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

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  • DUFOUR, Jean-Marie
  • 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.

Suggested Citation

  • DUFOUR, Jean-Marie & TAREK, Jouini, 2005. "Asymptotic Distribution of a Simple Linear Estimator for VARMA Models in Echelon Form," Cahiers de recherche 2005-09, Universite de Montreal, Departement de sciences economiques.
  • Handle: RePEc:mtl:montde:2005-09
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    1. 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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    7. Holger Bartel & Helmut Lutkepohl, 1998. "Estimating the Kronecker indices of cointegrated echelon-form VARMA models," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages 76-99.
    8. 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.
    9. 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.
    10. B. L. Shea, 1989. "The Exact Likelihood of a Vector Autoregressive Moving Average Model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 38(1), pages 161-184, March.
    11. 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.
    12. Poskitt, D. & Lütkepohl, H., 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.
    13. Hannan, E J, 1976. "The Identification and Parameterization of ARMAX and State Space Forms," Econometrica, Econometric Society, vol. 44(4), pages 713-723, July.
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    15. José Alberto Mauricio, 2002. "An algorithm for the exact likelihood of a stationary vector autoregressive‐moving average model," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(4), pages 473-486, July.
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    Cited by:

    1. 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.
    2. Dias, Gustavo Fruet, 2017. "The time-varying GARCH-in-mean model," Economics Letters, Elsevier, vol. 157(C), pages 129-132.
    3. Dias, Gustavo Fruet & Kapetanios, George, 2018. "Estimation and forecasting in vector autoregressive moving average models for rich datasets," Journal of Econometrics, Elsevier, vol. 202(1), pages 75-91.
    4. Jean-Marie Dufour & Tarek Jouini, 2011. "Asymptotic Distributions for Some Quasi-Efficient Estimators in Echelon VARMA Models," CIRANO Working Papers 2011s-25, CIRANO.
    5. 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.
    6. Dufour, Jean-Marie & Taamouti, Abderrahim, 2010. "Short and long run causality measures: Theory and inference," Journal of Econometrics, Elsevier, vol. 154(1), pages 42-58, January.

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    More about this item

    Keywords

    Time series ; VARMA ; stationary ; invertible ; echelon form ; estimation ; asymotic normality ; bootstra; Hannan-Rissanen;
    All these keywords.

    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; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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