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

In this work we present a new method for Quickest Change Detection (QCD) and Quickest Hub Discovery (QHD) in correlation structures that geometrically represents solutions from asymptotic Random Matrix theory (RMT) consistently, and allows to incorporate new distance metrics for both tests. We present a new distance metric that combines both, QCD and QHD tests, with information about previous evolution of correlation in time. We apply this solution to financial time series correlations. Future developments on this topic are highly important in finance for Risk Management, Portfolio Management, Market Shocks Forecast which can save billions of dollars to the global economy. The topic falls within the scope of sequential, non-parametric, highdimensional QCD and QHD, from which state-of-the-art settings developed global and local summary statistics (for QCD and QHD respectively) from asymptotic RMT to detect changes in law. These settings work only for uncorrelated pre-change variables. With our geometric representation of the tests via clustering, we can test the hypothesis that we can improve state-of-the-art settings for QHD, combining QCD and QHD simultaneously, as well as including information about pre-change time-evolution in correlations. We use a new definition of how information about time-evolution of correlations is transmitted to return asset variables with a Dirichlet-Multinomial distributionfrom a distance matrix of rolling correlations with threshold (we name it Diversification Measure Distribution). We proof consistency for our version of the tests, we analyse the behaviour of our setup with respect to the state-of-the-art hyper-parameters and our method parameters, as well as the different versions of the test hypothesis. We are able to verify all these hypothesis for a large range of parameters