Testing the bivariate distribution of daily equity returns using copulas: an application to the Spanish stock market

In this paper we deal with the identification of dependencies between time series of equity returns. Marginal distribution functions are assumed to be known, and a bivariate chi-square test of fit is applied in a fully parametric copula approach. Several families of copulas are fitted and compared with Spanish stock market data. The results show that the t-copula generally outperforms other dependence structures, and highlight the difficulty in adjusting a significant number of bivariate data series

On the consequences of misspecifing assumptions concerning residuals distribution in a repeated measures and nonlinear mixed modelling context

In this paper we describe the results of a simulation study performed to elucidate the robustness of the Lindstrom and Bates (1990) approximation method under non-normality of the residuals, under different situations. Concerning the fixed effects, the observed coverage probabilities and the true bias and mean square error values, show that some aspects of this inferential approach are not completely reliable. When the true distribution of the residuals is asymmetrical, the true coverage is markedly lower than the nominal one. The best results are obtained for the skew normal distribution, and not for the normal distribution. On the other hand, the results are partially reversed concerning the random effects. Soybean genotypes data are used to illustrate the methods and to motivate the simulation scenarios

Cation distribution and magnetization of BaFe12-2xCoxSnxO19 (x=0.9,1.28) single crystals

The distribution of Sn4+ cations within the five crystallographic sites of the magnetoplumbite (M) ‐like compound BaFe12−2xCoxSnxO19 has been analyzed using single‐crystal x‐ray‐diffraction data. The species Fe3+ and Co2+ cannot be distinguished using x rays because of their very similar atomic numbers; however, the calculation of the apparent valencies for the different sites allows an insight into the Co2+ cation segregation. The use of previous data from neutron powder diffraction allows a precise picture of the cation distribution, which indicates a pronounced site selectivity for both Sn4+ and Co2+ cations. The Sn4+ cations prefer the 4f2 sites and to a much lower extent the 12k sites, while they do not enter the octahedral 2a sites at all. Co2+ cations are distributed among tetrahedral and octahedral sites displaying a clear preference for the tetrahedral 4f1 sites. Magnetic measurements indicate that the compound still exhibits uniaxial anisotropy with the easy direction parallel to the c axis. Nevertheless, the magnetic structure shows a considerable degree of noncolinearity. A strong reduction of the magnetic anisotropy regarding that of the undoped compound is also detected.

Particle orientation distribution in Y-Fe2O3magnetic tapes by Mössbauer and hysteresis loop measurements

The particle orientation in several Y-Fe2O3magnetic tapes has been quantitatively evaluated by using the data of both Mössbauer and hysteresis loop measurements performed in the three orthogonal directions. A texture function has been obtained as a development of real harmonics. The profile of the texture function gives the quality of the different magnetic tapes. A different degree of particle orientation at the surface of the tape is evidenced by means of conversion electron Mössbauer spectra.

Rapid radiation in spiny lobsters (Palinurus spp) as revealed by classic and ABC methods using mtDNA and microsatellite data

Background: Molecular tools may help to uncover closely related and still diverging species from a wide variety of taxa and provide insight into the mechanisms, pace and geography of marine speciation. There is a certain controversy on the phylogeography and speciation modes of species-groups with an Eastern Atlantic-Western Indian Ocean distribution, with previous studies suggesting that older events (Miocene) and/or more recent (Pleistocene) oceanographic processes could have influenced the phylogeny of marine taxa. The spiny lobster genus Palinurus allows for testing among speciation hypotheses, since it has a particular distribution with two groups of three species each in the Northeastern Atlantic (P. elephas, P. mauritanicus and P. charlestoni) and Southeastern Atlantic and Southwestern Indian Oceans (P. gilchristi, P. delagoae and P. barbarae). In the present study, we obtain a more complete understanding of the phylogenetic relationships among these species through a combined dataset with both nuclear and mitochondrial markers, by testing alternative hypotheses on both the mutation rate and tree topology under the recently developed approximate Bayesian computation (ABC) methods. Results Our analyses support a North-to-South speciation pattern in Palinurus with all the South-African species forming a monophyletic clade nested within the Northern Hemisphere species. Coalescent-based ABC methods allowed us to reject the previously proposed hypothesis of a Middle Miocene speciation event related with the closure of the Tethyan Seaway. Instead, divergence times obtained for Palinurus species using the combined mtDNA-microsatellite dataset and standard mutation rates for mtDNA agree with known glaciation-related processes occurring during the last 2 my. Conclusion The Palinurus speciation pattern is a typical example of a series of rapid speciation events occurring within a group, with very short branches separating different species. Our results support the hypothesis that recent climate change-related oceanographic processes have influenced the phylogeny of marine taxa, with most Palinurus species originating during the last two million years. The present study highlights the value of new coalescent-based statistical methods such as ABC for testing different speciation hypotheses using molecular data.

