Flexible multivariate GARCH modeling with an application to international stock markets

The goal of this paper is to estimate time-varying covariance matrices.Since the covariance matrix of financial returns is known to changethrough time and is an essential ingredient in risk measurement, portfolioselection, and tests of asset pricing models, this is a very importantproblem in practice. Our model of choice is the Diagonal-Vech version ofthe Multivariate GARCH(1,1) model. The problem is that the estimation ofthe general Diagonal-Vech model model is numerically infeasible indimensions higher than 5. The common approach is to estimate more restrictive models which are tractable but may not conform to the data. Our contributionis to propose an alternative estimation method that is numerically feasible,produces positive semi-definite conditional covariance matrices, and doesnot impose unrealistic a priori restrictions. We provide an empiricalapplication in the context of international stock markets, comparing thenew estimator to a number of existing ones.

An Introduction to parametric and non-parametric models for bivariate positive insurance claim severity distributions

We present a real data set of claims amounts where costs related to damage are recorded separately from those related to medical expenses. Only claims with positive costs are considered here. Two approaches to density estimation are presented: a classical parametric and a semi-parametric method, based on transformation kernel density estimation. We explore the data set with standard univariate methods. We also propose ways to select the bandwidth and transformation parameters in the univariate case based on Bayesian methods. We indicate how to compare the results of alternative methods both looking at the shape of the overall density domain and exploring the density estimates in the right tail.

Secondhand tobacco smoke exposure in open and semi-open settings: a systematic review

Background: Some countries have recently extended smoke-free policies to particular outdoor settings; however, there is controversy regarding whether this is scientifically and ethically justifiable. Objectives: The objective of the present study was to review research on secondhand smoke (SHS) exposure in outdoor settings. Data sources: We conducted different searches in PubMed for the period prior to September 2012. We checked the references of the identified papers, and conducted a similar search in Google Scholar. Study selection: Our search terms included combinations of"secondhand smoke,""environmental tobacco smoke,""passive smoking" OR"tobacco smoke pollution" AND"outdoors" AND"PM" (particulate matter),"PM2.5" (PM with diameter ≤ 2.5 µm),"respirable suspended particles,""particulate matter,""nicotine,""CO" (carbon monoxide),"cotinine,""marker,""biomarker" OR"airborne marker." In total, 18 articles and reports met the inclusion criteria. Results: Almost all studies used PM2.5 concentration as an SHS marker. Mean PM2.5 concentrations reported for outdoor smoking areas when smokers were present ranged from 8.32 to 124 µg/m3 at hospitality venues, and 4.60 to 17.80 µg/m3 at other locations. Mean PM2.5 concentrations in smoke-free indoor settings near outdoor smoking areas ranged from 4 to 120.51 µg/m3. SHS levels increased when smokers were present, and outdoor and indoor SHS levels were related. Most studies reported a positive association between SHS measures and smoker density, enclosure of outdoor locations, wind conditions, and proximity to smokers. Conclusions: The available evidence indicates high SHS levels at some outdoor smoking areas and at adjacent smoke-free indoor areas. Further research and standardization of methodology is needed to determine whether smoke-free legislation should be extended to outdoor settings.

Some remarks on the class of continuous (Semi-) strictcly quasiconvex functions

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Growth of positive words and lower bounds of the growth rate for Thompson's group (F)p

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Sensitivity of simulation results to competing SAM updates

Recently there has been a renewed research interest in the properties of non survey updates of input-output tables and social accounting matrices (SAM). Along with the venerable and well known scaling RAS method, several alternative new procedures related to entropy minimization and other metrics have been suggested, tested and used in the literature. Whether these procedures will eventually substitute or merely complement the RAS approach is still an open question without a definite answer. The performance of many of the updating procedures has been tested using some kind of proximity or closeness measure to a reference input-output table or SAM. The first goal of this paper, in contrast, is the proposal of checking the operational performance of updating mechanisms by way of comparing the simulation results that ensue from adopting alternative databases for calibration of a reference applied general equilibrium model. The second goal is to introduce a new updatin! g procedure based on information retrieval principles. This new procedure is then compared as far as performance is concerned to two well-known updating approaches: RAS and cross-entropy. The rationale for the suggested cross validation is that the driving force for having more up to date databases is to be able to conduct more current, and hopefully more credible, policy analyses.

Semigroups of matrices of intermediate growth

Finitely generated linear semigroups over a field K that have intermediate growth are considered. New classes of such semigroups are found and a conjecture on the equivalence of the subexponential growth of a finitely generated linear semigroup S and the nonexistence of free noncommutative subsemigroups in S, or equivalently the existence of a nontrivial identity satisfied in S, is stated. This ‘growth alternative’ conjecture is proved for linear semigroups of degree 2, 3 or 4. Certain results supporting the general conjecture are obtained. As the main tool, a new combinatorial property of groups is introduced and studied.

Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.

Two weight inequalities for discrete positive operators

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Spectral analysis of random sparse matrices

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School composition effects in Spain

Drawing on PISA data of 2006, this study examines the impact of socio-economic school composition on science test score achievement for Spanish students in compulsory secondary schools. We define school composition in terms of the average parental human capital of students in the same school. These contextual peer effects are estimated using a semi-parametric methodology, which enables the spillovers to affect all the parameters of the educational production function. We also deal with the potential problem of self-selection of student into schools, using an artificial sorting that we argue to be independent from unobserved student’s abilities. The results indicate that the association between socio-economic school composition and test score results is clearly positive and significantly higher when computed with the semi-parametric approach. However, we find that the endogenous sorting of students into schools plays a fundamental role, given that the spillovers are significantly reduced when this selection process is ruled out from our measure of school composition effects. Specifically, the estimations suggest that the contextual peer effects are moderately positive only in those schools where the socio-economic composition is considerably elevated. In addition, we find some evidence of asymmetry of how the external effects and the sorting process actually operate, which seem affect in a different way males and females as well as high and low performance students.

Generic optimality conditions for semi-algebraic convex programs

We consider linear optimization over a nonempty convex semi-algebraic feasible region F. Semidefinite programming is an example. If F is compact, then for almost every linear objective there is a unique optimal solution, lying on a unique \active" manifold, around which F is \partly smooth", and the second-order sufficient conditions hold. Perturbing the objective results in smooth variation of the optimal solution. The active manifold consists, locally, of these perturbed optimal solutions; it is independent of the representation of F, and is eventually identified by a variety of iterative algorithms such as proximal and projected gradient schemes. These results extend to unbounded sets F.

Topologías en espacios de matrices y sistemas Leontief y Leontief-Sraffa

Se demuestra que todo sistema tipo Leontief (o Leontief-Sraffa) puede ser transformado en uno estructuralmente equivalente en el que la matriz tecnológica A tenga la propiedad de que la suma de los elementos de cada columna sea el autovalor máximo a de A; lo que equivale a transformar las unidades físicas originales en unidades que (haciendo abstracción de la componente trabajo) tengan idéntica composición de capital. A un tal sistema transformado lo denominaremos homogeneizado. En este tipo de sistemas aparecen más cómodos los estudios del sistema de precios de Sraffa, la limitación del tipo de beneficio, el reparto del excedente, la interpretación económica de 1/(I - A), la interpretación de los precios utilizando el teorema del punto fijo, la evolución de los precios al variar el tipo de beneficio, etc. Se demuestra que en un sistema homogeneizado "idéntica composición orgánica de capital" (Marx) equivale a idéntica cantidad de trabajo directo.