Related papers: Identifying Highly Correlated Stocks Using the Las…
Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics.
We study the dynamic interactions and structural changes in global financial indices in the years 1998-2012. We apply a principal component analysis (PCA) to cross-correlation coefficients of the stock indices. We calculate the correlations…
The presence of significant cross-correlations between the synchronous time evolution of a pair of equity returns is a well-known empirical fact. The Pearson correlation is commonly used to indicate the level of similarity in the price…
Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal,…
The properties of q-dependent cross-correlation matrices of stock market have been analyzed by using the random matrix theory and complex network. The correlation structures of the fluctuations at different magnitudes have unique…
A simple and fast analysis method to sort large data sets into groups with shared distinguishing characteristics is described, and applied to single molecular break junction conductance versus electrode displacement data. The method, based…
We aim to cluster financial assets in order to identify a small set of stocks to approximate the level of diversification of the whole universe of stocks. We develop a data-driven approach to clustering based on a correlation blockmodel in…
This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions,…
Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value…
Community detection methods can be used to explore the structure of complex systems. The well-known modular configurations in complex financial systems indicate the existence of community structures. Here we analyze the community properties…
Principal component analysis (PCA), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as…
In this paper the exact linear relation between the leading eigenvectors of the modularity matrix and the singular vectors of an uncentered data matrix is developed. Based on this analysis the concept of a modularity component is defined,…
A new look on the principal component analysis has been presented. Firstly, a geometric interpretation of determination coefficient was shown. In turn, the ability to represent the analyzed data and their interdependencies in the form of…
Principal Component analysis (PCA) is a useful statistical technique that is commonly used for multivariate analysis of correlated variables. It is usually applied as a dimension reduction method: the top principal components (PCs)…
We introduce a technique to filter out complex data-sets by extracting a subgraph of representative links. Such a filtering can be tuned up to any desired level by controlling the genus of the resulting graph. We show that this technique is…
In this short paper, a matrix perturbation bound on the eigenvalues found by principal component analysis is investigated, for the case in which the data matrix on which principal component analysis is performed is a convex combination of…
We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson…
Intermittency analysis of factorial moments is a promising method used for the detection of power-law scaling in high-energy collision data. In particular, it has been employed in the search of fluctuations characteristic of the critical…
We present two diagnostic methods based on ideas of Principal Component Analysis and demonstrate their efficiency for sophisticated processing of multicolour photometric observations of variable objects.
This paper presents a method for predicting stock returns using principal component analysis (PCA) and the hidden Markov model (HMM) and tests the results of trading stocks based on this approach. Principal component analysis is applied to…