A proposal for a new specification for a conditionally heteroskedastic variance model: the Quadratic Moving-Average Conditional Heteroskedasticity and an application to the D. Mark-U.S. dollar Exchange Rate

Ever since the appearance of the ARCH model [Engle(1982a)], an impressive array of variance specifications belonging to the same class of models has emerged [i.e. Bollerslev's (1986) GARCH; Nelson's (1990) EGARCH]. This recent domain has achieved very successful developments. Nevertheless, several empirical studies seem to show that the performance of such models is not always appropriate [Boulier(1992)]. In this paper we propose a new specification: the Quadratic Moving Average Conditional heteroskedasticity model. Its statistical properties, such as the kurtosis and the symmetry, as well as two estimators (Method of Moments and Maximum Likelihood) are studied. Two statistical tests are presented, the first one tests for homoskedasticity and the second one, discriminates between ARCH and QMACH specification. A Monte Carlo study is presented in order to illustrate some of the theoretical results. An empirical study is undertaken for the DM-US exchange rate.

Calculation of the variance in surveys of the economic climate

Public opinion surveys have become progressively incorporated into systems of official statistics. Surveys of the economic climate are usually qualitative because they collect opinions of businesspeople and/or experts about the long-term indicators described by a number of variables. In such cases the responses are expressed in ordinal numbers, that is, the respondents verbally report, for example, whether during a given trimester the sales or the new orders have increased, decreased or remained the same as in the previous trimester. These data allow to calculate the percent of respondents in the total population (results are extrapolated), who select every one of the three options. Data are often presented in the form of an index calculated as the difference between the percent of those who claim that a given variable has improved in value and of those who claim that it has deteriorated. As in any survey conducted on a sample the question of the measurement of the sample error of the results has to be addressed, since the error influences both the reliability of the results and the calculation of the sample size adequate for a desired confidence interval. The results presented here are based on data from the Survey of the Business Climate (Encuesta de Clima Empresarial) developed through the collaboration of the Statistical Institute of Catalonia (Institut d’Estadística de Catalunya) with the Chambers of Commerce (Cámaras de Comercio) of Sabadell and Terrassa.

(No)competition in the Spanish retailing gasoline market: a variance filter approach

Various methodologies in economic literature have been used to analyse the international hydrocarbon retail sector. Nevertheless at a Spanish level these studies are much more recent and most conclude that generally there is no effective competition present in this market, regardless of the approach used. In this paper, in order to analyse the price levels in the Spanish petrol market, our starting hypothesis is that in uncompetitive markets the prices are higher and the standard deviation is lower. We use weekly retail petrol price data from the ten biggest Spanish cities, and apply Markov chains to fill the missing values for petrol 95 and diesel, and we also employ a variance filter. We conclude that this market demonstrates reduced price dispersion, regardless of brand or city.

The additive genetic variance after bottlenecks is affected by the number of loci involved in epistatic interactions.

We investigated the role of the number of loci coding for a neutral trait on the release of additive variance for this trait after population bottlenecks. Different bottleneck sizes and durations were tested for various matrices of genotypic values, with initial conditions covering the allele frequency space. We used three different types of matrices. First, we extended Cheverud and Routman's model by defining matrices of "pure" epistasis for three and four independent loci; second, we used genotypic values drawn randomly from uniform, normal, and exponential distributions; and third we used two models of simple metabolic pathways leading to physiological epistasis. For all these matrices of genotypic values except the dominant metabolic pathway, we find that, as the number of loci increases from two to three and four, an increase in the release of additive variance is occurring. The amount of additive variance released for a given set of genotypic values is a function of the inbreeding coefficient, independently of the size and duration of the bottleneck. The level of inbreeding necessary to achieve maximum release in additive variance increases with the number of loci. We find that additive-by-additive epistasis is the type of epistasis most easily converted into additive variance. For a wide range of models, our results show that epistasis, rather than dominance, plays a significant role in the increase of additive variance following bottlenecks.

