Aggregations and Marginalization of GARCH and Stochastic Volatility Models

The GARCH and Stochastic Volatility paradigms are often brought into conflict as two competitive views of the appropriate conditional variance concept : conditional variance given past values of the same series or conditional variance given a larger past information (including possibly unobservable state variables). The main thesis of this paper is that, since in general the econometrician has no idea about something like a structural level of disaggregation, a well-written volatility model should be specified in such a way that one is always allowed to reduce the information set without invalidating the model. To this respect, the debate between observable past information (in the GARCH spirit) versus unobservable conditioning information (in the state-space spirit) is irrelevant. In this paper, we stress a square-root autoregressive stochastic volatility (SR-SARV) model which remains true to the GARCH paradigm of ARMA dynamics for squared innovations but weakens the GARCH structure in order to obtain required robustness properties with respect to various kinds of aggregation. It is shown that the lack of robustness of the usual GARCH setting is due to two very restrictive assumptions : perfect linear correlation between squared innovations and conditional variance on the one hand and linear relationship between the conditional variance of the future conditional variance and the squared conditional variance on the other hand. By relaxing these assumptions, thanks to a state-space setting, we obtain aggregation results without renouncing to the conditional variance concept (and related leverage effects), as it is the case for the recently suggested weak GARCH model which gets aggregation results by replacing conditional expectations by linear projections on symmetric past innovations. Moreover, unlike the weak GARCH literature, we are able to define multivariate models, including higher order dynamics and risk premiums (in the spirit of GARCH (p,p) and GARCH in mean) and to derive conditional moment restrictions well suited for statistical inference. Finally, we are able to characterize the exact relationships between our SR-SARV models (including higher order dynamics, leverage effect and in-mean effect), usual GARCH models and continuous time stochastic volatility models, so that previous results about aggregation of weak GARCH and continuous time GARCH modeling can be recovered in our framework.

"Car ils ne savent pas ce qu'ils font" : au coeur du pardon et de sa dynamique spirituelle

Cette thèse est une recherche pluridisciplinaire sur le concept du pardon interpersonnel. Elle cherche à circonscrire la portée et la dynamique du pardon, entre autres en répondant à la question Pourquoi pardonner ? Jusqu’à récemment on trouvait peu d’écrits sur le pardon. Mais les deux dernières décennies ont vu un foisonnement de travaux de recherche sur le sujet de la part de psychologues éveillés à ses bienfaits thérapeutiques. Parallèlement, des philosophes et des théologiens se sont aussi intéressés à la question et ont commencé à publier leurs réflexions. Deux hypothèses marquent le parcours de notre recherche. La première porte sur la signification de la deuxième partie de l’énoncé biblique en Luc 23, 34 « Père, pardonne-leur car ils ne savent pas ce qu’ils font ». Elle avance que le « motif de l’ignorance » que cette parole affirme a une portée universelle et soutient que l’offenseur est en état d’ignorance inconsciente lorsqu’il fait le mal. Le pardon des offenses serait donc le pardon de cette ignorance inconsciente. La seconde hypothèse conjecture que le pardon interpersonnel s’inscrit dans une dynamique spirituelle même s’il a quitté ses amarres religieuses. Nous avançons que la relation pardon-spiritualité est significative et que sa compréhension peut aider à mieux saisir l’essence d’un pardon devenu séculier et à en permettre l’éclosion. Pour établir la valeur de cette hypothèse, nous devons étudier la dynamique d’une démarche de pardon de même qu’à déterminer le statut actuel de la spiritualité. La thèse se divise en trois parties. La première partie expose la pensée d’auteurs significatifs dans chacune des principales disciplines concernées par le pardon : philosophie, théologie, psychologie et spiritualité. Il y est question d’offense pardonnable ou impardonnable, de pardon conditionnel ou inconditionnel, de corrélats du pardon comme l’oubli, la colère, la culpabilité, le repentir et des résultats d’études empiriques psychothérapeutiques sur le pardon. Cette première partie se termine par une réflexion sur la spiritualité de façon à voir dans quelle mesure le pardon devient une dynamique spirituelle. La deuxième partie est consacrée à l’examen de l’hypothèse concernant le sens et la portée du « car ils ne savent pas ce qu’ils font ». Dans un premier temps on fait appel à l’expertise exégétique pour situer l’authenticité et la portée de ce passage. Nous explorons ensuite la pensée philosophique à travers l’histoire pour comprendre le véritable sens du libre-arbitre et son impact sur la conception de la faute. La remise en cause philosophique du libre-arbitre nous ramènera à la thèse socratique selon laquelle « Nul n’est méchant volontairement ». La théorie mimétique de René Girard vient démontrer que les persécuteurs sont fondamentalement inconscients de ce qu’ils font et la théologienne Lytta Basset identifie le fantasme de la connaissance du bien et du mal comme accroissant cette ignorance qui s’ignore. La troisième partie de la thèse intègre les réflexions et découvertes des deux premières parties, et les situent dans un parcours qui va de l’impardonnable à la guérison, tout en les conceptualisant avec une matrice de verticalité et d’horizontalité qui schématise leurs interactions. Nous découvrons que si « car ils ne savent pas ce qu’ils font » fournit la réponse logique à la question Pourquoi pardonner ?, il existe aussi une deuxième voie qui conduit au pardon, l’amour. L’amour est la clé du pardon basé sur le message évangélique, alors que l’empathie est celle de l’approche psychothérapeutique. Enfin, la comparaison entre le « pardon psychothérapeutique » et le « pardon évangélique » nous fait conclure qu’il y a deux modes d’accès majeurs au pardon : la raison et l’amour.

