Correlation Matrix

From sectorial coarse graining to extreme coarse graining of S&P 500 correlation matrices ArXiv ID: 2511.05463 “View on arXiv” Authors: Manan Vyas, M. Mijaíl Martínez-Ramos, Parisa Majari, Thomas H. Seligman Abstract Starting from the Pearson Correlation Matrix of stock returns and from the desire to obtain a reduced number of parameters relevant for the dynamics of a financial market, we propose to take the idea of a sectorial matrix, which would have a large number of parameters, to the reduced picture of a real symmetric $2 \times 2$ matrix, extreme case, that still conserves the desirable feature that the average correlation can be one of the parameters. This is achieved by averaging the correlation matrix over blocks created by choosing two subsets of stocks for rows and columns and averaging over each of the resulting blocks. Averaging over these blocks, we retain the average of the correlation matrix. We shall use a random selection for two equal block sizes as well as two specific, hopefully relevant, ones that do not produce equal block sizes. The results show that one of the non-random choices has somewhat different properties, whose meaning will have to be analyzed from an economy point of view. ...

Signal inference in financial stock return correlations through phase-ordering kinetics in the quenched regime ArXiv ID: 2409.19711 “View on arXiv” Authors: Unknown Abstract Financial stock return correlations have been analyzed through the lens of random matrix theory to differentiate the underlying signal from spurious correlations. The continuous spectrum of the eigenvalue distribution derived from the stock return correlation matrix typically aligns with a rescaled Marchenko-Pastur distribution, indicating no detectable signal. In this study, we introduce a stochastic field theory model to establish a detection threshold for signals present in the limit where the eigenvalues are within the continuous spectrum, which itself closely resembles that of a random matrix where standard methods such as principal component analysis fail to infer a signal. We then apply our method to Standard & Poor’s 500 financial stocks’ return correlations, detecting the presence of a signal in the largest eigenvalues within the continuous spectrum. ...