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Generalized Covariance Estimator

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  • Christian Gourieroux
  • Joann Jasiak

Abstract

We consider a class of semi-parametric dynamic models with iid errors, including the nonlinear mixed causal-noncausal Vector Autoregressive (VAR), Double-Autoregressive (DAR) and stochastic volatility models. To estimate the parameters characterizing the (nonlinear) serial dependence, we introduce a generic Generalized Covariance (GCov) estimator, which minimizes a residual-based multivariate portmanteau statistic. In comparison to the standard methods of moments, the GCov estimator has an interpretable objective function, circumvents the inversion of high-dimensional matrices, and achieves semi-parametric efficiency in one step. We derive the asymptotic properties of the GCov estimator and show its semi-parametric efficiency. We also prove that the associated residual-based portmanteau statistic is asymptotically chi-square distributed. The finite sample performance of the GCov estimator is illustrated in a simulation study. The estimator is then applied to a dynamic model of commodity futures.

Suggested Citation

  • Christian Gourieroux & Joann Jasiak, 2023. "Generalized Covariance Estimator," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(4), pages 1315-1327, October.
    • Handle: RePEc:taf:jnlbes:v:41:y:2023:i:4:p:1315-1327
    DOI: 10.1080/07350015.2022.2120486
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    1. Alain Hecq & Lenard Lieb & Sean Telg, 2016. "Identification of Mixed Causal-Noncausal Models in Finite Samples," Annals of Economics and Statistics, GENES, issue 123-124, pages 307-331.
    2. Jin, Ze & Matteson, David S., 2018. "Generalizing distance covariance to measure and test multivariate mutual dependence via complete and incomplete V-statistics," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 304-322.
    3. 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.
    4. Pena D. & Rodriguez J., 2002. "A Powerful Portmanteau Test of Lack of Fit for Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 601-610, June.
    5. Niu, Lu & Liu, Xiumin & Zhao, Junlong, 2020. "Robust estimator of the correlation matrix with sparse Kronecker structure for a high-dimensional matrix-variate," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    6. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
    7. Anderson, T. W., 1999. "Asymptotic Theory for Canonical Correlation Analysis," Journal of Multivariate Analysis, Elsevier, vol. 70(1), pages 1-29, July.
    8. Thomas J. Fisher & Colin M. Gallagher, 2012. "New Weighted Portmanteau Statistics for Time Series Goodness of Fit Testing," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 777-787, June.
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    Cited by:

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    2. Hall, Mauri K. & Jasiak, Joann, 2024. "Modelling common bubbles in cryptocurrency prices," Economic Modelling, Elsevier, vol. 139(C).

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