Efficient Estimation of Conditional Asset Pricing Models

A semiparametric efficient estimation procedure is developed for the parameters of multivariate GARCH-in-mean models when the disturbances have a distribution that is assumed to be elliptically symmetric but is otherwise unrestricted. Under high level restrictions, the resulting estimator achieves the asymptotic semiparametric efficiency bound. The elliptical symmetry assumption allows us to avert the curse of dimensionality problem that would otherwise arise in estimating the unknown error distribution. This framework is suitable for the estimation and testing of conditional asset pricing models such as the conditional CAPM, and we apply our estimator in an empirical study of stock prices, with Monte Carlo simulation results also being reported. Nous développons un nouvel estimateur pour les paramètres d'un modèle de GARCH en moyenne (" GARCH-M ") avec plusieurs variables. L'estimateur a l'efficacité semiparamétrique quand les erreurs suivent une loi de probabilité qui est elliptiquement symétrique mais n'aucune autre restriction. Sous les hypothèses de haut niveau, notre estimateur obtient la limite d'efficacité semiparamétrique. L'hypothèse de la symétrie elliptique nous permet d'éviter le problème d'estimer non-paramétriquement une fonction de haut dimension, parce qu'on peut écrire la densité d'un loi elliptique comme un fonction d'une transformation unidimensionnelle de la variable aléatoire multidimensionnelle. Ce cadre est approprié pour analyser des modèles conditionnels des prix des actifs financiers, comme le CAPM conditionnel. Nous appliquons notre méthodologie à l'étude des prix des actions, et nous rendons compte des résultats d'une étude simulation "Monte-Carlo".Capital asset pricing model, elliptical symmetry, semiparametric efficiency, GARCH.

Testing mean-variance efficiency in CAPM with possibly non-gaussian errors: an exact simulation-based approach

In this paper we propose exact likelihood-based mean-variance efficiency tests of the market portfolio in the context of Capital Asset Pricing Model (CAPM), allowing for a wide class of error distributions which include normality as a special case. These tests are developed in the framework of multivariate linear regressions (MLR). It is well known however that despite their simple statistical structure, standard asymptotically justified MLR-based tests are unreliable. In financial econometrics, exact tests have been proposed for a few specific hypotheses [Jobson and Korkie (Journal of Financial Economics, 1982), MacKinlay (Journal of Financial Economics, 1987), Gibbons, Ross and Shanken (Econometrica, 1989), Zhou (Journal of Finance 1993)] most of which depend on normality. For the gaussian model, our tests correspond to Gibbons, Ross and Shanken's mean-variance efficiency tests. In non-gaussian contexts, we reconsider mean-variance efficiency tests allowing for multivariate Student-t and gaussian mixture errors. Our framework allows to cast more evidence on whether the normality assumption is too restrictive when testing the CAPM. We also propose exact multivariate diagnostic checks (including tests for multivariate GARCH and multivariate generalization of the well known variance ratio tests) and goodness of fit tests as well as a set estimate for the intervening nuisance parameters. Our results [over five-year subperiods] show the following: (i) multivariate normality is rejected in most subperiods, (ii) residual checks reveal no significant departures from the multivariate i.i.d. assumption, and (iii) mean-variance efficiency tests of the market portfolio is not rejected as frequently once it is allowed for the possibility of non-normal errors. -- In diesem Papier schlagen wir exakte likelihood-basierte Tests auf Mittelwert-Varianz- Effizienz im Rahmen des CAPM vor. Dabei wird eine breite Klasse von Verteilungen für den stochastischen Term zugelassen. Normalverteilung ist ein Spezialfall. Die Tests werden im Rahmen von multivariablen linearen Regressionen (MLR) entwickelt. Bekanntlich sind Standardtests, die auf MLR basieren und asymptotisch gerechtfertigt werden, nicht zuverlässig. In der Finanzökonometrie sind exakte Tests für einige wenige Hypothesen vorgeschlagen worden. Die meisten hängen von der Annahme der Normalverteilung ab (Jobson und Korkie (1982), Mac Kinley (1987), Gibbons, Ross und Shanken (1989), Zhou (1993)). Für das gaussianische Modell entsprechen unsere Tests denen von Gibbons, Ross und Shanken. Im nichtgaussianischen Modell betrachten wir Mittelwert-Varianz-Effizienz-Tests, wobei multivariate-Student-t und ?gemischte? Normalverteilungen zugelassen werden. Unser Ansatz gibt mehr Aufschluß darüber, ob die Annahme der Normalverteilung zu restriktiv ist, wenn das CAPM gestestet wird. Wir schlagen auch exakte multivariate Diagnosen (einschließlich Tests für multivariate GARCH-Modelle und multivariate Verallgemeinerungen der bekannten Varianz- Relationen-Tests) sowie Tests auf die Anpassungsgüte und eine Schätzung für die störenden Verschmutzungsparameter vor. Unsere Ergebnisse (für 5-Jahres-Perioden) zeigen das Folgende: (i) multivariate Normalität wird für die meisten Perioden verworfen (ii) die Überprüfung der Residuen zeigt keine signifikante Abweichung von der Annahme einer multivariaten i.i.d. Verteilung (iii), wenn man nichtnormalverteilte Fehler zulässt, werden Mittelwert-Varianz-Effizienz Tests des Marktportfolios seltener verworfen.capital assed pricing model,CAPM,mean-variance efficiency,nonnormality,multivariate linear regression,uniform linear hypothesis,exact test

