybrid model to model the linear and nonlinear patterns underlying financial time series. To assess the contribution of high-frequency information, we compare model performance when using only low-frequency inputs versus combining both data types. The experimental findings indicate that the LSTM-GEM model consistently achieves superior performance compared to both standalone GARCH-family and LSTM models. Furthermore, incorporating high-frequency data improves forecasting accuracy. The findings demonstrate that the LSTM-GEM model attains lower prediction errors, with the inclusion of high-frequency data further improving its accuracy.

Keywords

LSTM; GARCH; Volatility Prediction

References

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