Sparse Gaussianized Canonical Correlation Analysis with Applications to Portfolio Analysis

Canonical correlation analysis (CCA) is an important statistical technique that explores the linear relationships between two sets of variables. In this paper, we propose a new generalization of CCA named sparse Gaussianized CCA (SGCCA) for high-dimensional data analysis. SGCCA has a number of favorable properties. First, it is conceptually easy to comprehend and efficient to implement. Second, it not only yields sparse and nested canonical vectors, but is also invariant against monotone transformations of any of the variables and hence robust to heavy-tailed data which is a well-known issue that severely dampens the classical CCA. Furthermore, SGCCA is shown to enjoy both the estimation consistency and variable selection consistency under a semiparametric copula model with mild regularity conditions. Extensive simulations demonstrate the superior performance of SGCCA over existing CCA methods with or without the underlying data-generating model being a semiparametric copula model. An analysis of correlation structures between consumer cyclical and non-cyclical stocks is illustrated as an empirical application.