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Statistical Inference for Independent Component Analysis: Application to Structural VAR Models


  • Christian Gouriéroux

    () (CREST, University of Toronto)

  • Alain Monfort

    () (CREST,Banque de France)

  • Jean-Paul Renne

    (University of Lausanne, Faculty of Business and Economics)


The well-known problem of non-identi?ability of structural VAR models disappears if the structural shocks are independent and if at most one of them is Gaussian. In that case, the relevant estimation technique is the Independent Component Analysis (ICA). Since the introduction of ICA by Comon (1994), various semi-parametric estimation methods have been proposed for "orthogonalizing" the error terms. These methods include pseudo-maximum likelihood (PML) approaches and recursive PML. However several of these approaches are not consistent and others are signi?cantly subef?cient. The aim of our paper is to derive the asymptotic properties of the PML approaches, in particular to study their consistency (or lack of consistency). We conduct Monte Carlo studies exploring the relative performances of these methods. Finally, an application based on real data shows that structural VAR models can be estimated without additional identi?cation restrictions in the non-Gaussian case and that the usual restrictions can be tested.

Suggested Citation

  • Christian Gouriéroux & Alain Monfort & Jean-Paul Renne, 2016. "Statistical Inference for Independent Component Analysis: Application to Structural VAR Models," Working Papers 2016-20, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2016-20

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    References listed on IDEAS

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    Cited by:

    1. Mattia Guerini & Alessio Moneta & Mauro Napoletano & Andrea Roventini, 2017. "The Janus-faced nature of debt : result from a data-driven cointegrated SVAR approach," Documents de Travail de l'OFCE 2017-02, Observatoire Francais des Conjonctures Economiques (OFCE).
    2. Christian Gouriéroux & Alain Monfort & Eric Renault, 2017. "Consistent Pseudo-Maximum Likelihood Estimators," Working Papers 2017-10, Center for Research in Economics and Statistics.

    More about this item


    Independent Component Analysis; Pseudo-Maximum Likelihood; Identi?cation; Cayley Transform; Structural Shocks; Structural VAR ; Impulse Response Functions.;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric 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


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