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.

On Ito's formula for elliptic diffusion processes

Bardina and Jolis [Stochastic process. Appl. 69 (1997) 83-109] prove an extension of Ito's formula for F(Xt, t), where F(x, t) has a locally square-integrable derivative in x that satisfies a mild continuity condition in t and X is a one-dimensional diffusion process such that the law of Xt has a density satisfying certain properties. This formula was expressed using quadratic covariation. Following the ideas of Eisenbaum [Potential Anal. 13 (2000) 303-328] concerning Brownian motion, we show that one can re-express this formula using integration over space and time with respect to local times in place of quadratic covariation. We also show that when the function F has a locally integrable derivative in t, we can avoid the mild continuity condition in t for the derivative of F in x.

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Post-Nonlinear Mixtures and Beyond

Although sources in general nonlinear mixturm arc not separable iising only statistical independence, a special and realistic case of nonlinear mixtnres, the post nonlinear (PNL) mixture is separable choosing a suited separating system. Then, a natural approach is based on the estimation of tho separating Bystem parameters by minimizing an indcpendence criterion, like estimated mwce mutual information. This class of methods requires higher (than 2) order statistics, and cannot separate Gaarsian sources. However, use of [weak) prior, like source temporal correlation or nonstationarity, leads to other source separation Jgw rithms, which are able to separate Gaussian sourra, and can even, for a few of them, works with second-order statistics. Recently, modeling time correlated s011rces by Markov models, we propose vcry efficient algorithms hmed on minimization of the conditional mutual information. Currently, using the prior of temporally correlated sources, we investigate the fesihility of inverting PNL mixtures with non-bijectiw non-liacarities, like quadratic functions. In this paper, we review the main ICA and BSS results for riunlinear mixtures, present PNL models and algorithms, and finish with advanced resutts using temporally correlated snu~sm

Trust region versus line search for computing the optical flow

We consider the numerical treatment of the optical flow problem by evaluating the performance of the trust region method versus the line search method. To the best of our knowledge, the trust region method is studied here for the first time for variational optical flow computation. Four different optical flow models are used to test the performance of the proposed algorithm combining linear and nonlinear data terms with quadratic and TV regularization. We show that trust region often performs better than line search; especially in the presence of non-linearity and non-convexity in the model.

Conditional maximum likelihood timing recovery: estimators and bounds

This paper is concerned with the derivation of new estimators and performance bounds for the problem of timing estimation of (linearly) digitally modulated signals. The conditional maximum likelihood (CML) method is adopted, in contrast to the classical low-SNR unconditional ML (UML) formulationthat is systematically applied in the literature for the derivationof non-data-aided (NDA) timing-error-detectors (TEDs). A new CML TED is derived and proved to be self-noise free, in contrast to the conventional low-SNR-UML TED. In addition, the paper provides a derivation of the conditional Cramér–Rao Bound (CRB ), which is higher (less optimistic) than the modified CRB (MCRB)[which is only reached by decision-directed (DD) methods]. It is shown that the CRB is a lower bound on the asymptotic statisticalaccuracy of the set of consistent estimators that are quadratic with respect to the received signal. Although the obtained boundis not general, it applies to most NDA synchronizers proposed in the literature. A closed-form expression of the conditional CRBis obtained, and numerical results confirm that the CML TED attains the new bound for moderate to high Eg/No.

Second-order parameter estimation

This work provides a general framework for the design of second-order blind estimators without adopting anyapproximation about the observation statistics or the a prioridistribution of the parameters. The proposed solution is obtainedminimizing the estimator variance subject to some constraints onthe estimator bias. The resulting optimal estimator is found todepend on the observation fourth-order moments that can be calculatedanalytically from the known signal model. Unfortunately,in most cases, the performance of this estimator is severely limitedby the residual bias inherent to nonlinear estimation problems.To overcome this limitation, the second-order minimum varianceunbiased estimator is deduced from the general solution by assumingaccurate prior information on the vector of parameters.This small-error approximation is adopted to design iterativeestimators or trackers. It is shown that the associated varianceconstitutes the lower bound for the variance of any unbiasedestimator based on the sample covariance matrix.The paper formulation is then applied to track the angle-of-arrival(AoA) of multiple digitally-modulated sources by means ofa uniform linear array. The optimal second-order tracker is comparedwith the classical maximum likelihood (ML) blind methodsthat are shown to be quadratic in the observed data as well. Simulationshave confirmed that the discrete nature of the transmittedsymbols can be exploited to improve considerably the discriminationof near sources in medium-to-high SNR scenarios.

