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Méthodes d’inférence exactes pour un modèle de régression avec erreurs AR(2) gaussiennes

Listed author(s):
  • Dufour, Jean-Marie

    (Université de Montréal)

  • Neifar, Malika

    (Institut Supérieur de Gestion de Sousse)

In this paper, we consider a linear regression model with Gaussian autoregressive errors of order p = 2, which may be nonstationary. Exact inference methods (tests and confidence regions) are developed for the autoregressive parameters and the regression coefficients. We generalize the method proposed in Dufour (1990) for linear regression models with autoregressive errors of order p = 1. The proposed approach consists in three stages. First, we build an exact confidence set for the complete vector of the autoregressive coefficients (φ). This region is obtained by inverting independence tests for model errors after the model has been transformed to get independent errors under the null hypothesis. The independence tests are based on combining tests for the presence of autocorrelation at lags one and two. Exploiting the duality between tests and confidence sets, an exact confidence set is then built by finding the set of autoregressive parameter values which are not rejected (test inversion). Second, using this confidence set for φ, simultaneous confidence sets for the autoregressive parameters and regression coefficients are obtained. Finally, marginal confidence intervals for the regression coefficients are derived using a projection approach. We also propose generalized bounds tests for the regression parameters. These methods are applied to time series models of the U.S. money stock (M2) and GNP deflator. Ce texte propose des méthodes d’inférence exactes (tests et régions de confiance) sur des modèles de régression linéaires avec erreurs autocorrélées suivant un processus autorégressif d’ordre deux [AR(2)], qui peut être non stationnaire. L’approche proposée est une généralisation de celle décrite dans Dufour (1990) pour un modèle de régression avec erreurs AR(1) et comporte trois étapes. Premièrement, on construit une région de confiance exacte pour le vecteur des coefficients du processus autorégressif (φ). Cette région est obtenue par inversion de tests d’indépendance des erreurs sur une forme transformée du modèle contre des alternatives de dépendance aux délais un et deux. Deuxièmement, en exploitant la dualité entre tests et régions de confiance (inversion de tests), on détermine une région de confiance conjointe pour le vecteur φ et un vecteur d’intérêt γ de combinaisons linéaires des coefficients de régression du modèle. Troisièmement, par une méthode de projection, on obtient des intervalles de confiance « marginaux » ainsi que des tests à bornes exacts pour les composantes de γ. Ces méthodes sont appliquées à des modèles du stock de monnaie (M2) et du niveau des prix (indice implicite du PNB) américains.

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Article provided by Société Canadienne de Science Economique in its journal L'Actualité économique.

Volume (Year): 80 (2004)
Issue (Month): 4 (Décembre)
Pages: 593-618

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Handle: RePEc:ris:actuec:v:80:y:2004:i:4:p:593-618
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