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

ABSTRACT

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.

KEY WORDS:

• Multivariate models
• performance evaluation
• realized volatility forecast
• time-varying sparsity

Supplementary Material

Supplementary data for this article can be accessed here.

Notes

1. For a special case that no predictor is incorporated in the forecast model, K = 2^m.

2. Frobenius norm of $m\times m$ matrix A is defined as ${∥A∥}_F^2=\sum _{i,j}^{\hspace{0.17em}}|a_{ij}{|}^2$.

3. The $T_R$ statistics is defined as $T_R=\underset{i,j\in M}{max}|t_{ij}|=\underset{i,j\in M}{max}\frac{|{\bar{d}}_{ij}|}{\sqrt{\widehat{var}({\bar{d}}_{ij})}}$.

Additional information

Funding

This work is supported by National Natural Science Foundation of China under grant nos.71803049 and 71720107002, Ministry of Education in China Project of Humanities and Social Sciences [no.17YJC630099, no.17YJC90011], National Natural Science Foundation of Guangdong Province [2018A030310400, 2017A030311038, 2017A030312001], and Fundamental Fund for the central Universities [grant no. 2018BSXM10].