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When dealing with non-stationary systems, for which many time series areavailable, it is common to divide time in epochs, i.e. smaller time intervalsand deal with short time series in the hope to have some form of approximatestationarity on that time scale. We can then study time evolution by looking atproperties as a function of the epochs. This leads to singular correlationmatrices and thus poor statistics. In the present paper, we propose an ensembletechnique to deal with a large set of short time series without anyconsideration of non-stationarity. Given a singular data matrix, we randomlyselect subsets of time series and thus create an ensemble of non-singularcorrelation matrices. As the selection possibilities are binomially large, wewill obtain good statistics for eigenvalues of correlation matrices, which aretypically not independent. Once we defined the ensemble, we analyze itsbehavior for constant and block-diagonal correlations and compare numerics withanalytic results for the corresponding correlated Wishart ensembles. We discussdifferences resulting from spurious correlations due to repetitive use oftime-series. The usefulness of this technique should extend beyond thestationary case if, on the time scale of the epochs, we have quasi-stationarityat least for most epochs.

Multivariate analysis of short time series in terms of ensembles of correlation matrices