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A note on time-reversibility of multivariate linear processes

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  • Kung-Sik Chan
  • Lop-Hing Ho
  • Howell Tong

Abstract

We derive some readily verifiable necessary and sufficient conditions for a multivariate non-Gaussian linear process to be time-reversible, under two sets of conditions on the contemporaneous dependence structure of the innovations. One set of conditions concerns the case of independent-component innovations, in which case a multivariate non-Gaussian linear process is time-reversible if and only if the coefficients consist of essentially asymmetric columns with column-specific origins of symmetry or symmetric pairs of columns with pair-specific origins of symmetry. On the other hand, for dependent-component innovations plus other regularity conditions, a multivariate non-Gaussian linear process is time-reversible if and only if the coefficients are essentially symmetric about some origin. Copyright 2006, Oxford University Press.

Suggested Citation

  • Kung-Sik Chan & Lop-Hing Ho & Howell Tong, 2006. "A note on time-reversibility of multivariate linear processes," Biometrika, Biometrika Trust, vol. 93(1), pages 221-227, March.
    • Handle: RePEc:oup:biomet:v:93:y:2006:i:1:p:221-227
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    File URL: http://hdl.handle.net/10.1093/biomet/93.1.221
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    Cited by:

    1. Pascual, Lorenzo & Fresoli, Diego Eduardo, 2011. "Bootstrap forecast of multivariate VAR models without using the backward representation," DES - Working Papers. Statistics and Econometrics. WS ws113426, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Davis, Richard A. & Song, Li, 2020. "Noncausal vector AR processes with application to economic time series," Journal of Econometrics, Elsevier, vol. 216(1), pages 246-267.
    3. Gourieroux, C. & Jasiak, J. & Monfort, A., 2020. "Stationary bubble equilibria in rational expectation models," Journal of Econometrics, Elsevier, vol. 218(2), pages 714-735.
    4. Christian Gourieroux & Joann Jasiak, 2016. "Filtering, Prediction and Simulation Methods for Noncausal Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 405-430, May.
    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. Wilmer Martínez-Rivera & Thomaz Carvalhaes & Petar Jevtić & T. Agami Reddy, 2023. "A treatment-effect model to quantify human dimensions of disaster impacts: the case of Hurricane Maria in Puerto Rico," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 116(2), pages 2033-2068, March.
    7. Hamidi Sahneh, Mehdi, 2013. "Testing for Noncausal Vector Autoregressive Representation," MPRA Paper 68867, University Library of Munich, Germany, revised 16 Aug 2014.
    8. Lanne, Markku & Saikkonen, Pentti, 2013. "Noncausal Vector Autoregression," Econometric Theory, Cambridge University Press, vol. 29(3), pages 447-481, June.
    9. 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.
    10. Christian Gourieroux & Joann Jasiak, 2023. "Dynamic deconvolution and identification of independent autoregressive sources," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(2), pages 151-180, March.
    11. Phillip Wild & John Foster, 2012. "On testing for non-linear and time irreversible probabilistic structure in high frequency ASX financial time series data," Discussion Papers Series 466, School of Economics, University of Queensland, Australia.
    12. 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.
    13. Fresoli, Diego & Ruiz, Esther & Pascual, Lorenzo, 2015. "Bootstrap multi-step forecasts of non-Gaussian VAR models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 834-848.
    14. Funovits, Bernd, 2024. "Identifiability and estimation of possibly non-invertible SVARMA Models: The normalised canonical WHF parametrisation," Journal of Econometrics, Elsevier, vol. 241(2).
    15. Christian Gouriéroux & Jean-Michel Zakoïan, 2015. "On Uniqueness of Moving Average Representations of Heavy-tailed Stationary Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 876-887, November.
    16. Lanne, Markku & Meitz, Mika & Saikkonen, Pentti, 2017. "Identification and estimation of non-Gaussian structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 196(2), pages 288-304.
    17. Joann Jasiak & Aryan Manafi Neyazi, 2023. "GCov-Based Portmanteau Test," Papers 2312.05373, arXiv.org.
    18. Miguel Cabello, 2022. "Robust Estimation of the non-Gaussian Dimension in Structural Linear Models," Papers 2212.07263, arXiv.org, revised Sep 2023.

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