Spectra of empirical autocorrelation matrices: A random-matrix-theory–inspired perspective
Department of Physics, Shahid Beheshti University - G.C., Evin, Tehran 19839, Iran
Received: 13 January 2015
Accepted: 26 June 2015
We construct an autocorrelation matrix of a time series and analyze it based on the random-matrix theory (RMT) approach. The autocorrelation matrix is capable of extracting information which is not easily accessible by the direct analysis of the autocorrelation function. In order to provide a precise conclusion based on the information extracted from the autocorrelation matrix, the results must be first evaluated. In other words they need to be compared with some sort of criterion to provide a basis for the most suitable and applicable conclusions. In the context of the present study, the criterion is selected to be the well-known fractional Gaussian noise (fGn). We illustrate the applicability of our method in the context of stock markets. For the former, despite the non-Gaussianity in returns of the stock markets, a remarkable agreement with the fGn is achieved.
PACS: 02.50.-r – Probability theory, stochastic processes, and statistics / 05.10.-a – Computational methods in statistical physics and nonlinear dynamics / 89.65.Gh – Economics; econophysics, financial markets, business and management
© EPLA, 2015