Related papers: Asymmetric correlation matrices: an analysis of fi…
Random matrix theory is used to assess the significance of weak correlations and is well established for Gaussian statistics. However, many complex systems, with stock markets as a prominent example, exhibit statistics with power-law tails,…
This paper studies the asymptotic spectral properties of a renormalized sample correlation matrix, including the limiting spectral distribution, the properties of largest eigenvalues, and the central limit theorem for linear spectral…
We study complex networks under random matrix theory (RMT) framework. Using nearest-neighbor and next-nearest-neighbor spacing distributions we analyze the eigenvalues of adjacency matrix of various model networks, namely, random,…
Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations…
We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated.…
Standard methods and theories in finance can be ill-equipped to capture highly non-linear interactions in financial prediction problems based on large-scale datasets, with deep learning offering a way to gain insights into correlations in…
The association between log-price increments of exchange-traded equities, as measured by their spot correlation estimated from high-frequency data, exhibits a pronounced upward-sloping and almost piecewise linear relationship at the…
The price impact for a single trade is estimated by the immediate response on an event time scale, i.e., the immediate change of midpoint prices before and after a trade. We work out the price impacts across a correlated financial market.…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…
To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…
We analyze cross-correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of…
We construct an ensemble of correlation matrices from high-frequency foreign exchange market data, with one matrix for every day for 446 days. The matrices are symmetric and have vanishing diagonal elements after subtracting the identity…
We investigate how in complex systems the eigenpairs of the matrices derived from the correlations of multichannel observations reflect the cluster structure of the underlying networks. For this we use daily return data from the NYSE and…
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…
Correlation function of complex eigenvalues of N by N random matrices drawn from non-Hermitean random matrix ensemble of symplectic symmetry is given in terms of a quaternion determinant. Spectral properties of Gaussian ensembles are…
Time-varying volatility is an inherent feature of most economic time-series, which causes standard correlation estimators to be inconsistent. The quadrant correlation estimator is consistent but very inefficient. We propose a novel…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
We consider a versatile matrix model of the form ${\bf A}+i {\bf B}$, where ${\bf A}$ and ${\bf B}$ are real random circulant matrices with independent but, in general, nonidentically distributed Gaussian entries. For this model, we derive…
We apply a method to filter relevant information from the correlation coefficient matrix by extracting a network of relevant interactions. This method succeeds to generate networks with the same hierarchical structure of the Minimum…
We study fluctuation properties of embedded random matrix ensembles of non-interacting particles. For ensemble of two non-interacting particle systems, we find that unlike the spectra of classical random matrices, correlation functions are…