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Identification and Estimation in Non-Fundamental Structural VARMA Models

Author

Listed:
  • Christian Gouriéroux

    (CREST; University of Toronto)

  • Alain Monfort

    (CREST)

  • Jean-Paul Renne

    (University of Lausanne)

Abstract

The basic assumption of a structural VARMA model (SVARMA) is that it is driven by a white noise whose components are independent and can be interpreted as economic shocks, called “structural” shocks. When the errors are Gaussian, independence is equivalent to noncorrelation and these models face two kinds of identi?cation issues. The ?rst identi?cation problem is “static” and is due to the fact that there is an in?nite number of linear transformations of a given random vector making its components uncorrelated. The second identi?cation problem is “dynamic” and is a consequence of the fact that the SVARMA process may have a non invertible AR and/or MA matrix polynomial but, still, has the same second-order properties as a VARMA process in which both the AR and MA matrix polynomials are invertible (the fundamental representation). Moreover the standard Box-Jenkins approach [Box and Jenkins (1970)] automatically estimates the fundamental representation and, therefore, may lead to misspeci?ed Impulse Response Functions. The aim of this paper is to explain that these dif?culties are mainly due to the Gaussian assumption, and that both identi?cation challenges are solved in a non-Gaussian framework. We develop new simple parametric and semi-parametric estimation methods when there is non-fundamentalness in the moving average dynamics. The functioning and performances of these methods are illustrated by applications conducted on both simulated and real data.

Suggested Citation

  • Christian Gouriéroux & Alain Monfort & Jean-Paul Renne, 2017. "Identification and Estimation in Non-Fundamental Structural VARMA Models," Working Papers 2017-08, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2017-08
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    References listed on IDEAS

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    1. Uhlig, Harald, 2005. "What are the effects of monetary policy on output? Results from an agnostic identification procedure," Journal of Monetary Economics, Elsevier, vol. 52(2), pages 381-419, March.
    2. Anton Velinov & Wenjuan Chen, 2014. "Are There Bubbles in Stock Prices?: Testing for Fundamental Shocks," Discussion Papers of DIW Berlin 1375, DIW Berlin, German Institute for Economic Research.
    3. Frank Smets & Raf Wouters, 2003. "An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1123-1175, September.
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    Citations

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    Cited by:

    1. Mélard, Guy, 2022. "An indirect proof for the asymptotic properties of VARMA model estimators," Econometrics and Statistics, Elsevier, vol. 21(C), pages 96-111.
    2. Zema, Sebastiano Michele, 2022. "Directed acyclic graph based information shares for price discovery," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).
    3. Fiorentini, Gabriele & Sentana, Enrique, 2023. "Discrete mixtures of normals pseudo maximum likelihood estimators of structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 235(2), pages 643-665.
    4. Jarociński, Marek, 2024. "Estimating the Fed’s unconventional policy shocks," Journal of Monetary Economics, Elsevier, vol. 144(C).
    5. Drautzburg, Thorsten & Wright, Jonathan H., 2023. "Refining set-identification in VARs through independence," Journal of Econometrics, Elsevier, vol. 235(2), pages 1827-1847.
    6. Moneta, Alessio & Pallante, Gianluca, 2022. "Identification of Structural VAR Models via Independent Component Analysis: A Performance Evaluation Study," Journal of Economic Dynamics and Control, Elsevier, vol. 144(C).
    7. Sebastiano Michele Zema & Francesco Cordoni, 2023. "A non-Normal framework for price discovery: The independent component based information shares measure," LEM Papers Series 2023/03, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    8. Paul Levine & Joseph Pearlman & Stephen Wright & Bo Yang, 2023. "Imperfect Information and Hidden Dynamics," School of Economics Discussion Papers 1223, School of Economics, University of Surrey.
    9. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.
    10. Christis Katsouris, 2023. "Structural Analysis of Vector Autoregressive Models," Papers 2312.06402, arXiv.org, revised Feb 2024.
    11. Miguel Cabello, 2022. "Robust Estimation of the non-Gaussian Dimension in Structural Linear Models," Papers 2212.07263, arXiv.org, revised Sep 2023.
    12. Sascha A. Keweloh, 2023. "Structural Vector Autoregressions and Higher Moments: Challenges and Solutions in Small Samples," Papers 2310.08173, arXiv.org.
    13. Guay, Alain & Pelgrin, Florian, 2023. "Structural VAR models in the Frequency Domain," Journal of Econometrics, Elsevier, vol. 236(1).

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    More about this item

    Keywords

    Structural VARMA; Fundamental Representation; Identi?cation; Shocks; Impulse Response Function; Incomplete Likelihood; Composite Likelihood; Economic Scenario Generators;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • 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
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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