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Semi-Parametric Estimation of Noncausal Vector Autoregression

Author

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  • Christian Gouriéroux

    (CREST and University of Toronto)

  • Joann Jasiak

    (York University)

Abstract

This paper introduces consistent semi-parametric estimation methods for mixed causal/noncausal multivariate non-Gaussian processes. We show that in the VAR(1) model, the second-order identification is feasible to some limited extent, contrary to the common belief that non-Gaussian processes are not second-order identifiable. In general, in the mixed VAR (1) it is possible to distinguish the mixed processes with different numbers of causal and noncausal components.For detecting the causal and noncausal components, a semi-parametric exploratory analysis is proposed. It includes a semi-parametric estimation method that does not require any distributional assumptions on the errors. For direct estimation of the matrix of autoregressive coefficients of a VAR (1), we use the generalized covariance estimator. Although this estimator is not fully efficient, it provides the estimates in one single optimization while the MLE requires a number of optimizations, which is equal to the number of all possible causal dimensions. The methods are illustrated by a simulation study.

Suggested Citation

  • Christian Gouriéroux & Joann Jasiak, 2015. "Semi-Parametric Estimation of Noncausal Vector Autoregression," Working Papers 2015-02, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2015-02
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    Cited by:

    1. Gouriéroux, Christian & Monfort, Alain & Zakoian, Jean-Michel, 2017. "Pseudo-Maximum Likelihood and Lie Groups of Linear Transformations," MPRA Paper 79623, University Library of Munich, Germany.
    2. Hecq Alain & Sun Li, 2021. "Selecting between causal and noncausal models with quantile autoregressions," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(5), pages 393-416, December.
    3. Gianluca Cubadda & Alain Hecq & Sean Telg, 2019. "Detecting Co‐Movements in Non‐Causal Time Series," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 81(3), pages 697-715, June.
    4. Alain Hecq & Li Sun, 2019. "Identification of Noncausal Models by Quantile Autoregressions," Papers 1904.05952, arXiv.org.
    5. Gouriéroux, Christian & Monfort, Alain & Renne, Jean-Paul, 2017. "Statistical inference for independent component analysis: Application to structural VAR models," Journal of Econometrics, Elsevier, vol. 196(1), pages 111-126.

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