Related papers: A Random Matrix Approach to Cross-Correlations in …
Several works have observed heavy-tailed behavior in the distributions of returns in different markets, which are observable indicators of underlying complex dynamics. Such prior works study return distributions that are marginalized across…
We consider linear spectral statistics built from the block-normalized correlation matrix of a set of $M$ mutually independent scalar time series. This matrix is composed of $M \times M$ blocks that contain the sample cross correlation…
In this article, the long-term behavior of the stock market index of the New York Stock Exchange is studied, for the period 1950 to 2013. Specifically, the CRSP Value-Weighted and CRSP Equal-Weighted index are analyzed in terms of market…
We investigate joint spectral characteristics of a family of matrices $\mathcal F $, associated with products in the semigroup generated by $\mathcal F$. In the literature, extremal measures such as the well-known joint spectral radius and…
In addressing the question of the time scales characteristic for the market formation, we analyze high frequency tick-by-tick data from the NYSE and from the German market. By using returns on various time scales ranging from seconds or…
We study the stochastic structure of cryptocurrency rates of returns as compared to stock returns by focusing on the associated cross-sectional distributions. We build two datasets. The first comprises forty-six major cryptocurrencies, and…
We review some methods recently used in the literature to detect the existence of a certain degree of common behavior of stock returns belonging to the same economic sector. Specifically, we discuss methods based on random matrix theory and…
Random matrix theory (RMT) provides a framework to study the spectral fluctuations in physical systems. RMT is capable of making predictions for the fluctuations only after the removal of the secular properties of the spectrum. Spectral…
We discuss the phenomenon of universal fluctuations in mesoscopic systems and nuclei. For this purpose we use Random Matrix Theory (RMT). The statistical $S$-matrix is used to obtain the physical observables in the case of Quantum Dots,…
Let $G=G(n,p_n)$ be a homogeneous Erd\"os-R\'enyi graph, and $A$ its adjacency matrix with eigenvalues $\lambda_1(A) \geq \lambda_2(A) \geq ... \geq \lambda_n(A).$ Local laws have been used to show that $lambda_2(A)$ can exhibit…
This paper examines the applicability of Random Matrix Theory to portfolio management in finance. Starting from a group of normally distributed stochastic processes with given correlations we devise an algorithm for removing noise from the…
We introduce a method for describing eigenvalue distributions of correlation matrices from multidimensional time series. Using our newly developed matrix H theory, we improve the description of eigenvalue spectra for empirical correlation…
Traded corporations are required by law to have a majority of outside directors on their board. This requirement allows the existence of directors who sit on the board of two or more corporations at the same time, generating what is…
This paper describes the dependence of market-based statistical moments of returns on statistical moments and correlations of the current and past trade values. We use Markowitz's definition of value weighted return of a portfolio as the…
We analyze the asymptotic fluctuations of linear eigenvalue statistics of random centrosymmetric matrices with i.i.d. entries. We prove that for a complex analytic test function, the centered and normalized linear eigenvalue statistics of…
We study random normal matrix models whose eigenvalues tend to be distributed within a narrow "band" around the unit circle of width proportional to $\frac1n$, where $n$ is the size of matrices. For general radially symmetric potentials…
The correlation matrix formalism is used to study temporal aspects of the stock market evolution. This formalism allows to decompose the financial dynamics into noise as well as into some coherent repeatable intraday structures. The present…
Market timing is an investment technique that tries to continuously switch investment into assets forecast to have better returns. What is the likelihood of having a successful market timing strategy? With an emphasis on modeling…
We study random walks on a family of treelike regular fractals with a trap fixed on a central node. We obtain all the eigenvalues and their corresponding multiplicities for the associated stochastic master equation, with the eigenvalues…
Technical trading rules and linear regressive models are often used by practitioners to find trends in financial data. However, these models are unsuited to find non-linearly separable patterns. We propose a decision tree forecasting model…