Asymmetric multivariate HAR models for realized covariance matrix: A study based on volatility timing strategies

Forecasting high-dimensional covariance matrices is crucial for portfolio optimization and risk management. Recent studies focus on modelling the realized covariance matrices constructed with intraday prices using multivariate heterogeneous autoregressive (MHAR) models. Considering the mounting evidence of the asymmetric volatility phenomenon, this paper extends the literature by investigating whether volatility timing investors could achieve economic gains through incorporating asymmetry in the MHAR models. Empirical results in China's stock markets show that our proposed method of incorporating the asymmetric logistic smooth transition structure in the MHAR model achieves the highest economic values out-of-sample under various market conditions. Furthermore, we uncover that the most diversified portfolio strategy is more applicable when the market is in tranquil stage, while the global minimum variance strategy is more applicable during market turbulence.