Forecasting intraday volatility and densities using deep learning

Bruno Morier, Pedro L. Valls Pereira,
Forecasting intraday volatility and densities using deep learning,
The Quarterly Review of Economics and Finance,
Volume 104,
2025,
102076,
ISSN 1062-9769,
https://doi.org/10.1016/j.qref.2025.102076.
(https://www.sciencedirect.com/science/article/pii/S1062976925001176)
Abstract: In this paper, we develop a new model for forecasting high-frequency, intraday, conditional, discrete return densities and volatility using deep learning. Specifically, we model the conditional distribution using a modified Skellam distribution, where the mean follows an auto-regressive specification. We then train feed-forward neural networks to generate predictions for the underlying high-frequency volatility. We test four different specifications, including different sets of features and parameters. Then, we conduct a comprehensive walk-forward forecasting experiment to compare the forecasting accuracy of the proposed models. All of the proposed models outperform the empirical non-parametric forecasting rules considered. The new forecasting procedure also provides better out-of-sample forecasts compared to all state space models based on Koopman et al. (2017). We conclude that the bid–ask spread, high-low interval spread, and the volume traded are predictive variables for the volatility process. According to our model estimates, these variables appear to have a positive non-linear S-shaped relationship with volatility.
Keywords: Volatility models; High-frequency data; Discrete price changes; Deep learning; Neural networks; Skellam; Non-Gaussian time series models; Dynamic discrete data