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The spectra of empirical correlation matrices, constructed from multivariatedata, are widely used in many areas of sciences, engineering and socialsciences as a tool to understand the information contained in typically largedatasets. In the last two decades, random matrix theory-based tools such as thenearest neighbour eigenvalue spacing and eigenvector distributions have beenemployed to extract the significant modes of variability present in suchempirical correlations. In this work, we present an alternative analysis interms of the recently introduced spacing ratios, which does not require thecumbersome unfolding process. It is shown that the higher order spacing ratiodistributions for the Wishart ensemble of random matrices, characterized by theDyson index $\beta$, is related to the first order spacing ratio distributionwith a modified value of co-dimension $\beta'$. This scaling is demonstratedfor Wishart ensemble and also for the spectra of empirical correlation matricesdrawn from the observed stock market and atmospheric pressure data. Using acombination of analytical and numerics, such scalings in spacing distributionsare also discussed.

Scaling in the eigenvalue fluctuations of the empirical correlation matrices