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

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  • DUFOUR, Jean-Marie
  • JOUINI, Tarek

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 & JOUINI, Tarek, 2005. "Asymptotic Distribution of a Simple Linear Estimator for VARMA Models in Echelon Form," Cahiers de recherche 10-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    • Handle: RePEc:mtl:montec:10-2005
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    3. 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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    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; asymptotic normality; bootstrap; 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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