Extremal properties of certain risk models

Cette thèse s'intéresse à étudier les propriétés extrémales de certains modèles de risque d'intérêt dans diverses applications de l'assurance, de la finance et des statistiques. Cette thèse se développe selon deux axes principaux, à savoir: Dans la première partie, nous nous concentrons sur deux modèles de risques univariés, c'est-à- dire, un modèle de risque de déflation et un modèle de risque de réassurance. Nous étudions le développement des queues de distribution sous certaines conditions des risques commun¬s. Les principaux résultats sont ainsi illustrés par des exemples typiques et des simulations numériques. Enfin, les résultats sont appliqués aux domaines des assurances, par exemple, les approximations de Value-at-Risk, d'espérance conditionnelle unilatérale etc. La deuxième partie de cette thèse est consacrée à trois modèles à deux variables: Le premier modèle concerne la censure à deux variables des événements extrême. Pour ce modèle, nous proposons tout d'abord une classe d'estimateurs pour les coefficients de dépendance et la probabilité des queues de distributions. Ces estimateurs sont flexibles en raison d'un paramètre de réglage. Leurs distributions asymptotiques sont obtenues sous certaines condi¬tions lentes bivariées de second ordre. Ensuite, nous donnons quelques exemples et présentons une petite étude de simulations de Monte Carlo, suivie par une application sur un ensemble de données réelles d'assurance. L'objectif de notre deuxième modèle de risque à deux variables est l'étude de coefficients de dépendance des queues de distributions obliques et asymétriques à deux variables. Ces distri¬butions obliques et asymétriques sont largement utiles dans les applications statistiques. Elles sont générées principalement par le mélange moyenne-variance de lois normales et le mélange de lois normales asymétriques d'échelles, qui distinguent la structure de dépendance de queue comme indiqué par nos principaux résultats. Le troisième modèle de risque à deux variables concerne le rapprochement des maxima de séries triangulaires elliptiques obliques. Les résultats théoriques sont fondés sur certaines hypothèses concernant le périmètre aléatoire sous-jacent des queues de distributions. -- This thesis aims to investigate the extremal properties of certain risk models of interest in vari¬ous applications from insurance, finance and statistics. This thesis develops along two principal lines, namely: In the first part, we focus on two univariate risk models, i.e., deflated risk and reinsurance risk models. Therein we investigate their tail expansions under certain tail conditions of the common risks. Our main results are illustrated by some typical examples and numerical simu¬lations as well. Finally, the findings are formulated into some applications in insurance fields, for instance, the approximations of Value-at-Risk, conditional tail expectations etc. The second part of this thesis is devoted to the following three bivariate models: The first model is concerned with bivariate censoring of extreme events. For this model, we first propose a class of estimators for both tail dependence coefficient and tail probability. These estimators are flexible due to a tuning parameter and their asymptotic distributions are obtained under some second order bivariate slowly varying conditions of the model. Then, we give some examples and present a small Monte Carlo simulation study followed by an application on a real-data set from insurance. The objective of our second bivariate risk model is the investigation of tail dependence coefficient of bivariate skew slash distributions. Such skew slash distributions are extensively useful in statistical applications and they are generated mainly by normal mean-variance mixture and scaled skew-normal mixture, which distinguish the tail dependence structure as shown by our principle results. The third bivariate risk model is concerned with the approximation of the component-wise maxima of skew elliptical triangular arrays. The theoretical results are based on certain tail assumptions on the underlying random radius.

Genetics of cadmium hyperaccumulation variance in Thlaspi caerulescens natural populations from Switzerland

