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Second‐Order Noncausality in Multivariate GARCH Processes

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  • Fabienne Comte
  • Offer Lieberman

Abstract

Typical multivariate economic time series may exhibit co‐behavior patterns not only in the conditional means, but also in the conditional variances. In this paper we give two new definitions of variance noncausality in a multivariate setting a Granger‐type noncausality and a linear Granger noncausality through projections on Hilbert spaces. Both definitions are related to a previous second‐order noncausality concept defined by Granger et al. in a bivariate setting. The implications of second‐order noncausality on multivariate ARMA processes with GARCH‐type errors are investigated. We derive exact testable restrictions on the parameters of the processes considered, implied by this type of noncausality. Conditions for the finiteness of the fourth‐order moment of the multivariate GARCH process are derived and related to earlier results in the univariate framework. We include an illustration of second‐order noncausality in a trivariate model of daily financial returns.

Suggested Citation

  • Fabienne Comte & Offer Lieberman, 2000. "Second‐Order Noncausality in Multivariate GARCH Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(5), pages 535-557, September.
    • Handle: RePEc:bla:jtsera:v:21:y:2000:i:5:p:535-557
    DOI: 10.1111/1467-9892.00197
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    Cited by:

    1. Rituparna Sen & Anandamayee Majumdar & Shubhangi Sikaria, 2022. "Bayesian Testing of Granger Causality in Functional Time Series," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 191-210, September.
    2. Andrea Silvestrini & David Veredas, 2008. "Temporal Aggregation Of Univariate And Multivariate Time Series Models: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 22(3), pages 458-497, July.
    3. Aromi, Daniel & Clements, Adam, 2019. "Spillovers between the oil sector and the S&P500: The impact of information flow about crude oil," Energy Economics, Elsevier, vol. 81(C), pages 187-196.
    4. Leong, Soon Heng & Urga, Giovanni, 2023. "A practical multivariate approach to testing volatility spillover," Journal of Economic Dynamics and Control, Elsevier, vol. 153(C).
    5. Bonaccolto, Giovanni & Caporin, Massimiliano & Panzica, Roberto, 2019. "Estimation and model-based combination of causality networks among large US banks and insurance companies," Journal of Empirical Finance, Elsevier, vol. 54(C), pages 1-21.
    6. Vellachami, Sanggetha & Hasanov, Akram Shavkatovich & Brooks, Robert, 2023. "Risk transmission from the energy markets to the carbon market: Evidence from the recursive window approach," International Review of Financial Analysis, Elsevier, vol. 89(C).
    7. Asai, Manabu & Chang, Chia-Lin & McAleer, Michael, 2022. "Realized matrix-exponential stochastic volatility with asymmetry, long memory and higher-moment spillovers," Journal of Econometrics, Elsevier, vol. 227(1), pages 285-304.

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