Equity market interdependence: the relationship between European and US stock markets.

In this article, the degree of interdependence between European and US stock markets is measured by the conditional correlation between stock returns: the correlation coefficient is estimated using a model describing the variations over time in a number of variables (returns and volatility, for example), and its estimate takes account of all available information at a given time. We estimate conditional variance in the same way. Moreover, two statistical tools, recently introduced in applied finance, are combined. The first, developed by Engle in 2001 – an original specification of the conditional correlations in multivariate models – enables us to describe time-varying correlations between two or more assets. The second tool, copula functions, allows us to apply distributions that are more consistent with the stylised facts observed on financial markets than those commonly used. The approach used in this study is original in that it combines both the above tools. Using a multivariate model implies rejecting the two assumptions traditionally adopted in empirical studies in finance: correlations between assets are presumed to be constant; asymmetry or the presence of rare events are not taken into account in asset price distributions. Consequently, our empirical findings corroborate the assumption that correlations vary over time and validate the choice of an asymmetric joint distribution integrating the presence of rare events. We also observe the presence of periods of strong and weak correlations and similar periods for volatility. Furthermore, our results highlight a close link between the correlations and volatilities observed on the different equity markets: in phases of high volatility, the correlation tends to rise above its medium-term average; inversely, in phases of low volatility, markets seem to display greater independence. Lastly, the correlation coefficient of close to 1 confirms that French and German stock market indices have been converging in recent years. This may reflect the growing integration of these two markets and of the economies of these two countries within Economic and Monetary Union.

Covariant Bardeen Perturbation Formalism

In a previous work we obtained a set of necessary conditions for the linear approximation in cosmology. Here we discuss the relations of this approach with the so called covariant perturbations. It is often argued in the literature that one of the main advantages of the covariant approach to describe cosmological perturbations is that the Bardeen formalism is coordinate dependent. In this paper we will reformulate the Bardeen approach in a completely covariant manner. For that, we introduce the notion of pure and mixed tensors, which yields an adequate language to treat both perturbative approaches in a common framework. We then stress that in the referred covariant approach one necessarily introduces an additional hyper-surface choice to the problem. Using our mixed and pure tensors approach, we were able to construct a one-to-one map relating the usual gauge dependence of the Bardeen formalism with the hyper-surface dependence inherent to the covariant approach. Finally, through the use of this map, we define full non-linear tensors that at first order correspond to the three known gauge invariant variables $\Phi$, $\Psi$ and $\Xi$, which are simultaneously foliation and gauge invariant. We then stress that the use of the proposed mixed tensors allows one to construct simultaneously gauge and hyper-surface invariant variables at any order.Comment: 15 pages, no figures, revtex4-1, accepted for publication in PRD, typos fixed, improved discussion about higher order gauge and foliation invarianc

Electronic compressibility of a graphene bilayer

We calculate the electronic compressibility arising from electron-electron interactions for a graphene bilayer within the Hartree-Fock approximation. We show that, due to the chiral nature of the particles in this system, the compressibility is rather different from those of either the two-dimensional electron gas or ordinary semiconductors. We find that an inherent competition between the contributions coming from intra-band exchange interactions (dominant at low densities) and inter-band interactions (dominant at moderate densities) leads to a non-monotonic behavior of the compressibility as a function of carrier density.Comment: 4 pages, 4 figures. Final versio

Causal graphical models in systems genetics: A unified framework for joint inference of causal network and genetic architecture for correlated phenotypes

Causal inference approaches in systems genetics exploit quantitative trait loci (QTL) genotypes to infer causal relationships among phenotypes. The genetic architecture of each phenotype may be complex, and poorly estimated genetic architectures may compromise the inference of causal relationships among phenotypes. Existing methods assume QTLs are known or inferred without regard to the phenotype network structure. In this paper we develop a QTL-driven phenotype network method (QTLnet) to jointly infer a causal phenotype network and associated genetic architecture for sets of correlated phenotypes. Randomization of alleles during meiosis and the unidirectional influence of genotype on phenotype allow the inference of QTLs causal to phenotypes. Causal relationships among phenotypes can be inferred using these QTL nodes, enabling us to distinguish among phenotype networks that would otherwise be distribution equivalent. We jointly model phenotypes and QTLs using homogeneous conditional Gaussian regression models, and we derive a graphical criterion for distribution equivalence. We validate the QTLnet approach in a simulation study. Finally, we illustrate with simulated data and a real example how QTLnet can be used to infer both direct and indirect effects of QTLs and phenotypes that co-map to a genomic region.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS288 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org