Clustering for Block Correlation Models

Block correlation models have emerged as powerful tools for analyzing dependence in high-dimensional financial time series. Predetermined group assignments have recently been used to define block structures, but these approaches can suffer from statistical inefficiency. This paper introduces a novel block correlation matrix specification and employs an efficient likelihood-based k-means algorithm to estimate the underlying block structure. We demonstrate that both the optimal number of groups and the group memberships are consistently estimated. Furthermore, we establish the asymptotic distribution of the estimated correlations. Simulation studies reveal the strong performance of the proposed method in finite samples. Applying this method to U.S. stock return data, we find that it outperforms existing block-forming techniques.