SUMMARY Heavy metal presence in the environment is a serious concern since some of them can be toxic to plants, animals and humans once accumulated along the food chain. Cadmium (Cd) is one of the most toxic heavy metal. It is naturally present in soils at various levels and its concentration can be increased by human activities. Several plants however have naturally developed strategies allowing them to grow on heavy metal enriched soils. One of them consists in the accumulation and sequestration of heavy metals in the above-ground biomass. Some plants present in addition an extreme strategy by which they accumulate a limited number of heavy metals in their shoots in amounts 100 times superior to those expected for a non-accumulating plant in the same conditions. Understanding the genetic basis of the hyperaccumulation trait - particularly for Cd - remains an important challenge which may lead to biotechnological applications in the soil phytoremediation. In this thesis, Thlaspi caerulescens J. & C. Presl (Brassicaceae) was used as a model plant to study the Cd hyperaccumulation trait, owing to its physiological and genetic characteristics. Twenty-four wild populations were sampled in different regions of Switzerland. They were characterized for environmental and soil parameters as well as intrinsic characteristics of plants (i.e. metal concentrations in shoots). They were as well genetically characterized by AFLPs, plastid DNA polymorphism and genes markers (CAPS and microsatellites) mainly developed in this thesis. Some of the investigated genes were putatively linked to the Cd hyperaccumulation trait. Since the study of the Cd hyperaccumulation in the field is important as it allows the identification of patterns of selection, the present work offered a methodology to define the Cd hyperaccumulation capacity of populations from different habitats permitting thus their comparison in the field. We showed that Cd, Zn, Fe and Cu accumulations were linked and that populations with higher Cd hyperaccumulation capacity had higher shoot and reproductive fitness. Using our genetic data, statistical methods (Beaumont & Nichols's procedure, partial Mantel tests) were applied to identify genomic signatures of natural selection related to the Cd hyperaccumulation capacity. A significant genetic difference between populations related to their Cd hyperaccumulation capacity was revealed based on somè specific markers (AFLP and candidate genes). Polymorphism at the gene encoding IRTl (Iron-transporter also participating to the transport of Zn) was suggested as explaining part of the variation in Cd hyperaccumulation capacity of populations supporting previous physiological investigations. RÉSUMÉ La présence de métaux lourds dans l'environnement est un phénomène préoccupant. En effet, certains métaux lourds - comme le cadmium (Cd) -sont toxiques pour les plantes, les animaux et enfin, accumulés le long de la chaîne alimentaire, pour les hommes. Le Cd est naturellement présent dans le sol et sa concentration peut être accrue par différentes activités humaines. Certaines plantes ont cependant développé des stratégies leur permettant de pousser sur des sols contaminés en métaux lourds. Parmi elles, certaines accumulent et séquestrent les métaux lourds dans leurs parties aériennes. D`autres présentent une stratégie encore plus extrême. Elles accumulent un nombre limité de métaux lourds en quantités 100 fois supérieures à celles attendues pour des espèces non-accumulatrices sous de mêmes conditions. La compréhension des bases génétiques de l'hyperaccumulation -particulièrement celle du Cd - représente un défi important avec des applications concrètes en biotechnologies, tout particulièrement dans le but appliqué de la phytoremediation des sols contaminés. Dans cette thèse, Thlaspi caerulescens J. & C. Presl (Brassicaceae) a été utilisé comme modèle pour l'étude de l'hyperaccumulation du Cd de par ses caractéristiques physiologiques et génétiques. Vingt-quatre populations naturelles ont été échantillonnées en Suisse et pour chacune d'elles les paramètres environnementaux, pédologique et les caractéristiques intrinsèques aux plantes (concentrations en métaux lourds) ont été déterminés. Les populations ont été caractérisées génétiquement par des AFLP, des marqueurs chloroplastiques et des marqueurs de gènes spécifiques, particulièrement ceux potentiellement liés à l'hyperaccumulation du Cd (CAPS et microsatellites). La plupart ont été développés au cours de cette thèse. L'étude de l'hyperaccumulation du Cd en conditions naturelles est importante car elle permet d'identifier la marque, éventuelle de sélection naturelle. Ce travail offre ainsi une méthodologie pour définir et comparer la capacité des populations à hyperaccumuler le Cd dans différents habitats. Nous avons montré que les accumulations du Cd, Zn, Fe et Cu sont liées et que les populations ayant une grande capacité d'hyperaccumuler le Cd ont également une meilleure fitness végétative et reproductive. Des méthodes statistiques (l'approche de Beaumont & Nichols, tests de Martel partiels) ont été utilisées sur les données génétiques pour identifier la signature génomique de la sélection naturelle liée à la capacité d'hyperaccumuler le Cd. Une différenciation génétique des populations liée à leur capacité d'hyperaccumuler le Cd a été mise en évidence sur certains marqueurs spécifiques. En accord avec les études physiologiques connues, le polymorphisme au gène codant IRT1 (un transporteur de Fe impliqué dans le transport du Zn) pourrait expliquer une partie de la variance de la capacité des populations à hyperaccumuler le Cd.

