Modeling and Forecasting the Multivariate Realized Volatility of Financial Markets with Time-Varying Sparsity

We develop a Multivariate Heterogeneous Autoregressive (MHAR) model with time-varying sparsity (TVS), or the TVS-MHAR-X model, to model and forecast the realized covariance matrices by employing the data from China's financial markets. We employ the matrix decomposition method to ensure the positivity of the forecasted covariance matrix and incorporate a set of predictors including the lagged daily, weekly and monthly volatilities, the leverage variables, and the jump variables. The proposed model allows the sparsity of coefficients to change over time based on the importance of predictors. We compare the forecast performances of the proposed models with the competing models based on the statistical evaluation and the economic evaluation. The results show that the proposed MHAR-TVS-X model outperforms the competing models for the short-term forecasts in terms of statistical evaluation. The results also suggest that the MHAR-TVS-X model significantly improves the efficient frontier and economic values for the short-term and long-term forecasts in terms of economic evaluation.