A dynamic state-space HAR model

The Heterogeneous AutoRegressive model for the logs of Realised Volatility (HARL) has established itself as the benchmark specification for modelling and forecasting return volatility, owing to its parsimony and ability to capture the strong persistence typically observed in RV. To address potential concerns such as measurement errors, nonlinearities, and non-spherical residuals, numerous variants of the baseline HARL model have been developed in the literature. This paper contributes to this body of work by proposing a new class of dynamic state-space models with time-varying parameters. The parameter dynamics are assumed to follow an autoregressive process, with or without stochastic volatility, giving rise to two specifications: SHARP and SHARP-SV. Both models are designed to capture the evolving nature of return volatility and are estimated via Bayesian inference using Particle Gibbs sampling. Empirical applications to high-frequency data on SPY, sector ETFs, representative NYSE stocks, and the VIX index demonstrate that our proposed models on average outperform alternative HARL-based specifications in forecasting volatility, particularly at medium- and long-term horizons. An extensive Monte Carlo analysis further illustrates the advantages of our approach in terms of both estimation accuracy and predictive performance.