Improved estimation of the covariance matrix of stock returns with an application to portofolio selection

This paper proposes to estimate the covariance matrix of stock returnsby an optimally weighted average of two existing estimators: the samplecovariance matrix and single-index covariance matrix. This method isgenerally known as shrinkage, and it is standard in decision theory andin empirical Bayesian statistics. Our shrinkage estimator can be seenas a way to account for extra-market covariance without having to specifyan arbitrary multi-factor structure. For NYSE and AMEX stock returns from1972 to 1995, it can be used to select portfolios with significantly lowerout-of-sample variance than a set of existing estimators, includingmulti-factor models.

Extreme times in financial markets.

We apply the theory of continuous time random walks (CTRWs) to study some aspects involving extreme events in financial time series. We focus our attention on the mean exit time (MET). We derive a general equation for this average and compare it with empirical results coming from high-frequency data of the U.S. dollar and Deutsche mark futures market. The empirical MET follows a quadratic law in the return length interval which is consistent with the CTRW formalism.

The poor stay poor: Non-convergence across countries and regions

We study the issue of income convergence across countries and regions witha Bayesian estimator which allows us to use information in an efficient andflexible way. We argue that the very slow convergence rates to a commonlevel of per-capita income found, e.g., by Barro and Xavier Sala-i-Martin,is due to a 'fixed effect bias' that their cross-sectional analysisintroduces in the results. Our approach permits the estimation of differentconvergence rates to different steady states for each cross sectional unit.When this diversity is allowed, we find that convergence of each unit to(its own) steady state income level is much faster than previously estimatedbut that cross sectional differences persist: inequalities will only bereduced by a small amount by the passage of time. The cross countrydistribution of the steady state is largely explained by the cross countrydistribution of initial conditions.

Semiquantitative RT-PCR measurement of gene expression in rat tissues including a correction for varying cell size and number

Background: Current methodology of gene expression analysis limits the possibilities of comparison between cells/tissues of organs in which cell size and/or number changes as a consequence of the study (e.g. starvation). A method relating the abundance of specific mRNA copies per cell may allow direct comparison or different organs and/or changing physiological conditions. Methods: With a number of selected genes, we analysed the relationship of the number of bases and the fluorescence recorded at a present level using cDNA standards. A lineal relationship was found between the final number of bases and the length of the transcript. The constants of this equation and those of the relationship between fluorescence and number of bases in cDNA were determined and a general equation linking the length of the transcript and the initial number of copies of mRNA was deduced for a given pre-established fluorescence setting. This allowed the calculation of the concentration of the corresponding mRNAs per g of tissue. The inclusion of tissue RNA and the DNA content per cell, allowed the calculation of the mRNA copies per cell. Results: The application of this procedure to six genes: Arbp, cyclophilin, ChREBP, T4 deiodinase 2, acetyl-CoA carboxylase 1 and IRS-1, in liver and retroperitoneal adipose tissue of food-restricted rats allowed precise measures of their changes irrespective of the shrinking of the tissue, the loss of cells or changes in cell size, factors that deeply complicate the comparison between changing tissue conditions. The percentage results obtained with the present methods were essentially the same obtained with the delta-delta procedure and with individual cDNA standard curve quantitative RT-PCR estimation. Conclusion: The method presented allows the comparison (i.e. as copies of mRNA per cell) between different genes and tissues, establishing the degree of abundance of the different molecular species tested.

Propagation through fractal media: The Sierpinski gasket and the Koch curve

We present new analytical tools able to predict the averaged behavior of fronts spreading through self-similar spatial systems starting from reaction-diffusion equations. The averaged speed for these fronts is predicted and compared with the predictions from a more general equation (proposed in a previous work of ours) and simulations. We focus here on two fractals, the Sierpinski gasket (SG) and the Koch curve (KC), for two reasons, i.e. i) they are widely known structures and ii) they are deterministic fractals, so the analytical study of them turns out to be more intuitive. These structures, despite their simplicity, let us observe several characteristics of fractal fronts. Finally, we discuss the usefulness and limitations of our approa

Entrepreneurial intention, cognitive social capital and culture: empirical anaylisis for Spain and Taiwan

The main purpose of this paper is building a research model to integrate the socioeconomic concept of social capital within intentional models of new firm creation. Nevertheless, some researchers have found cultural differences between countries and regions to have an effect on economic development. Therefore, a second objective of this study is exploring whether those cultural differences affect entrepreneurial cognitions. Research design and methodology: Two samples of last year university students from Spain and Taiwan are studied through an Entrepreneurial Intention Questionnaire (EIQ). Structural equation models (Partial Least Squares) are used to test the hypotheses. The possible existence of differences between both sub-samples is also empirically explored through a multigroup analysis. Main outcomes and results: The proposed model explains 54.5% of the variance in entrepreneurial intention. Besides, there are some significant differences between both subsamples that could be attributed to cultural diversity. Conclusions: This paper has shown the relevance of cognitive social capital in shaping individuals’ entrepreneurial intentions across different countries. Furthermore, it suggests that national culture could be shaping entrepreneurial perceptions, but not cognitive social capital. Therefore, both cognitive social capital and culture (made up essentially of values and beliefs), may act together to reinforce the entrepreneurial intention.

