Predictive Modeling of Correlation and Volatility in Multivariate Financial Time Series

This paper focuses on risk prediction in multivariate financial return time series by decomposing the asset covariance into its correlation and volatility components. Using a machine learning approach, we develop predictive models which ensure positive definiteness of the resulting matrices. The proposed approach allows us to separately study the contributions of correlation and volatility prediction to overall risk forecasting performance. To evaluate the proposed approach, we compare multiple performance metrics and assess the economic significance of our findings through a portfolio optimization application. The results provide insights into the relative predictability of correlation and volatility and their roles in portfolio optimization and risk management.