The Role of Uncertainty in Forecasting Realized Covariance of US State-Level Stock Returns: A Reverse-MIDAS Approach

In this paper, we construct a set of reverse-Mixed Data Sampling (MIDAS) models to forecast the daily realized covariance matrix of United States (US) state-level stock returns, derived from 5-minute intraday data, by incorporating the information of volatility of weekly economic condition indices, which serve as proxies for economic uncertainty. We decompose the realized covariance matrix into a diagonal variance matrix and a correlation matrix and forecasting them separately using a two-step procedure. Particularly, the realized variances are forecasted by combining Heterogeneous Autoregressive (HAR) model with the reverse-MIDAS framework, incorporating the low-frequency uncertainty variable as a predictor. While the forecasting of the correlation matrix relies on the scalar MHAR model and a new log correlation matrix parameterization of Archakov and Hansen (2021). Our empirical results demonstrate that the forecast models incorporating uncertainty associated with economic conditions outperform the benchmark model in terms of both in-sample fit and out-of-sample forecasting accuracy. Moreover, economic evaluation results suggest that portfolios based on the proposed reverse-MIDAS covariance forecast models generally achieve higher annualized returns and Sharpe ratios, as well as lower portfolio concentrations and short positions.