Salivary cotinine concentrations in daily smokers in Barcelona, Spain: a cross-sectional study

Background: Characterizing and comparing the determinant of cotinine concentrations in different populations should facilitate a better understanding of smoking patterns and addiction. This study describes and characterizes determinants of salivary cotinine concentration in a sample of Spanish adult daily smoker men and women. Methods: A cross-sectional study was carried out between March 2004 and December 2005 in a representative sample of 1245 people from the general population of Barcelona, Spain. A standard questionnaire was used to gather information on active tobacco smoking and passive exposure, and a saliva specimen was obtained to determine salivary cotinine concentration. Two hundred and eleven adult smokers (>16 years old) with complete data were included in the analysis. Determinants of cotinine concentrations were assessed using linear regression models. Results: Salivary cotinine concentration was associated with the reported number of cigarettes smoked in the previous 24 hours (R2 = 0.339; p < 0.05). The inclusion of a quadratic component for number of cigarettes smoked in the regression analyses resulted in an improvement of the fit (R2 = 0.386; p < 0.05). Cotinine concentration differed significantly by sex, with men having higher levels. Conclusion: This study shows that salivary cotinine concentration is significantly associated with the number of cigarettes smoked and sex, but not with other smoking-related variables.

Trust region versus line search for computing the optical flow

We consider the numerical treatment of the optical flow problem by evaluating the performance of the trust region method versus the line search method. To the best of our knowledge, the trust region method is studied here for the first time for variational optical flow computation. Four different optical flow models are used to test the performance of the proposed algorithm combining linear and nonlinear data terms with quadratic and TV regularization. We show that trust region often performs better than line search; especially in the presence of non-linearity and non-convexity in the model.

The induced generalized OWA operator

We present the induced generalized ordered weighted averaging (IGOWA) operator. It is a new aggregation operator that generalizes the OWA operator by using the main characteristics of two well known aggregation operators: the generalized OWA and the induced OWA operator. Then, this operator uses generalized means and order inducing variables in the reordering process. With this formulation, we get a wide range of aggregation operators that include all the particular cases of the IOWA and the GOWA operator, and a lot of other cases such as the induced ordered weighted geometric (IOWG) operator and the induced ordered weighted quadratic averaging (IOWQA) operator. We further generalize the IGOWA operator by using quasi-arithmetic means. The result is the Quasi-IOWA operator. Finally, we also develop a numerical example of the new approach in a financial decision making problem.

Contratación de la mano de obra y desempeño en los servicios intensivos en conocimiento: una visión del capital intelectual

Objeto: El desempeño de las actividades de servicios de alto valor añadido ofrecidospor las empresas manufactureras, de la misma forma que el de los servicios intensivosen conocimiento, puede verse afectado por las formas de contratación de la mano deobra utilizadas en ellas. Se estudia el impacto del uso de trabajo contingente (temporal y autónomo) sobre la productividad del trabajo en las empresas de servicios intensivos en conocimiento. Para desarrollar las hipótesis, se tiene en cuenta el impacto potencial del trabajo contingente sobre el capital intangible de la empresa, así como los resultados de la literatura empírica.Diseño/metodología: Se analizan los datos de una muestra de 279 empresas de servicios intensivos en conocimiento localizadas en Cataluña, mediante dos modelos de regresión lineal.Aportaciones y resultados: Los resultados muestran que el empleo de formas de trabajo contingentes, como el trabajo temporal y los trabajadores autónomos, tiene un impacto negativo en la productividad del trabajo. No existe, en cambio, una relación cuadrática entre estas variables. Limitaciones: La muestra utilizada procede exclusivamente de Cataluña (España), noes perfectamente extrapolable al conjunto de empresas de servicios intensivos enconocimiento y se obtuvo en la fase alcista del ciclo económico. El diseño del estudio estransversal. La clasificación de las empresas como intensivas en conocimiento esdicotómica, en función del sector al que pertenecen. Implicaciones prácticas:Las decisiones sobre la contratación de mano de obra en actividades de servicios de alto valor añadido deberían minimizar las formas de trabajocontingentes, si quieren mejorar su productividad.Implicaciones sociales: Un modelo productivo que pretenda potenciar los servicios de mayor valor añadido no puede descansar sobre la base de un mercado laboral en el que las empresas utilizan una elevada proporción de trabajo contingente en su mano de obra. Valor añadido: Este artículo ofrece nuevos datos para a la escasa literatura que relaciona el uso de trabajo contingente con la productividad en el sector de los servicios intensivos en conocimiento. La creciente importancia de los servicios de alto valor añadido, tanto en empresas de servicios como manufactureras, y el interés por conocer los determinantes de su productividad justifican la necesidad de realizar estudios como el que se presenta.

Minimum-uncertaity states and pseudoclassical dynamics. II

The set of initial conditions for which the pseudoclassical evolution algorithm (and minimality conservation) is verified for Hamiltonians of degrees N (N>2) is explicitly determined through a class of restrictions for the corresponding classical trajectories, and it is proved to be at most denumerable. Thus these algorithms are verified if and only if the system is quadratic except for a set of measure zero. The possibility of time-dependent a-equivalence classes is studied and its physical interpretation is presented. The implied equivalence of the pseudoclassical and Ehrenfest algorithms and their relationship with minimality conservation is discussed in detail. Also, the explicit derivation of the general unitary operator which linearly transforms minimum-uncertainty states leads to the derivation, among others, of operators with a general geometrical interpretation in phase space, such as rotations (parity, Fourier).