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Information filtering of high correlation matrices.
Mantegna R.N., Garcia Medina A., Miccichè S.
We discuss the concept of information filtering in correlation matrices describing multivariate stochastic processes monitored with limited number of records. Specifically, we investigate block diagonal and hierarchical nested stochastic multivariate Gaussian models by studying their sample cross-correlation matrix. By performing numerical simulations, we compare a filtered sample cross-correlation with the population cross-correlation matrices by using several rotationally invariant estimators (RIE) and hierarchical clustering estimators (HCE) under several loss functions. We show that the two approaches rely on different sets of eigenvectors and that sample cross-correlation filtered by RIE estimators are often outperformed by HCE estimators for several of the loss functions. We also show that for block models and for hierarchically nested block models the best determination of the filtered sample cross-correlation is achieved by introducing two-step estimators combining state-of-the-art non-linear shrinkage models with hierarchical clustering estimators.