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Finite-Sample Diagnostics for Multivariate Regressions with Applications to Linear Asset Pricing Models

DUFOUR, Jean-Marie; KHALAF, Lynda; BEAULIEU, Marie-Claude
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Artigo de Revista Científica Formato: 219916 bytes; application/pdf
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In this paper, we propose several finite-sample specification tests for multivariate linear regressions (MLR) with applications to asset pricing models. We focus on departures from the assumption of i.i.d. errors assumption, at univariate and multivariate levels, with Gaussian and non-Gaussian (including Student t) errors. The univariate tests studied extend existing exact procedures by allowing for unspecified parameters in the error distributions (e.g., the degrees of freedom in the case of the Student t distribution). The multivariate tests are based on properly standardized multivariate residuals to ensure invariance to MLR coefficients and error covariances. We consider tests for serial correlation, tests for multivariate GARCH and sign-type tests against general dependencies and asymmetries. The procedures proposed provide exact versions of those applied in Shanken (1990) which consist in combining univariate specification tests. Specifically, we combine tests across equations using the MC test procedure to avoid Bonferroni-type bounds. Since non-Gaussian based tests are not pivotal, we apply the “maximized MC” (MMC) test method [Dufour (2002)], where the MC p-value for the tested hypothesis (which depends on nuisance parameters) is maximized (with respect to these nuisance parameters) to control the test’s significance level. The tests proposed are applied to an asset pricing model with observable risk-free rates...

Exact Skewness-Kurtosis Tests for Multivariate Normality and Goodness-of-fit in Multivariate Regressions with Application to Asset Pricing Models

DUFOUR, Jean-Marie; KHALAF, Lynda; BEAULIEU, Marie-Claude
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Artigo de Revista Científica Formato: 225374 bytes; application/pdf
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We study the problem of testing the error distribution in a multivariate linear regression (MLR) model. The tests are functions of appropriately standardized multivariate least squares residuals whose distribution is invariant to the unknown cross-equation error covariance matrix. Empirical multivariate skewness and kurtosis criteria are then compared to simulation-based estimate of their expected value under the hypothesized distribution. Special cases considered include testing multivariate normal, Student t; normal mixtures and stable error models. In the Gaussian case, finite-sample versions of the standard multivariate skewness and kurtosis tests are derived. To do this, we exploit simple, double and multi-stage Monte Carlo test methods. For non-Gaussian distribution families involving nuisance parameters, confidence sets are derived for the the nuisance parameters and the error distribution. The procedures considered are evaluated in a small simulation experi-ment. Finally, the tests are applied to an asset pricing model with observable risk-free rates, using monthly returns on New York Stock Exchange (NYSE) portfolios over five-year subperiods from 1926-1995.; Dans cet article, nous proposons des tests sur la forme de la distribution des erreurs dans un modèle de régression linéaire multivarié (RLM). Les tests que nous développons sont fonction des résidus obtenus par moindres carrés multivariés...

Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions

BEAULIEU, Marie-Claude; DUFOUR, Jean-Marie; KHALAF, Lynda
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Artigo de Revista Científica Formato: 204421 bytes; application/pdf
Português
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In this paper, we propose exact inference procedures for asset pricing models that can be formulated in the framework of a multivariate linear regression (CAPM), allowing for stable error distributions. The normality assumption on the distribution of stock returns is usually rejected in empirical studies, due to excess kurtosis and asymmetry. To model such data, we propose a comprehensive statistical approach which allows for alternative - possibly asymmetric - heavy tailed distributions without the use of large-sample approximations. The methods suggested are based on Monte Carlo test techniques. Goodness-of-fit tests are formally incorporated to ensure that the error distributions considered are empirically sustainable, from which exact confidence sets for the unknown tail area and asymmetry parameters of the stable error distribution are derived. Tests for the efficiency of the market portfolio (zero intercepts) which explicitly allow for the presence of (unknown) nuisance parameter in the stable error distribution are derived. The methods proposed are applied to monthly returns on 12 portfolios of the New York Stock Exchange over the period 1926-1995 (5 year subperiods). We find that stable possibly skewed distributions provide statistically significant improvement in goodness-of-fit and lead to fewer rejections of the efficiency hypothesis.