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

Duan Wang; Xin Zhang; Davor Horvatic; Boris Podobnik; H Eugene Stanley

doi:10.1063/1.4975217

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

Chaos. 2017 Feb;27(2):023104. doi: 10.1063/1.4975217.

Authors

Duan Wang¹, Xin Zhang², Davor Horvatic³, Boris Podobnik¹, H Eugene Stanley¹

Affiliations

¹ Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
² College of Communication and Transport, Shanghai Maritime University, Shanghai 201306, China.
³ Physics Department, Faculty of Science, University of Zagreb, Bijenička c. 32, 10000 Zagreb, Croatia.

PMID: 28249401
DOI: 10.1063/1.4975217

Abstract

To study the statistical structure of crosscorrelations 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 eigenvalue 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.

Publication types

Research Support, Non-U.S. Gov't