Testing for causality in variance under nonstationarity in variance

Van Dijk, Osborn and Sensier [van Dijk, D., Osborn, D.R., Sensier, M., 2005, Testing for causality in variance in the presence of breaks. Economics Letters 89, 193-199.] have recently shown, through Monte Carlo simulation, that causality-in-variance tests may suffer severe finite sample size distortions in the presence of neglected structural breaks. In this paper we provide the theoretical foundation to characterize such departures. The asymptotic theory allows to depict a more complete and general analysis.