A class of bivariate Erlang distributions and ruin probabilities in multivariate risk models

Nous y introduisons une nouvelle classe de distributions bivariées de type Marshall-Olkin, la distribution Erlang bivariée. La transformée de Laplace, les moments et les densités conditionnelles y sont obtenus. Les applications potentielles en assurance-vie et en finance sont prises en considération. Les estimateurs du maximum de vraisemblance des paramètres sont calculés par l'algorithme Espérance-Maximisation. Ensuite, notre projet de recherche est consacré à l'étude des processus de risque multivariés, qui peuvent être utiles dans l'étude des problèmes de la ruine des compagnies d'assurance avec des classes dépendantes. Nous appliquons les résultats de la théorie des processus de Markov déterministes par morceaux afin d'obtenir les martingales exponentielles, nécessaires pour établir des bornes supérieures calculables pour la probabilité de ruine, dont les expressions sont intraitables.

Quadratic M-Estimators for ARCH-Type Processes

This paper addresses the issue of estimating semiparametric time series models specified by their conditional mean and conditional variance. We stress the importance of using joint restrictions on the mean and variance. This leads us to take into account the covariance between the mean and the variance and the variance of the variance, that is, the skewness and kurtosis. We establish the direct links between the usual parametric estimation methods, namely, the QMLE, the GMM and the M-estimation. The ususal univariate QMLE is, under non-normality, less efficient than the optimal GMM estimator. However, the bivariate QMLE based on the dependent variable and its square is as efficient as the optimal GMM one. A Monte Carlo analysis confirms the relevance of our approach, in particular, the importance of skewness.

Conditional Expected Utility

Let 'epsilon' be a class of event. Conditionally Expected Utility decision makers are decision makers whose conditional preferences ≿E, E є 'epsilon', satisfy the axioms of Subjective Expected Utility theory (SEU). We extend the notion of unconditional preference that is conditionally EU to unconditional preferences that are not necessarily SEU. We give a representation theorem for a class of such preferences, and show that they are Invariant Bi-separable in the sense of Ghirardato et al.[7]. Then, we consider the special case where the unconditional preference is itself SEU, and compare our results with those of Fishburn [6].

Melanosomal targeting sequences from gp100 are essential for MHC class II-restricted endogenous epitope presentation and mobilization to endosomal compartments

