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Asymptotic Distribution of a Simple Linear Estimator for VARMA Models in Echelon Form

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Author Info
DUFOUR, Jean-Marie
TAREK, Jouini

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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.

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Publisher Info
Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2005-09.

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Length: 37 pages
Date of creation: 2005
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Handle: RePEc:mtl:montde:2005-09

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Related research
Keywords: Time series ; VARMA ; stationary ; invertible ; echelon form ; estimation ; asymotic normality ; bootstra; Hannan-Rissanen;

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Find related papers by JEL classification:
C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Boudjellaba, H. & Dufour, J.M. & Roy, R., 1992. "Simplified Conditions for Non-Causality Between Vectors in Multivariate Arma Models," Cahiers de recherche 9236, Universite de Montreal, Departement de sciences economiques.
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  2. Lutkepohl, Helmut & Claessen, Holger, 1997. "Analysis of cointegrated VARMA processes," Journal of Econometrics, Elsevier, vol. 80(2), pages 223-239, October. [Downloadable!] (restricted)
  3. Hannan, E J, 1976. "The Identification and Parameterization of ARMAX and State Space Forms," Econometrica, Econometric Society, vol. 44(4), pages 713-23, July. [Downloadable!] (restricted)
  4. D. Poskitt & H. L"Utkepohl, . "Consistent Specification of Cointegrated Autoregressive Moving-Average Systems," Sonderforschungsbereich 373 1995-54, Humboldt Universitaet Berlin.
  5. 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.
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  6. 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. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. 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.
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  9. 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.
  10. 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. [Downloadable!] (restricted)
  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 & Poskitt, D S, 1996. "Specification of Echelon-Form VARMA Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 69-79, January.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
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