Semiparametric inference for non-LAN models

This thesis consists of three essays in theory of econometrics and statistics, focusing on the issue of semiparametric efficiency in non-LAN (Locally Asymptotically Normality) models. The first essay starts with a univariate case of the unit root testing problem, of which the limit experiment is of the LABF (Locally Asymptotically Brownian Functional) model. A novel approach is designed for developing the semiparametric power envelope and a family of rank-based tests that are semiparametrically efficient is proposed. The second essay generalizes the approach to all LAQ (Locally Asymptotically Quadratic) models. Moreover, it expands the rank statistics in a unique way from the univariate case to the multivariate case. Using these results, in the third essay, the semiparametric power envelop of all invariant tests for stock return predictability is developed. And subsequently, a new family of tests that are more efficient than the existing ones is proposed

Testing Mean-Variance Efficiency in CAPM with Possibly Non-Gaussian Errors: an Exact Simulation-Based Approach

In this paper we propose exact likelihood-based mean-variance efficiency tests of the market portfolio in the context of Capital Asset Pricing Model (CAPM), allowing for a wide class of error distributions which include normality as a special case. These tests are developed in the framework of multivariate linear regressions (MLR). It is well known however that despite their simple statistical structure, standard asymptotically justified MLR-based tests are unreliable. In financial econometrics, exact tests have been proposed for a few specific hypotheses [Jobson and Korkie (Journal of Financial Economics, 1982), MacKinlay (Journal of Financial Economics, 1987), Gibbons, Ross and Shanken (Econometrica, 1989), Zhou (Journal of Finance 1993)], most of which depend on normality. For the gaussian model, our tests correspond to Gibbons, Ross and Shanken's mean-variance efficiency tests. In non-gaussian contexts, we reconsider mean-variance efficiency tests allowing for multivariate Student-t and gaussian mixture errors. Our framework allows to cast more evidence on whether the normality assumption is too restrictive when testing the CAPM. We also propose exact multivariate diagnostic checks (including tests for multivariate GARCH and multivariate generalization of the well known variance ratio tests) and goodness of fit tests as well as a set estimate for the intervening nuisance parameters. Our results [over five-year subperiods] show the following: (i) multivariate normality is rejected in most subperiods, (ii) residual checks reveal no significant departures from the multivariate i.i.d. assumption, and (iii) mean-variance efficiency tests of the market portfolio is not rejected as frequently once it is allowed for the possibility of non-normal errors. Dans cet article, nous proposons des tests exacts, basés sur la vraisemblance de l'efficience du portefeuille de marché dans l'espace moyenne-variance. Ces tests, utilisés ici dans le contexte du modèle du CAPM (Capital Asset Pricing Model), permettent de considérer diverses classes de distributions incluant la loi normale. Les tests sont développés dans le cadre de modèles de régression linéaires multivariés (RLM). Il est, par ailleurs, bien établi que, malgré leur structure simple, les écart-types et tests usuels asymptotiques de ces modèles ne sont pas fiables. En économétrie financière, des tests en échantillons finis ont été proposés pour quelques hypothèses spécifiques, lesquels dépendent pour la plupart de l'hypothèse de normalité [Jobson et Korkie (Journal of Financial Economics, 1982), MacKinlay (Journal of Financial Economics, 1987), Gibbons, Ross et Shanken (Econometrica, 1989), Zhou (Journal of Finance 1993)]. Dans le contexte gaussien, nos tests d'efficience correspondent à ceux de Gibbons, Ross et Shanken. Dans un contexte non-gaussien, nous reconsidérons l'efficience moyenne-variance du portefeuille de marché en permettant des distributions multivariées de Student et des « mélanges de lois normales ». Notre démarche nous permet d'évaluer si l'hypothèse de normalité est trop restrictive lorsque l'on teste le CAPM. Nous proposons aussi des tests diagnostiques multivariés (incluant des tests pour les effets GARCH multivariés et une généralisation multivariée des tests de ratio de variance), des tests de spécification ainsi qu'un estimateur ensembliste pour les paramètres de nuisance pertinents. Nos résultats montrent que i) l'hypothèse de normalité multivariée est rejetée sur la plupart des sous-périodes, ii) les tests diagnostiques appliqués aux résidus de nos estimations ne montrent pas de différences importantes par rapport à l'hypothèse des erreurs i.i.d. multivariées, et iii) les tests d'efficience du portefeuille de marché dans l'espace moyenne-variance ne rejettent aussi fréquemment l'hypothèse d'efficience lorsqu'on s'autorise à considérer des lois non normales sur les erreurs.Capital asset pricing model, CAPM, mean-variance efficiency, non-normality, multivariate linear regression, uniform linear hypothesis, exact test, Monte Carlo test, bootstrap, nuisance parameters, specification test, diagnostics, GARCH, variance ratio test, Modèle d'évaluation d'actifs financiers, CAPM, efficience de portefeuille, non-normalité, modèle de régression multivarié, hypothèse linéaire uniforme, test exact, test de Monte Carlo, bootstrap, paramètres de nuisance, test de spécification, tests diagnostiques, GARCH, test de ratio des variances