CD4+ T lymphocytes play an important role in CD8+ T cell-mediated responses against tumors. Considering that about 20% of melanomas express major histocompatibility complex (MHC) class II, it is plausible that concomitant antigenic presentation by MHC class I and class II complexes shapes positive (helper T cells) or negative (regulatory T cells) anti-tumor responses. Interestingly, gp100, a melanoma antigen, can be presented by both MHC class I and class II when expressed endogenously, suggesting that it can reach endosomal/MHC class II compartments (MIIC). Here, we demonstrated that the gp100 putative amino-terminal signal sequence and the last 70 residues in carboxy-terminus, are essential for MIIC localization and MHC class II presentation. Confocal microscopy analyses confirmed that gp100 was localized in LAMP-1+ endosomal/MIIC. Gp100-targeting sequences were characterized by deleting different sections in the carboxy-terminus (residues 590 to 661). Transfection in 293T cells, expressing MHC class I and class II molecules, revealed that specific deletions in carboxy-terminus resulted in decreased MHC class II presentation, without effects on MHC class I presentation, suggesting a role in MIIC trafficking for these deleted sections. Then, we used these gp100-targeting sequences to mobilize the green fluorescent protein (GFP) to endosomal compartments, and to allow MHC class II and class I presentation of minimal endogenous epitopes. Thus, we concluded that these specific sequences are MIIC targeting motifs. Consequently, these sequences could be included in expression cassettes for endogenously expressed tumor or viral antigens to promote MHC class II and class I presentation and optimize in vivo T cell responses, or as an in vitro tool for characterization of new MHC class II epitopes.

Markovian Processes, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes.

In this paper, we develop finite-sample inference procedures for stationary and nonstationary autoregressive (AR) models. The method is based on special properties of Markov processes and a split-sample technique. The results on Markovian processes (intercalary independence and truncation) only require the existence of conditional densities. They are proved for possibly nonstationary and/or non-Gaussian multivariate Markov processes. In the context of a linear regression model with AR(1) errors, we show how these results can be used to simplify the distributional properties of the model by conditioning a subset of the data on the remaining observations. This transformation leads to a new model which has the form of a two-sided autoregression to which standard classical linear regression inference techniques can be applied. We show how to derive tests and confidence sets for the mean and/or autoregressive parameters of the model. We also develop a test on the order of an autoregression. We show that a combination of subsample-based inferences can improve the performance of the procedure. An application to U.S. domestic investment data illustrates the method.

Simulation-Based Finite-Sample Tests for Heteroskedasticity and ARCH Effects.

A wide range of tests for heteroskedasticity have been proposed in the econometric and statistics literature. Although a few exact homoskedasticity tests are available, the commonly employed procedures are quite generally based on asymptotic approximations which may not provide good size control in finite samples. There has been a number of recent studies that seek to improve the reliability of common heteroskedasticity tests using Edgeworth, Bartlett, jackknife and bootstrap methods. Yet the latter remain approximate. In this paper, we describe a solution to the problem of controlling the size of homoskedasticity tests in linear regression contexts. We study procedures based on the standard test statistics [e.g., the Goldfeld-Quandt, Glejser, Bartlett, Cochran, Hartley, Breusch-Pagan-Godfrey, White and Szroeter criteria] as well as tests for autoregressive conditional heteroskedasticity (ARCH-type models). We also suggest several extensions of the existing procedures (sup-type of combined test statistics) to allow for unknown breakpoints in the error variance. We exploit the technique of Monte Carlo tests to obtain provably exact p-values, for both the standard and the new tests suggested. We show that the MC test procedure conveniently solves the intractable null distribution problem, in particular those raised by the sup-type and combined test statistics as well as (when relevant) unidentified nuisance parameter problems under the null hypothesis. The method proposed works in exactly the same way with both Gaussian and non-Gaussian disturbance distributions [such as heavy-tailed or stable distributions]. The performance of the procedures is examined by simulation. The Monte Carlo experiments conducted focus on : (1) ARCH, GARCH, and ARCH-in-mean alternatives; (2) the case where the variance increases monotonically with : (i) one exogenous variable, and (ii) the mean of the dependent variable; (3) grouped heteroskedasticity; (4) breaks in variance at unknown points. We find that the proposed tests achieve perfect size control and have good power.

Tests of Conditional Asset Pricing Models in the Brazilian Stock Market

In this paper, we test a version of the conditional CAPM with respect to a local market portfolio, proxied by the Brazilian stock index during the 1976-1992 period. We also test a conditional APT model by using the difference between the 30-day rate (Cdb) and the overnight rate as a second factor in addition to the market portfolio in order to capture the large inflation risk present during this period. The conditional CAPM and APT models are estimated by the Generalized Method of Moments (GMM) and tested on a set of size portfolios created from a total of 25 securities exchanged on the Brazilian markets. The inclusion of this second factor proves to be crucial for the appropriate pricing of the portfolios.