Spanning tests in return and stochastic discount factor mean-variance frontiers: A unifying approach

We propose new spanning tests that assess if the initial and additional assets share theeconomically meaningful cost and mean representing portfolios. We prove their asymptoticequivalence to existing tests under local alternatives. We also show that unlike two-step oriterated procedures, single-step methods such as continuously updated GMM yield numericallyidentical overidentifyng restrictions tests, so there is arguably a single spanning test.To prove these results, we extend optimal GMM inference to deal with singularities in thelong run second moment matrix of the influence functions. Finally, we test for spanningusing size and book-to-market sorted US stock portfolios.

Breeding system and genetic variance in the monogamous, semi-social shrew, Crocidura russula

The population-genetic consequences of monogamy and male philopatry (a rare breeding system in mammals) were investigated using microsatellite markers in the semisocial and anthropophilic shrew Crocidura russula. A hierarchical sampling design over a 16-km geographical transect revealed a large genetic diversity (h = 0.813) with significant differentiation among subpopulations (F-ST = 5-6%), which suggests an exchange of 4.4 migrants per generation. Demic effective-size estimates were very high, due both to this limited gene inflow and to the inner structure of subpopulations. These were made of 13-20 smaller units (breeding groups), comprising an estimate of four breeding pairs each. Members of the same breeding groups displayed significant coancestries (F-LS = 9-10%), which was essentially due to strong male kinship: syntopic males were on average related at the half-sib level. Female dispersal among breeding groups was not complete (similar to 39%), and insufficient to prevent inbreeding. From our results, the breeding strategy of C. russula seems less efficient than classical mammalian systems (polygyny and male dispersal) in disentangling coancestry from inbreeding, but more so in retaining genetic variance.

Variance reduction methods for simulation of densities on Wiener space

We develop a general error analysis framework for the Monte Carlo simulationof densities for functionals in Wiener space. We also study variancereduction methods with the help of Malliavin derivatives. For this, wegive some general heuristic principles which are applied to diffusionprocesses. A comparison with kernel density estimates is made.

Duality in mean-variance frontiers with conditioning information

Portfolio and stochastic discount factor (SDF) frontiers are usually regarded as dual objects, and researchers sometimes use one to answer questions about the other. However, the introduction of conditioning information and active portfolio strategies alters this relationship. For instance, the unconditional portfolio frontier in Hansen and Richard (1987) is not dual to the unconditional SDF frontier in Gallant, Hansen and Tauchen (1990). We characterise the dual objects to those frontiers, and relate them to the frontiers generated with managed portfolios, which are commonly used in empirical work. We also study the implications of a safe asset and other special cases.

Sample size and statistical power in the hierarchical analysis of variance: applications in morphometry of the nervous system.

Analysis of variance is commonly used in morphometry in order to ascertain differences in parameters between several populations. Failure to detect significant differences between populations (type II error) may be due to suboptimal sampling and lead to erroneous conclusions; the concept of statistical power allows one to avoid such failures by means of an adequate sampling. Several examples are given in the morphometry of the nervous system, showing the use of the power of a hierarchical analysis of variance test for the choice of appropriate sample and subsample sizes. In the first case chosen, neuronal densities in the human visual cortex, we find the number of observations to be of little effect. For dendritic spine densities in the visual cortex of mice and humans, the effect is somewhat larger. A substantial effect is shown in our last example, dendritic segmental lengths in monkey lateral geniculate nucleus. It is in the nature of the hierarchical model that sample size is always more important than subsample size. The relative weight to be attributed to subsample size thus depends on the relative magnitude of the between observations variance compared to the between individuals variance.

The mean-variance model from the inverse of the variance-covariance matrix

En este artículo, a partir de la inversa de la matriz de varianzas y covarianzas se obtiene el modelo Esperanza-Varianza de Markowitz siguiendo un camino más corto y matemáticamente riguroso. También se obtiene la ecuación de equilibrio del CAPM de Sharpe.