Modeling and estimation of correlation coefficients is a fundamental step in risk management, especially with the aftermath of the financial crisis in 2008, which challenged the traditional measuring of dependence in the financial market. Because of the serial dependence and small signal-to-noise ratio, patterns of the dependence in the data cannot be easily detected and modeled. This paper introduces a common factor analysis into the conditional correlation coefficients to extract the features of dependence. While statistical properties are thoroughly derived, extensive empirical analysis provides us with common patterns for the conditional correlation coefficients that give new insight into a number of important questions in financial data, especially the asymmetry of cross-correlations and the factors that drive the cross-correlations.
"Asymmetric conditional correlations in stock returns." Ann. Appl. Stat. 10 (2) 989 - 1018, June 2016. https://doi.org/10.1214/16-AOAS924