Testing the bivariate distribution of daily equity returns using copulas: an application to the Spanish stock market

In this paper we deal with the identification of dependencies between time series of equity returns. Marginal distribution functions are assumed to be known, and a bivariate chi-square test of fit is applied in a fully parametric copula approach. Several families of copulas are fitted and compared with Spanish stock market data. The results show that the t-copula generally outperforms other dependence structures, and highlight the difficulty in adjusting a significant number of bivariate data series

Polydispersity index from linear viscoelastic data: Unimodal and bimodal linear polymer melts

This article describes a method for determining the polydispersity index Ip2=Mz/Mw of the molecular weight distribution (MWD) of linear polymeric materials from linear viscoelastic data. The method uses the Mellin transform of the relaxation modulus of a simple molecular rheological model. One of the main features of this technique is that it enables interesting MWD information to be obtained directly from dynamic shear experiments. It is not necessary to achieve the relaxation spectrum, so the ill-posed problem is avoided. Furthermore, a determinate shape of the continuous MWD does not have to be assumed in order to obtain the polydispersity index. The technique has been developed to deal with entangled linear polymers, whatever the form of the MWD is. The rheological information required to obtain the polydispersity index is the storage G′(ω) and loss G″(ω) moduli, extending from the terminal zone to the plateau region. The method provides a good agreement between the proposed theoretical approach and the experimental polydispersity indices of several linear polymers for a wide range of average molecular weights and polydispersity indices. It is also applicable to binary blends.

Finite mixture analysis of beauty-contest data using generalised beta distributions

This paper introduces a mixture model based on the beta distribution, without preestablishedmeans and variances, to analyze a large set of Beauty-Contest data obtainedfrom diverse groups of experiments (Bosch-Domenech et al. 2002). This model gives a bettert of the experimental data, and more precision to the hypothesis that a large proportionof individuals follow a common pattern of reasoning, described as iterated best reply (degenerate),than mixture models based on the normal distribution. The analysis shows thatthe means of the distributions across the groups of experiments are pretty stable, while theproportions of choices at dierent levels of reasoning vary across groups.

The normal distribution in some constrained sample spaces

Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data, or with compositional data, like percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from the usual Euclidean geometry in real space, and with a measure different from the usual Lebesgue measure, leading to alternative models which better fit the phenomenon under study. The general approach is presented and illustrated using the normal distribution, both on the positive real line and on the D-part simplex. The original ideas of McAlister in his introduction to the lognormal distribution in 1879, are recovered and updated

Wave-height hazard analysis in Eastern Coast of Spain : Bayesian approach using generalized Pareto distribution

Standard practice of wave-height hazard analysis often pays little attention to the uncertainty of assessed return periods and occurrence probabilities. This fact favors the opinion that, when large events happen, the hazard assessment should change accordingly. However, uncertainty of the hazard estimates is normally able to hide the effect of those large events. This is illustrated using data from the Mediterranean coast of Spain, where the last years have been extremely disastrous. Thus, it is possible to compare the hazard assessment based on data previous to those years with the analysis including them. With our approach, no significant change is detected when the statistical uncertainty is taken into account. The hazard analysis is carried out with a standard model. Time-occurrence of events is assumed Poisson distributed. The wave-height of each event is modelled as a random variable which upper tail follows a Generalized Pareto Distribution (GPD). Moreover, wave-heights are assumed independent from event to event and also independent of their occurrence in time. A threshold for excesses is assessed empirically. The other three parameters (Poisson rate, shape and scale parameters of GPD) are jointly estimated using Bayes' theorem. Prior distribution accounts for physical features of ocean waves in the Mediterranean sea and experience with these phenomena. Posterior distribution of the parameters allows to obtain posterior distributions of other derived parameters like occurrence probabilities and return periods. Predictives are also available. Computations are carried out using the program BGPE v2.0

Analysis of sensitivity with respect to a compositional parameter : A comment on 'Local sensitivity analysis for compositional data with application to soil texture in hydrologic modelling' by L. Loosvelt and co-authors

A comment about the article “Local sensitivity analysis for compositional data with application to soil texture in hydrologic modelling” writen by L. Loosvelt and co-authors. The present comment is centered in three specific points. The first one is related to the fact that the authors avoid the use of ilr-coordinates. The second one refers to some generalization of sensitivity analysis when input parameters are compositional. The third tries to show that the role of the Dirichlet distribution in the sensitivity analysis is irrelevant

Spectral analysis of the angular distribution function of back reflectors for thin film silicon solar cells

Nowadays, one of the most important challenges to enhance the efficiency of thin film silicon solar cells is to increase the short circuit intensity by means of optical confinement methods, such as textured back-reflector structures. In this work, two possible textured structures to be used as back reflectors for n-i-p solar cells have been optically analyzed and compared to a smooth one by using a system which is able to measure the angular distribution function (ADF) of the scattered light in a wide spectral range (350-1000 nm). The accurate analysis of the ADF data corresponding to the reflector structures and to the μc-Si:H films deposited onto them allows the optical losses due to the reflector absorption and its effectiveness in increasing light absorption in the μc-Si:H layer, mainly at long wavelengths, to be quantified.

