A Clustering Algorithm for Correlation Quickest Hub Discovery Mixing Time Evolution and Random Matrix Theory

We present a geometric version of Quickest Change Detection (QCD) and Quickest Hub Discovery (QHD) tests in correlation structures that allows us to include and combine new information with distance metrics. The topic falls within the scope of sequential, nonparametric, high-dimensional QCD and QHD, from which state-of-the-art settings developed global and local summary statistics from asymptotic Random Matrix Theory (RMT) to detect changes in random matrix law. These settings work only for uncorrelated pre-change variables. With our geometric version of the tests via clustering, we can test the hypothesis that we can improve state-of-the-art settings for QHD, by combining QCD and QHD simultaneously, as well as including information about pre-change time-evolution in correlations. We can work with correlated pre-change variables and test if the time-evolution of correlation improves performance. We prove test consistency and design test hypothesis based on clustering performance. We apply this solution to financial time series correlations. Future developments on this topic are highly relevant in finance for Risk Management, Portfolio Management, and Market Shocks Forecasting which can save billions of dollars for the global economy. We introduce the Diversification Measure Distribution (DMD) for modeling the time-evolution of correlations as a function of individual variables which consists of a Dirichlet-Multinomial distribution from a distance matrix of rolling correlations with a threshold. Finally, we are able to verify all these hypotheses.