Forecasting Realized Volatility of State-Level Stock Markets of the United States: The Role of Sentiment

We investigate whether sentiment innovations help forecast realized volatility in U.S. state-level stock markets. We combine 5-minute intraday data for 50 U.S. states with a daily state-level Twitter-based sentiment index over the period August 2011 to August 2024. Realized variance, skewness, and kurtosis are constructed using intermittency-adjusted estimators that account for sparse trading and zero returns. We adopt a Heterogeneous Autoregressive framework and enrich it with higher-order realized moments and changes in state-level sentiment, estimating the models via weighted least squares to mitigate heteroskedasticity effects. Out-of-sample performance is assessed in a rolling-window forecasting design for daily, weekly, and monthly horizons, and formal forecast comparisons are conducted using Diebold-Mariano and Clark-West tests. Our results confirm that the Heterogeneous Autoregressive components remain the dominant drivers of realized volatility dynamics across all horizons. Importantly, tail-risk information, proxied by realized kurtosis, delivers the most systematic and economically meaningful improvements in predictive accuracy, particularly at short horizons. Sentiment changes exhibit an episodic but non-negligible predictive foot-print: while their average in-sample contribution is limited, they enhance forecast performance for a subset of states, especially when combined with higher-moment information in richer specifications. Overall, our findings highlight that integrating in-traday distributional characteristics and sentiment innovations can improve volatility forecasting at the regional level, albeit in a state- and horizon-dependent manner.