Related papers: Asymmetric correlation matrices: an analysis of fi…
With the random matrix theory, we study the spatial structure of the Chinese stock market, American stock market and global market indices. After taking into account the signs of the components in the eigenvectors of the cross-correlation…
Identifying and quantifying co-dependence between financial instruments is a key challenge for researchers and practitioners in the financial industry. Linear measures such as the Pearson correlation are still widely used today, although…
The value of stocks, indices and other assets, are examples of stochastic processes with unpredictable dynamics. In this paper, we discuss asymmetries in short term price movements that can not be associated with a long term positive trend.…
Detailed study of the financial empirical correlation matrix of the 30 companies comprised by DAX within the period of the last 11 years, using the time-window of 30 trading days, is presented. This allows to clearly identify a nontrivial…
Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of…
We investigate hierarchical structure in various complex systems according to Minimum Spanning Tree methods. Firstly, we investigate stock markets where the graphis obtained from the matrix of correlations coefficient computed between all…
Motivated by the importance ascribed to correlations in random matrices used to model phenomena in various scientific disciplines, we report how algebraic correlations between matrix elements affect the eigenvalue statistics and spectral…
Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…
We develop a theoretical approach to compute the conditioned spectral density of $N \times N$ non-invariant random matrices in the limit $N \rightarrow \infty$. This large deviation observable, defined as the eigenvalue distribution…
Through simple analytical calculations and numerical simulations, we demonstrate the generic existence of a self-organized macroscopic state in any large multivariate system possessing non-vanishing average correlations between a finite…
It recently has been found that methods of the statistical theories of spectra can be a useful tool in the analysis of spectra far from levels of Hamiltonian systems. Several examples originate from areas, such as quantitative linguistics…
The graphical representation of the correlation matrix by means of different multivariate statistical methods is reviewed, a comparison of the different procedures is presented with the use of an example data set, and an improved…
The analysis of the intraday dynamics of correlations among high-frequency returns is challenging due to the presence of asynchronous trading and market microstructure noise. Both effects may lead to significant data reduction and may…
We analyze statistical properties of complex eigenvalues of random matrices $\hat{A}$ close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with…
We describe a method to determine the eigenvalue density of empirical covariance matrix in the presence of correlations between samples. This is a straightforward generalization of the method developed earlier by the authors for…
It is well known that correlations in microarray data represent a serious nuisance deteriorating the performance of gene selection procedures. This paper is intended to demonstrate that the correlation structure of microarray data provides…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
Given an optimization problem, the Hessian matrix and its eigenspectrum can be used in many ways, ranging from designing more efficient second-order algorithms to performing model analysis and regression diagnostics. When nonlinear models…
In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution, and the Dyson and boundary indices characterizing…
We suggest that Free Random Variables, represented here by large random matrices with spectral Levy disorder, may be relevant for several problems related to the modeling of financial systems. In particular, we consider a financial…