Integrated random processes exhibiting long tails, finite moments, and power-law spectra

A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling assumption, takes on a form that is the basis of the results derived in the rest of the paper. One of these is an expansion for the cumulants, which are all finite, subject to mild conditions on the functions defining the process. This is in contrast with the Lévy distribution¿which can be obtained from our model in certain limits¿which has no finite moments. The evaluation of the spectral density and the form of the probability density function in the tails of the distribution shows that the model exhibits a power-law spectrum and long tails in a natural way. A careful analysis of the characteristic function shows that it may be separated into a part representing a Lévy process together with another part representing the deviation of our model from the Lévy process. This

Extreme times for volatility processes

Extreme times techniques, generally applied to nonequilibrium statistical mechanical processes, are also useful for a better understanding of financial markets. We present a detailed study on the mean first-passage time for the volatility of return time series. The empirical results extracted from daily data of major indices seem to follow the same law regardless of the kind of index thus suggesting an universal pattern. The empirical mean first-passage time to a certain level L is fairly different from that of the Wiener process showing a dissimilar behavior depending on whether L is higher or lower than the average volatility. All of this indicates a more complex dynamics in which a reverting force drives volatility toward its mean value. We thus present the mean first-passage time expressions of the most common stochastic volatility models whose approach is comparable to the random diffusion description. We discuss asymptotic approximations of these models and confront them to empirical results with a good agreement with the exponential Ornstein-Uhlenbeck model.

Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.

Scale decisions can reverse conclusions on community assembly processes.

AIM: Phylogenetic diversity patterns are increasingly being used to better understand the role of ecological and evolutionary processes in community assembly. Here, we quantify how these patterns are influenced by scale choices in terms of spatial and environmental extent and organismic scales. LOCATION: European Alps. METHODS: We applied 42 sampling strategies differing in their combination of focal scales. For each resulting sub-dataset, we estimated the phylogenetic diversity of the species pools, phylogenetic α-diversities of local communities, and statistics commonly used together with null models in order to infer non-random diversity patterns (i.e. phylogenetic clustering versus over-dispersion). Finally, we studied the effects of scale choices on these measures using regression analyses. RESULTS: Scale choices were decisive for revealing signals in diversity patterns. Notably, changes in focal scales sometimes reversed a pattern of over-dispersion into clustering. Organismic scale had a stronger effect than spatial and environmental extent. However, we did not find general rules for the direction of change from over-dispersion to clustering with changing scales. Importantly, these scale issues had only a weak influence when focusing on regional diversity patterns that change along abiotic gradients. MAIN CONCLUSIONS: Our results call for caution when combining phylogenetic data with distributional data to study how and why communities differ from random expectations of phylogenetic relatedness. These analyses seem to be robust when the focus is on relating community diversity patterns to variation in habitat conditions, such as abiotic gradients. However, if the focus is on identifying relevant assembly rules for local communities, the uncertainty arising from a certain scale choice can be immense. In the latter case, it becomes necessary to test whether emerging patterns are robust to alternative scale choices.

A comparison of the processes of institutionalisation of political economy in Spain and Italy (1860-1900)

[spa] El estudio de los procesos a través de los cuales la economía política se ha transformado en una disciplina académica es un área de creciente interés en la historia del pensamiento económico. Dicho estudio se ha abordado a través del análisis de la importancia de la economía política en un conjunto de instituciones, consideradas clave en la expansión de la economía en las sociedades occidentales en la segunda mitad del siglo XIX y primeras décadas del XX: universidades, sociedades económicas, publicaciones periódicas de contenido económico y los parlamentos nacionales. Este papel presenta una comparación entre los desarrollos del proceso de institutionalización de la economía política en España e Italia, a través del estudio de la presencia de esta disciplina en las instituciones mencionadas para el periodo 1860-1900. El objetivo es medir la posible existencia de una vía común en la institucionalización de la economía política en ambos países, como un primer paso hacia la elaboración de un modelo supranacional de institucionalización de la economía en este periodo.

Why Italy and not Spain?: comparing two industrialization processes from a dissagregate time-series perspective

This study presents new evidence concerning the uneven processes of industrialization innineteenth century Spain and Italy based on a disaggregate analysis of the productivesectors from which the behaviour of the aggregate indices is comprised. The use of multivariate time-series analysis techniques can aid our understanding and characterization of these two processes of industrialization. The identification of those sectors with key rolesin leading industrial growth provides new evidence concerning the factors that governed thebehaviour of the aggregates in the two economies. In addition, the analysis of the existenceof interindustry linkages reveals the scale of the industrialization process, and wheresignificant differences exist, accounts for many of the divergences recorded in the historiography for the period 1850-1913.

The role of oxidative stress during inflammatory processes.

Abstract The production of various reactive oxidant species in excess of endogenous antioxidant defense mechanisms promotes the development of a state of oxidative stress, with significant biological consequences. In recent years, evidence has emerged that oxidative stress plays a crucial role in the development and perpetuation of inflammation, and thus contributes to the pathophysiology of a number of debilitating illnesses, such as cardiovascular diseases, diabetes, cancer, or neurodegenerative processes. Oxidants affect all stages of the inflammatory response, including the release by damaged tissues of molecules acting as endogenous danger signals, their sensing by innate immune receptors from the Toll-like (TLRs) and the NOD-like (NLRs) families, and the activation of signaling pathways initiating the adaptive cellular response to such signals. In this article, after summarizing the basic aspects of redox biology and inflammation, we review in detail the current knowledge on the fundamental connections between oxidative stress and inflammatory processes, with a special emphasis on the danger molecule high-mobility group box-1, the TLRs, the NLRP-3 receptor, and the inflammasome, as well as the transcription factor nuclear factor-κB.

Geochemical and H-O-Sr-Nd isotope evidence for magmatic processes and meteoric-water interactions in the basal complex of La Gomera, Canary Islands

The plutonic rocks of the Basal Complex of La Gomera, Canary Islands, Spain, were studied by means of major and trace element contents and by H-O-Sr-Nd isotope compositions in order to distinguish primary magmatic characteristics and late-stage alteration products. Deciphering the effects of alteration allowed us to determine primary, plume-related compositions that indicated D- and (18)O-depletion relative to normal upper mantle, supporting the conclusions of earlier studies on the plutonic rocks of Fuerteventura and La Palma. Late-stage alteration took place during the formation of the intrusive series induced by interaction with meteoric water. Inferred isotopic compositions of the meteoric water indicate that the water infiltrated into the rock edifice at a height of about 1500 m above sea level, suggesting the existence of a subaerial volcano which was active during the intrusive activity and that it has been either distroyed or remain buried by later volcanic and landslide events.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.