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Noncausal vector autoregressive process: Representation, identification and semi-parametric estimation

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  • Gourieroux, Christian
  • Jasiak, Joann

Abstract

This paper introduces a representation theorem for a mixed VAR(p) process by distinguishing its causal and noncausal components. That representation is used to discuss the advantages and limitations of second-order identification in a mixed VAR. We show that it is possible to find the numbers of causal or noncausal components of the process from its multivariate autocovariance function, while nonlinear autocovariances are needed to distinguish between them. The paper introduces also a consistent semi-parametric estimator for mixed causal/noncausal multivariate non-Gaussian processes, called the Generalized Covariance (GCov) estimator, which relies on combined standard and nonlinear autocovariances of the process. The GCov does not require any distributional assumptions on the errors. The approach is illustrated by a simulation study and applied to commodity prices.

Suggested Citation

  • Gourieroux, Christian & Jasiak, Joann, 2017. "Noncausal vector autoregressive process: Representation, identification and semi-parametric estimation," Journal of Econometrics, Elsevier, vol. 200(1), pages 118-134.
    • Handle: RePEc:eee:econom:v:200:y:2017:i:1:p:118-134
    DOI: 10.1016/j.jeconom.2017.01.011
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    Citations

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    Cited by:

    1. 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.
    2. Gianluca Cubadda & Alain Hecq & Elisa Voisin, 2023. "Detecting Common Bubbles in Multivariate Mixed Causal–Noncausal Models," Econometrics, MDPI, vol. 11(1), pages 1-16, March.
    3. Gourieroux, Christian & Lu, Yang, 2019. "Least impulse response estimator for stress test exercises," Journal of Banking & Finance, Elsevier, vol. 103(C), pages 62-77.
    4. Gourieroux, C. & Jasiak, J. & Monfort, A., 2020. "Stationary bubble equilibria in rational expectation models," Journal of Econometrics, Elsevier, vol. 218(2), pages 714-735.
    5. Bernd Funovits, 2020. "Identifiability and Estimation of Possibly Non-Invertible SVARMA Models: A New Parametrisation," Papers 2002.04346, arXiv.org, revised Feb 2021.
    6. Gabriele Mingoli, 2024. "Modeling Common Bubbles: A Mixed Causal Non-Causal Dynamic Factor Model," Tinbergen Institute Discussion Papers 24-072/III, Tinbergen Institute.
    7. Gianluca Cubadda & Francesco Giancaterini & Alain Hecq & Joann Jasiak, 2023. "Optimization of the Generalized Covariance Estimator in Noncausal Processes," Papers 2306.14653, arXiv.org, revised Jan 2024.
    8. Anders Rygh Swensen, 2022. "On causal and non‐causal cointegrated vector autoregressive time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 178-196, March.
    9. Christian Gourieroux & Joann Jasiak, 2023. "Generalized Covariance Estimator," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(4), pages 1315-1327, October.
    10. Ye Chen & Jian Li & Qiyuan Li, 2023. "Seemingly Unrelated Regression Estimation for VAR Models with Explosive Roots," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(4), pages 910-937, August.
    11. Hall, Mauri K. & Jasiak, Joann, 2024. "Modelling common bubbles in cryptocurrency prices," Economic Modelling, Elsevier, vol. 139(C).
    12. Kramkov, Viacheslav & Maksimov, Andrey, 2020. "Loan market markups and noncausal autoregressions," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 60, pages 48-69.

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    More about this item

    Keywords

    Multivariate noncausal process; Identification; Representation; Semi-parametric estimation; Generalized covariance estimator; Speculative bubble; Alternative investment; Alternative investment;
    All these keywords.

    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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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