Second-order noncausality in multivariate garch processes

Fabienne Comte, Offer Lieberman

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


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 secondorder 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.

Original languageEnglish
Pages (from-to)535-557
Number of pages23
JournalJournal of Time Series Analysis
Issue number5
StatePublished - Sep 2000
Externally publishedYes


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  • Second-order noncausality


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