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

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  • Jean-Marie Dufour

    ()

  • Tarek Jouini

Abstract

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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Bibliographic Info

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

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Date of creation: 01 Feb 2005
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Handle: RePEc:cir:cirwor:2005s-06

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Keywords: time series; VARMA; stationary; invertible; echelon form; estimation; asymptotic normality; bootstrap; Hannan-Rissanen; séries chronologiques; VARMA; stationnaire; inversible; forme échelon; estimation; normalité asymptotique; bootstrap; Hannan-Rissanen;

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  1. D.S. Poskitt, . "Specification of echelon form VARMA models," Statistic und Oekonometrie 9305, Humboldt Universitaet Berlin.
  2. Boudjellaba, Hafida & Dufour, Jean-Marie & Roy, Roch, 1994. "Simplified conditions for noncausality between vectors in multivariate ARMA models," Journal of Econometrics, Elsevier, vol. 63(1), pages 271-287, July.
  3. 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.
  4. 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.
  5. 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.
  6. Bartel, Holger & Lütkepohl, Helmut, 1997. "Estimating the Kronecker indices of cointegrated echelon form VARMA models," SFB 373 Discussion Papers 1997,2, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  7. Hannan, E J, 1976. "The Identification and Parameterization of ARMAX and State Space Forms," Econometrica, Econometric Society, vol. 44(4), pages 713-23, July.
  8. 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.
  9. repec:wop:humbsf:1995-54 is not listed on IDEAS
  10. 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.
  11. 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.
  12. Lutkepohl, Helmut & Claessen, Holger, 1997. "Analysis of cointegrated VARMA processes," Journal of Econometrics, Elsevier, vol. 80(2), pages 223-239, October.
  13. 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.
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Cited by:
  1. Dufour, Jean-Marie & Jouini, Tarek, 2014. "Asymptotic distributions for quasi-efficient estimators in echelon VARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 69-86.
  2. Jean-Marie Dufour & Abderrahim Taamouti, 2008. "Short and long run causality measures: theory and inference," Economics Working Papers we083720, Universidad Carlos III, Departamento de Economía.
  3. Jean-Marie Dufour & Tarek Jouini, 2011. "Asymptotic Distributions for Some Quasi-Efficient Estimators in Echelon VARMA Models," CIRANO Working Papers 2011s-25, CIRANO.
  4. Melard, Guy & Roy, Roch & Saidi, Abdessamad, 2006. "Exact maximum likelihood estimation of structured or unit root multivariate time series models," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 2958-2986, July.

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