Extended-horizon realized volatility forecasting using state space models

Volatility forecasting is vital for financial risk management and decision-making, yet it remains challenging due to the heteroscedastic, nonlinear, and multi-scale nature of financial time series. This paper presents two novel heteroscedastic state space-based models: the first integrates state-space dynamics with Generalized Autoregressive Conditional Heteroskedasticity (GARCH)-type structures, referred to as HeSSM, and the second extends this framework by incorporating realized GARCH-type components to capture high-frequency data characteristics, referred to as RHeSSM. The approach integrates predictions from GARCH-based or realized GARCH-based models with the original input variables, enhancing the state-space model’s ability to capture complex volatility patterns and improve forecasting accuracy. To ensure robustness, the models are evaluated using three distinct realized volatility measures: Realized Variance, Realized Bipower Variation, and Realized Tripower Variation, and assessed over ten diverse datasets, including cryptocurrencies, commodities, and top equities. Extensive benchmarking against classical, hybrid, deep learning, and advanced models is conducted, complemented by multi-horizon forecasting, including long-term predictions, to test performance across forecasting horizons. The proposed models consistently demonstrate superior or highly competitive predictive accuracy, with improvements confirmed through multiple performance metrics and statistical significance validated by the Model Confidence Set (MCS) test. These results highlight the models’ practical utility, computational efficiency, and adaptability, offering a robust solution for realized volatility forecasting across varied financial environments.