Tests of Conditional Asset Pricing Models in the Brazilian Stock Market

In this paper, we test a version of the conditional CAPM with respect to a local market portfolio, proxied by the Brazilian stock index during the 1976-1992 period. We also test a conditional APT model by using the difference between the 30-day rate (Cdb) and the overnight rate as a second factor in addition to the market portfolio in order to capture the large inflation risk present during this period. the conditional CAPM and APT models are estimated by the Generalized Method of Moments (GMM) and tested on a set of size portfolios created from a total of 25 securities exchanged on the Brazilian markets. the inclusion of this second factor proves to be crucial for the appropriate pricing of the portfolios.

Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form

Conditional heteroskedasticity is an important feature of many macroeconomic and financial time series. Standard residual-based bootstrap procedures for dynamic regression models treat the regression error as i.i.d. These procedures are invalid in the presence of conditional heteroskedasticity. We establish the asymptotic validity of three easy-to-implement alternative bootstrap proposals for stationary autoregressive processes with m.d.s. errors subject to possible conditional heteroskedasticity of unknown form. These proposals are the fixed-design wild bootstrap, the recursive-design wild bootstrap and the pairwise bootstrap. In a simulation study all three procedures tend to be more accurate in small samples than the conventional large-sample approximation based on robust standard errors. In contrast, standard residual-based bootstrap methods for models with i.i.d. errors may be very inaccurate if the i.i.d. assumption is violated. We conclude that in many empirical applications the proposed robust bootstrap procedures should routinely replace conventional bootstrap procedures for autoregressions based on the i.i.d. error assumption.

Identification, Weak Instruments and Statistical Inference in Econometrics

We discuss statistical inference problems associated with identification and testability in econometrics, and we emphasize the common nature of the two issues. After reviewing the relevant statistical notions, we consider in turn inference in nonparametric models and recent developments on weakly identified models (or weak instruments). We point out that many hypotheses, for which test procedures are commonly proposed, are not testable at all, while some frequently used econometric methods are fundamentally inappropriate for the models considered. Such situations lead to ill-defined statistical problems and are often associated with a misguided use of asymptotic distributional results. Concerning nonparametric hypotheses, we discuss three basic problems for which such difficulties occur: (1) testing a mean (or a moment) under (too) weak distributional assumptions; (2) inference under heteroskedasticity of unknown form; (3) inference in dynamic models with an unlimited number of parameters. Concerning weakly identified models, we stress that valid inference should be based on proper pivotal functions —a condition not satisfied by standard Wald-type methods based on standard errors — and we discuss recent developments in this field, mainly from the viewpoint of building valid tests and confidence sets. The techniques discussed include alternative proposed statistics, bounds, projection, split-sampling, conditioning, Monte Carlo tests. The possibility of deriving a finite-sample distributional theory, robustness to the presence of weak instruments, and robustness to the specification of a model for endogenous explanatory variables are stressed as important criteria assessing alternative procedures.

Social Norms and Rationality of Choice

Ever since Sen (1993) criticized the notion of internal consistency of choice, there exists a wide spread perception that the standard rationalizability approach to the theory of choice has difficulties coping with the existence of external social norms. This paper introduces a concept of norm-conditional rationalizability and shows that external social norms can be accommodated so as to be compatible with norm-conditional rationalizability by means of suitably modified revealed preference axioms in the theory of rational choice on general domains à la Richter (1966;1971) and Hansson (1968)

Formation and differentiation of multiple mesenchymal lineages during lung development is regulated by {beta}-catenin signaling.

BACKGROUND: The role of ss-catenin signaling in mesodermal lineage formation and differentiation has been elusive. METHODOLOGY: To define the role of ss-catenin signaling in these processes, we used a Dermo1(Twist2)(Cre/+) line to target a floxed beta-catenin allele, throughout the embryonic mesenchyme. Strikingly, the Dermo1(Cre/+); beta-catenin(f/-) conditional Knock Out embryos largely phenocopy Pitx1(-/-)/Pitx2(-/-) double knockout embryos, suggesting that ss-catenin signaling in the mesenchyme depends mostly on the PITX family of transcription factors. We have dissected this relationship further in the developing lungs and find that mesenchymal deletion of beta-catenin differentially affects two major mesenchymal lineages. The amplification but not differentiation of Fgf10-expressing parabronchial smooth muscle progenitor cells is drastically reduced. In the angioblast-endothelial lineage, however, only differentiation into mature endothelial cells is impaired. CONCLUSION: Taken together these findings reveal a hierarchy of gene activity involving ss-catenin and PITX, as important regulators of mesenchymal cell proliferation and differentiation.