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Asymptotic distribution of a simple linear estimator for VARMA models in echelon form

  • Jean-Marie Dufour
  • Tarek Jouini

In this paper, we study the asymptotic distribution of a simple two-stage (Hannan-Rissanen-type) linear estimator for stationary invertible vector autoregressive moving average (VARMA) models in the echelon form representation. General conditions for consistency and asymptotic normality are given. A consistent estimator of the asymptotic covariance matrix of the estimator is also provided, so that tests and confidence intervals can easily be constructed. Dans cet article, nous étudions la distribution asymptotique d'un estimateur linéaire simple en deux étapes (de type Hannan-Rissanen) pour un processus vectoriel autorégressif-moyenne-mobile (VARMA) stationnaire et inversible, formulé sous la forme échelon. Nous donnons des conditions générales qui assurent la convergence et la normalité asymptotique de l'estimateur. Nous fournissons aussi un estimateur convergent de la matrice de covariance asymptotique de l'estimateur, ce qui permet de construire facilement des tests et des intervalles de confiance.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2005s-06.

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Length: 37 pages
Date of creation: 01 Feb 2005
Date of revision:
Handle: RePEc:cir:cirwor:2005s-06
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  1. D. Poskitt & H. Lütkepohl, 1995. "Consistent Specification of Cointegrated Autoregressive Moving-Average Systems," SFB 373 Discussion Papers 1995,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  2. Koreisha, Sergio G & Pukkila, Tarmo, 1995. "A Comparison between Different Order-Determination Criteria for Identification of ARIMA Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 127-31, January.
  3. Paparoditis, Efstathios, 1996. "Bootstrapping Autoregressive and Moving Average Parameter Estimates of Infinite Order Vector Autoregressive Processes," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 277-296, May.
  4. Boudjellaba, H. & Dufour, J.M. & Roy, R., 1992. "Simplified Conditions for Non-Causality Between Vectors in Multivariate Arma Models," Cahiers de recherche 9236, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. Lutkepohl, Helmut & Claessen, Holger, 1997. "Analysis of cointegrated VARMA processes," Journal of Econometrics, Elsevier, vol. 80(2), pages 223-239, October.
  6. D.S. Poskitt, . "Specification of echelon form VARMA models," Statistic und Oekonometrie 9305, Humboldt Universitaet Berlin.
  7. Boudjellaba, B. & Dufour, J.M. & Roy, R., 1991. "Testing Causality Between Two Vectors in Multivariate Arma Models," Cahiers de recherche 9119, Universite de Montreal, Departement de sciences economiques.
  8. Hannan, E J, 1976. "The Identification and Parameterization of ARMAX and State Space Forms," Econometrica, Econometric Society, vol. 44(4), pages 713-23, July.
  9. Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
  10. Holger Bartel & Helmut Lutkepohl, 1998. "Estimating the Kronecker indices of cointegrated echelon-form VARMA models," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages C76-C99.
  11. Deistler, M. & Hannan, E. J., 1981. "Some properties of the parameterization of ARMA systems with unknown order," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 474-484, December.
  12. Tsay, Ruey S, 1989. "Parsimonious Parameterization of Vector Autoregressive Moving Average Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 327-41, July.
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