On graph combinatorics to improve eigenvector-based measures of centrality in directed networks

Producción CientíficaWe present a combinatorial study on the rearrangement of links in the structure of directed networks for the purpose of improving the valuation of a vertex or group of vertices as established by an eigenvector-based centrality measure. We build our topological classification starting from unidirectional rooted trees and up to more complex hierarchical structures such as acyclic digraphs, bidirectional and cyclical rooted trees (obtained by closing cycles on unidirectional trees). We analyze different modifications on the structure of these networks and study their effect on the valuation given by the eigenvector-based scoring functions, with particular focus on α-centrality and PageRank.Ministerio de Economía, Industria y Competitividad (project TIN2014-57226-P)Generalitat de Catalunya (project SGR2014- 890)Ministerio de Ciencia, Innovación y Universidades (project MTM2012-36917-C03-01

On the computation of confluent hypergeometric functions for large imaginary part of parameters b and z

The final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-319-42432-3_30We present an efficient algorithm for the confluent hypergeometric functions when the imaginary part of b and z is large. The algorithm is based on the steepest descent method, applied to a suitable representation of the confluent hypergeometric functions as a highly oscillatory integral, which is then integrated by using various quadrature methods. The performance of the algorithm is compared with open-source and commercial software solutions with arbitrary precision, and for many cases the algorithm achieves high accuracy in both the real and imaginary parts. Our motivation comes from the need for accurate computation of the characteristic function of the Arcsine distribution or the Beta distribution; the latter being required in several financial applications, for example, modeling the loss given default in the context of portfolio credit risk.Peer ReviewedPostprint (author's final draft

Clustering of exchange rates and their dynamics under different dependence measures

This paper proposes an improvement to the method for clustering exchange rates given by D. J. Fenn et al, in Quantitative Finance, 12 (10) 2012, pp.1493-1520. To deal with the potentially non linear nature of currency time series dependence, we propose two alternative similarity metrics to use instead of the one used in the aforementioned paper based on Pearson correlation. Our proposed similarity metrics are based upon Kendall and distance correlations. We observe how each of the newly adapted clustering methods respond over several years of currency exchange data and find significant differences in the resulting clusters.Peer ReviewedPostprint (published version

On methods to assess the significance of community structure in networks of financial time series

We consider the problem of determining whether the community structure found by a clustering algorithm applied to nancial time series is statistically signi cant, or is due to pure chance, when no other information than the observed values and a similarity measure among time series are available. As a subsidiary problem we also analyse the in uence of the choice of similarity measure in the accuracy of the clustering method. We propose two raw-data based methods for assessing robustness of clustering algorithms on time-dependent data linked by a relation of similarity: One based on community scoring functions that quantify some topological property that characterises ground-truth communities, and another based on random perturbations and quanti cation of the variation in the community structure. These methodologies are well-established in the realm of unweighted networks; our contribution are versions of these methodologies properly adapted to complete weighted networks.Peer ReviewedPostprint (published version

Towards a sharp estimation of transfer entropy for identifying causality in financial time series

We present an improvement of an estimator of causality in financial time series via transfer entropy, which includes the side information that may affect the cause-effect relation in the system, i.e. a conditional information-transfer based causality. We show that for weakly stationary time series the conditional transfer entropy measure is nonnegative and bounded below by the Geweke's measure of Granger causality. We use k-nearest neighbor distances to estimate entropy and approximate the distribution of the estimator with bootstrap techniques. We give examples of the application of the estimator in detecting causal effects in a simulated autoregressive stationary system in three random variables with linear and non-linear couplings; in a system of non stationary variables; and with real financial data.Postprint (published version

A construction of continuous-time ARMA models by iterations of Ornstein-Uhlenbeck processes

We present a construction of a family of continuous-time ARMA processes based on p iterations of the linear operator that maps a Lévy process onto an Ornstein-Uhlenbeck process. The construction resembles the procedure to build an AR(p) from an AR(1). We show that this family is in fact a subfamily of the well-known CARMA(p,q) processes, with several interesting advantages, including a smaller number of parameters. The resulting processes are linear combinations of Ornstein-Uhlenbeck processes all driven by the same L´evy process. This provides a straightforward computation of covariances, a state-space model representation and methods for estimating parameters. Furthermore, the discrete and equally spaced sampling of the process turns to be an ARMA(p, p-1) process. We propose methods for estimating the parameters of the iterated Ornstein-Uhlenbeck process when the noise is either driven by a Wiener or a more general Lévy process, and show simulations and applications to real data.Peer ReviewedPostprint (published version