Spectral energy distribution of the gamma-ray microquasar LS 5039

The microquasar LS 5039 has recently been detected as a source of very high energy (VHE) $\gamma$-rays. This detection, that confirms the previously proposed association of LS 5039 with the EGRET source 3EG~J1824$-$1514, makes of LS 5039 a special system with observational data covering nearly all the electromagnetic spectrum. In order to reproduce the observed spectrum of LS 5039, from radio to VHE $\gamma$-rays, we have applied a cold matter dominated jet model that takes into account accretion variability, the jet magnetic field, particle acceleration, adiabatic and radiative losses, microscopic energy conservation in the jet, and pair creation and absorption due to the external photon fields, as well as the emission from the first generation of secondaries. The radiative processes taken into account are synchrotron, relativistic Bremsstrahlung and inverse Compton (IC). The model is based on a scenario that has been characterized with recent observational results, concerning the orbital parameters, the orbital variability at X-rays and the nature of the compact object. The computed spectral energy distribution (SED) shows a good agreement with the available observational data.

Characteristics of 2D convective structures in Catalonia (NE Spain): an analysis using radar data and GIS

Flood simulation studies use spatial-temporal rainfall data input into distributed hydrological models. A correct description of rainfall in space and in time contributes to improvements on hydrological modelling and design. This work is focused on the analysis of 2-D convective structures (rain cells), whose contribution is especially significant in most flood events. The objective of this paper is to provide statistical descriptors and distribution functions for convective structure characteristics of precipitation systems producing floods in Catalonia (NE Spain). To achieve this purpose heavy rainfall events recorded between 1996 and 2000 have been analysed. By means of weather radar, and applying 2-D radar algorithms a distinction between convective and stratiform precipitation is made. These data are introduced and analyzed with a GIS. In a first step different groups of connected pixels with convective precipitation are identified. Only convective structures with an area greater than 32 km2 are selected. Then, geometric characteristics (area, perimeter, orientation and dimensions of the ellipse), and rainfall statistics (maximum, mean, minimum, range, standard deviation, and sum) of these structures are obtained and stored in a database. Finally, descriptive statistics for selected characteristics are calculated and statistical distributions are fitted to the observed frequency distributions. Statistical analyses reveal that the Generalized Pareto distribution for the area and the Generalized Extreme Value distribution for the perimeter, dimensions, orientation and mean areal precipitation are the statistical distributions that best fit the observed ones of these parameters. The statistical descriptors and the probability distribution functions obtained are of direct use as an input in spatial rainfall generators.

Particle shape and orientation in laser diffraction and static image analysis size distribution analysis of micrometer sized rectangular particles

Laser diffraction (LD) and static image analysis (SIA) of rectangular particles [United States Pharmacopeia, USP30-NF25, General Chapter <776>, Optical Miroscopy.] have been systematically studied. To rule out sample dispersion and particle orientation as the root cause of differences in size distribution profiles, we immobilize powder samples on a glass plate by means of a dry disperser. For a defined region of the glass plate, we measure the diffraction pattern as induced by the dispersed particles, and the 2D dimensions of the individual particles using LD and optical microscopy, respectively. We demonstrate a correlation between LD and SIA, with the scattering intensity of the individual particles as the dominant factor. In theory, the scattering intensity is related to the square of the projected area of both spherical and rectangular particles. In traditional LD the size distribution profile is dominated by the maximum projected area of the particles (A). The diffraction diameters of a rectangular particle with length L and breadth B as measured by the LD instrument approximately correspond to spheres of diameter ØL and ØB respectively. Differences in the scattering intensity between spherical and rectangular particles suggest that the contribution made to the overall LD volume probability distribution by each rectangular particle is proportional to A2/L and A2/B. Accordingly, for rectangular particles the scattering intensity weighted diffraction diameter (SIWDD) explains an overestimation of their shortest dimension and an underestimation of their longest dimension. This study analyzes various samples of particles whose length ranges from approximately 10 to 1000 μm. The correlation we demonstrate between LD and SIA can be used to improve validation of LD methods based on SIA data for a variety of pharmaceutical powders all with a different rectangular particle size and shape.