Heuristic procedures for solving the General Assembly Line Balancing Problem with Setups (GALBPS)

The General Assembly Line Balancing Problem with Setups (GALBPS) was recently defined in the literature. It adds sequence-dependent setup time considerations to the classical Simple Assembly Line Balancing Problem (SALBP) as follows: whenever a task is assigned next to another at the same workstation, a setup time must be added to compute the global workstation time, thereby providing the task sequence inside each workstation. This paper proposes over 50 priority-rule-based heuristic procedures to solve GALBPS, many of which are an improvement upon heuristic procedures published to date.

Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model

Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel equation for the logarithmic interaction kernel in any dimension in the sub-critical case. Moreover, we show how this method performs numerically in one dimension. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudo-inverse of the cumulative distribution function. We demonstrate its capabilities to reproduce easily without the need of mesh-refinement the blow-up of solutions for super-critical masses.

On the density distribution across space: a probabilistic approach

This paper aims at providing a Bayesian parametric framework to tackle the accessibility problem across space in urban theory. Adopting continuous variables in a probabilistic setting we are able to associate with the distribution density to the Kendall's tau index and replicate the general issues related to the role of proximity in a more general context. In addition, by referring to the Beta and Gamma distribution, we are able to introduce a differentiation feature in each spatial unit without incurring in any a-priori definition of territorial units. We are also providing an empirical application of our theoretical setting to study the density distribution of the population across Massachusetts.

A one-dimensional Keller-Segel equation with a drift issued from the boundary

We investigate in this note the dynamics of a one-dimensional Keller-Segel type model on the half-line. On the contrary to the classical configuration, the chemical production term is located on the boundary. We prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass, they blow-up in finite time above the critical mass, and they converge to some equilibrium at the critical mass. Entropy techniques are presented which aim at providing quantitative convergence results for the subcritical case. This note is completed with a brief introduction to a more realistic model (still one-dimensional).

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

An empirical analysis of a merger between a network and low-cost airlines

We use a difference-in-difference estimator to examine the effects of a merger involving three airlines. The novelty lies in the examination of this operation in two distinct scenarios: (1) on routes where two low-cost carriers and (2) on routes where a network and one of the low-cost airlines had previously been competing. We report a reduction in frequencies but no substantial effect on prices in the first scenario, while in the second we report an increase in prices but no substantial effect on frequencies. These results may be attributed to the differences in passenger types flying on these routes.

News from compositions, the R package

The R-package “compositions”is a tool for advanced compositional analysis. Its basicfunctionality has seen some conceptual improvement, containing now some facilitiesto work with and represent ilr bases built from balances, and an elaborated subsys-tem for dealing with several kinds of irregular data: (rounded or structural) zeroes,incomplete observations and outliers. The general approach to these irregularities isbased on subcompositions: for an irregular datum, one can distinguish a “regular” sub-composition (where all parts are actually observed and the datum behaves typically)and a “problematic” subcomposition (with those unobserved, zero or rounded parts, orelse where the datum shows an erratic or atypical behaviour). Systematic classificationschemes are proposed for both outliers and missing values (including zeros) focusing onthe nature of irregularities in the datum subcomposition(s).To compute statistics with values missing at random and structural zeros, a projectionapproach is implemented: a given datum contributes to the estimation of the desiredparameters only on the subcompositon where it was observed. For data sets withvalues below the detection limit, two different approaches are provided: the well-knownimputation technique, and also the projection approach.To compute statistics in the presence of outliers, robust statistics are adapted to thecharacteristics of compositional data, based on the minimum covariance determinantapproach. The outlier classification is based on four different models of outlier occur-rence and Monte-Carlo-based tests for their characterization. Furthermore the packageprovides special plots helping to understand the nature of outliers in the dataset.Keywords: coda-dendrogram, lost values, MAR, missing data, MCD estimator,robustness, rounded zeros

Mapping sub-flows to p2mp LSPs

In previous work we proposed a multi-objective traffic engineering scheme (MHDB-S model) using different distribution trees to multicast several flows. In this paper, we propose a heuristic algorithm to create multiple point-to-multipoint (p2mp) LSPs based on the optimum sub-flow values obtained with our MHDB-S model. Moreover, a general problem for supporting multicasting in MPLS networks is the lack of labels. To reduce the number of labels used, a label space reduction algorithm solution is also considered

Bayesian nash equilibrium in ''linear'' cournot models with private information about costs

Calculating explicit closed form solutions of Cournot models where firms have private information about their costs is, in general, very cumbersome. Most authors consider therefore linear demands and constant marginal costs. However, within this framework, the nonnegativity constraint on prices (and quantities) has been ignored or not properly dealt with and the correct calculation of all Bayesian Nash equilibria is more complicated than expected. Moreover, multiple symmetric and interior Bayesianf equilibria may exist for an open set of parameters. The reason for this is that linear demand is not really linear, since there is a kink at zero price: the general ''linear'' inverse demand function is P (Q) = max{a - bQ, 0} rather than P (Q) = a - bQ.