Determinacy, indeterminacy and dynamic misspecification in linear rational expectations models

This paper proposes a testing strategy for the null hypothesis that a multivariate linear rational expectations (LRE) model has a unique stable solution (determinacy) against the alternative of multiple stable solutions (indeterminacy). Under a proper set of identification restrictions, determinacy is investigated by a misspecification-type approach in which the result of the overidentifying restrictions test obtained from the estimation of the LRE model through a version of generalized method of moments is combined with the result of a likelihood-based test for the cross-equation restrictions that the LRE places on its finite order reduced form under determinacy. This approach (i) circumvents the nonstandard inferential problem that a purely likelihood-based approach implies because of the presence of nuisance parameters that appear under the alternative but not under the null, (ii) does not involve inequality parametric restrictions and nonstandard asymptotic distributions, and (iii) gives rise to a joint test which is consistent against indeterminacy almost everywhere in the space of nuisance parameters, i.e. except for a point of zero measure which gives rise to minimum state variable solutions, and is also consistent against the dynamic misspecification of the LRE model. Monte Carlo simulations show that the testing strategy delivers reasonable size coverage and power in finite samples. An empirical illustration focuses on the determinacy/indeterminacy of a New Keynesian monetary business cycle model for the US.Determinatezza, Indeterminatezza, Massima verosimiglianza, Metodo generalizzato dei momenti, Modello lineare con aspettative, Identificazione, Variabili Strumentali, VAR,VARMA Determinacy, Generalized method of moments, Indeterminacy, LRE model, Identification, Instrumental Variables, Maximum Likelihood, VAR, VARMA

SPECIAL TOPICS FOR RECOMBINANT INBRED INTERCROSS DATA: MODEL IDENTIFIABILITY, HYPOTHESIS TESTING AND COMPOSITIONAL METHODS

This dissertation addresses statistical issues in studies comprised of mice derived from the Collaborative Cross (CC) project (Churchill, 2004). Briefly, the CC is a community effort to derive novel inbred mouse strains from a genetically diverse set of eight inbred founder strains. Specifically, our interest has been in studying the effects of the parental strains on phenotypes of interest among recombinant intercrosses (RIX) derived from those strains (i.e., pairings of them). The topics explored here involve properly accounting for the relatedness of the samples created in these breeding schemes. When polygenic effects are conceptualized as uncorrelated parental strain effects, a study design can be framed as a sparse diallel, or more generally “dyadic” data. In Chapter 2, we consider such designs, incorporating multiple variance components. This raises often-ignored identifiability issues, the most significant of which is the possibility of performing inference on an unidentifiable model parameter - a mistake which is actually not difficult to make in this setting. We develop a formal an easy-to-apply condition to check for model identifiability in this setting. In Chapter 3, our focus is on hypothesis testing in these same sparse diallels. Because variance parameters are boundary parameters, inference is considered a “non-standard’’ problem, with asymptotic reference distributions being (sometimes complicated) mixtures of chi-squared random variables, when they are available at all. This is further complicated by the fact that when the dependent variable is non-normal, the data structure in this complicated setting does not allow for likelihood-based methods, as integration over the random effects becomes computationally infeasible. We adapt an existing score statistic developed by Lin (1997), which is designed for models fit by penalized quasi-likelihood. In Chapter 4, we directly model the relatedness of the strains by replacing the diallel-like random design matrices with ones derived from similarity matrices. Further, we incorporate the contributions of the eight founder strains as fixed effects, and propose a framework incorporating the statistic employed in Chapter 3 to jointly test the fixed and random genetic effects. We show that the benefits of this approach include improved power and more meaningful interpretations of parameter estimates.Doctor of Philosoph