The dynamics of the equal-time cross-correlation matrix of multivariate financial time series is explored by examination of the eigenvalue spectrum over sliding time windows. Empirical results for the S&P 500 and the Dow Jones Euro Stoxx 50 indices reveal that the dynamics of the small eigenvalues of the cross-correlation matrix, over these time windows, oppose those of the largest eigenvalue. ...

We consider a class of matrices of the form Cn = (1/N)(Rn+σXn)(Rn+σXn) ∗, where Xn is an n × N matrix consisting of independent standardized complex entries, Rj is an n×N nonrandom matrix, and σ > 0. Among several applications, Cn can be viewed as a sample correlation matrix, where information is contained in (1/N)RnR ∗ n, but each column of Rn is contaminated by noise. As n → ∞, if n/N → c > 0...

We propose a novel feature ranking technique using discernibility matrix. Discernibility matrix is used in rough set theory for reduct computation. By making use of attribute frequency information in discernibility matrix, we develop a fast feature ranking mechanism. Based on the mechanism, two heuristic reduct computation algorithms are proposed. One is for optimal reduct and the other for app...

in the present paper, we introduce the sequence space [{l_p}(e,delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left|  sum_{j in {e_n}} x_j - sum_{j in e_{n + 1}} x_jright| ^p < infty right},] where $e=(e_n)$ is a partition of finite subsets of the positive integers and $pge 1$. we investigate its topological properties and inclusion relations. moreover, we consider the problem of fin...

 This paper is concerned with deriving, using logistic and Markov chain theoretic methodologies, a transition matrix for a multi-echelon educational system. The explanatory variables of the logistic model are the school differential variables, and the transition matrix of the Markov chain is the non-homogeneous empirical transition matrix (NHETM). We compare the NHETM with the periodically upd...

The empirical distribution of the eigenvalues of the matrix XX(T) divided by its trace is evaluated, where X is a random Hankel matrix. The distribution of eigenvalues for symmetric and nonsymmetric distributions is assessed with various criteria. This yields several important properties with broad application, particularly for noise reduction and filtering in signal processing and time series ...

We propose a simultaneous equation system with GARCHX errors to model the contemporaneous relations among Asian and American stock markets. We thus evaluate the correlation matrix over rolling windows and introduce a correlation matrix distance which allows a simple graphical analysis of contagion. The empirical analysis on Asian and American stock markets shows some evidences of contagion.

Let X be a matrix sampled uniformly from the set of doubly stochastic matrices of size n×n. We show that the empirical spectral distribution of the normalized matrix √ n(X − EX) converges almost surely to the circular law. This confirms a conjecture of Chatterjee, Diaconis and Sly.

Abstract. This work concerns estimation of multidimensional nonlinear regression models using multilayer perceptron (MLP). The main problem with such model is that we have to know the covariance matrix of the noise to get optimal estimator. however we show that, if we choose as cost function the logarithm of the determinant of the empirical error covariance matrix, we get an asymptotically opti...

Previous empirical research has shown that Mexico's Oportunidades program has succeeded in increasing schooling and improving health of disadvantaged children. This paper studies the program's potential longer-term consequences for the poverty and inequality of these children. It adapts methods developed in DiNardo, Fortin and Lemieux (1996) and incorporates existing experimental estimates of t...