A generalization of random matrix theory and its application to statistical physics

To study the statistical structure of crosscorrel ations in empirical data, we generalize random matrix theory and propose a new method of cross- correlation analysis, known as autoregressive random matrix theory (ARRMT). ARRMT takes into account the influence of auto-correlations in the study of cross- correlations in multiple time series. We first analytically and numerically determine how auto-correlations affect the eigenva lue distribution of the correlation matrix. Then we introduce ARRMT with a detailed procedure of how to implement the method. Finally, we illustrate the method using two examples taken from inflation rates for air pressure data for 95 US cities. Published by AIP Publishing