Testing for Causality in Variance Using Multivariate GARCH Models

Hafner · Herwartz

74 citations0/0 files storedAnnales d Économie et de Statistique

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Financial Risk and Volatility Modeling Stochastic processes and financial applications Market Dynamics and Volatility

Abstract

Tests of causality in variance in multiple time series\nhave been proposed recently, based on residuals of estimated\nunivariate models. Although such tests are applied frequently\nlittle is known about their power properties. In this paper we\nshow that a convenient alternative to residual based testing is to\nspecify a multivariate volatility model, such as multivariate\nGARCH (or BEKK), and construct a Wald test on noncausality in\nvariance. We compare both approaches to testing causality in\nvariance in terms of asymptotic and finite sample properties. The\nWald test is shown to have superior power properties under a\nsequence of local alternatives. Furthermore, we show by simulation\nthat the Wald test is quite robust to misspecification of the\norder of the BEKK model, but that empirical power decreases\nsubstantially when asymmetries in volatility are ignored.

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References

1969Investigating Causal Relations by Econometric Models and Cross-spectral Methods 1995Multivariate Simultaneous Generalized ARCH 1993Temporal Aggregation of Garch Processes 1977Causality in temporal systems 1996A causality-in-variance test and its application to financial market prices 2003Asymptotic theory for multivariate GARCH processes 1998Short Run and Long Run Causality in Time Series: Theory 2008Some Recent Developments in a Concept of Causality

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