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Méthodes d’inférence exactes pour des processus autorégressifs : une approche fondée sur des tests induits

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  • Dufour, Jean-Marie

    (Chaire de Recherche du Canada en économétrie)

  • Neifar, Malika

    (Institut Supérieur de Gestion de Sousse)

Abstract

In this paper, we consider a gaussian autoregressive model of order p, which may be nonstationary and includes a drift term (where p ≥ 1). Exact inference methods are developed for the autoregressive coefficients. We consider first the problem of testing any hypothesis that fixes the vector of the autoregressive coefficients. This is done by first transforming the observations in a way that eliminates serial dependence under the null hypothesis, and then testing whether autocorrelation remains present in the transformed data. The latter task is accomplished by combining several independence tests against serial correlation at lags 1, 2, ..., p. A valid confidence region for the autoregressive coefficients may then be obtained by inverting the latter tests. We show that this confidence region can be built numerically on solving 2p polynomials of order 2, where in each case p – 1 autoregressive coefficients are fixed, and then using a grid search over the latter p – 1 coefficients. For inference on individual coefficients or more general transformations of the autoregressive coefficients, we propose the use of a projection approach. The proposed method is applied to a time series model of real G.D.P. in Tunisia. Dans ce texte, nous considérons un modèle autorégressif d’ordre p (où p ≥ 1) gaussien, possiblement non stationnaire, avec un terme constant (tendance). Nous développons des méthodes d’inférence exactes pour les coefficients de ce modèle. Nous proposons une méthode qui permet de tester n’importe quelle hypothèse qui fixe le vecteur complet des coefficients autorégressifs du modèle puis, en « inversant » ces tests, de construire une région de confiance conjointe pour les coefficients du vecteur. Chaque hypothèse est testée en transformant d’abord les observations de façon à faire disparaître toute autocorrélation sous l’hypothèse nulle puis en testant si les observations transformées sont indépendantes. Pour ce faire, nous combinons plusieurs tests d’autocorrélation conçus pour détecter la dépendance aux délais 1, 2, ..., p. La méthode proposée permet de construire de façon simple les régions de confiance en résolvant 2p polynômes de second degré pour chaque coefficient (après un balayage des p – 1 coefficients restants du modèle et pour chaque configuration de ces p – 1 coefficients). Pour faire de l’inférence sur les coefficients individuels du modèle ou sur des transformations plus générales des coefficients autorégressifs, nous proposons d’utiliser une technique de projection. Nous appliquons la méthode développée à un modèle du P.I.B. réel tunisien.

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Bibliographic Info

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

Volume (Year): 78 (2002)
Issue (Month): 1 (Mars)
Pages: 19-40

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Handle: RePEc:ris:actuec:v:78:y:2002:i:1:p:19-40

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  1. Farebrother, R W, 1974. "The Stability of Laidler's Simple Monetary Model," The Manchester School of Economic & Social Studies, University of Manchester, vol. 42(3), pages 277-78, September.
  2. Wallis, Kenneth F, 1972. "Testing for Fourth Order Autocorrelation in Qtrly Regression Equations," Econometrica, Econometric Society, vol. 40(4), pages 617-36, July.
  3. Farebrother, R W, 1974. "Simplified Samuelson Conditions for Quintic Equations," The Manchester School of Economic & Social Studies, University of Manchester, vol. 42(3), pages 279-82, September.
  4. Farebrother, R W, 1973. "Simplified Samuelson Conditions for Cubic and Quartic Equations," The Manchester School of Economic & Social Studies, University of Manchester, vol. 41(4), pages 396-400, December.
  5. Dufour, J.-M., 1986. "Exact tests and confidence sets in linear regressions with autocorrelated errors," CORE Discussion Papers 1986037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  7. Blough, Stephen R, 1992. "The Relationship between Power and Level for Generic Unit Root Tests in Finite Samples," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(3), pages 295-308, July-Sept.
  8. Savin, N.E., 1984. "Multiple hypothesis testing," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 14, pages 827-879 Elsevier.
  9. Farebrother, R W, 1974. "Recursive Relations for the Samuelson Transformation Coefficients," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(3), pages 805-07, October.
  10. Farebrother, R W, 1976. "A Note on the Local Stability of the General First Order Difference Equation," The Manchester School of Economic & Social Studies, University of Manchester, vol. 44(2), pages 182-84, June.
  11. Francis X. Diebold & Marc Nerlove, 1988. "Unit roots in economic time series: a selective survey," Finance and Economics Discussion Series 49, Board of Governors of the Federal Reserve System (U.S.).
  12. Jean-Marie Dufour & Jan F. Kiviet, 1998. "Exact Inference Methods for First-Order Autoregressive Distributed Lag Models," Econometrica, Econometric Society, vol. 66(1), pages 79-104, January.
  13. Cochrane, John H., 1991. "A critique of the application of unit root tests," Journal of Economic Dynamics and Control, Elsevier, vol. 15(2), pages 275-284, April.
  14. Farebrother, Richard W, 1987. "Independent Conditions for the Stability of a Dynamic Linear Model," The Manchester School of Economic & Social Studies, University of Manchester, vol. 55(3), pages 305-09, September.
  15. Dufour, Jean-Marie & Jasiak, Joann, 2001. "Finite Sample Limited Information Inference Methods for Structural Equations and Models with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(3), pages 815-43, August.
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