Forecasting global stock market volatilities: A shrinkage heterogeneous autoregressive (HAR) model with a large cross-market predictor set

We propose a shrinkage heterogeneous autoregressive (HAR) model to explore the predictability of global stock market volatilities. To this end, we construct a big data environment using international stock market data, which comprises over 200 cross-market predictors, including realized variances (RVs), continuous components, jumps, leverages, overnight returns, and uncertainty indices. Two shrinkage models (LASSO and ENet) are considered for volatility modeling and forecasting. The results demonstrate that these models, notably LASSO, consistently improve predictive performance across global stock markets and daily, weekly, and monthly horizons. Their superiority extends to directional and density forecasting as well as asset allocation. There are several empirical findings of shrinkage: (i) the shrinkage degree varies significantly across forecast horizons, with longer horizons implying more predictors are needed for accurate estimation; (ii) no country/region's predictors show absolute superiority and utilize cross-market information leads to larger predictive gains, particularly for longer horizons; (iii) the predictors except for RVs and continuous components are more powerful, especially over longer horizons; and (iv) the uncertainty indices are the strongest predictors for all horizons.