Testing for causality in variance under nonstationarity in variance Paulo M.M. Rodrigues a,1 , Antonio Rubia b, ⁎ a Faculty of Economics, University of Algarve, Campus de Gambelas, 8005-139 Faro, Portugal b Department of Financial Economics, University of Alicante, Campus de San Vicente, CP 03080, Spain Received 25 August 2006; received in revised form 12 December 2006; accepted 12 February 2007 Available online 14 June 2007 Abstract 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. © 2007 Elsevier B.V. All rights reserved. Keywords: Structural changes; Volatility; Causality; Variance breaks JEL classification: C12; C22 1. Introduction In a recent paper, van Dijk, Osborn and Sensier (2005) [DOS] show, through Monte Carlo simulation, that causality-in-variance tests applied to macroeconomic series may suffer from severe finite sample size distortions in the presence of neglected structural breaks in variance. In this paper, we provide the theoretical justification for these findings as a particular case of a fairly general class of nonstationary volatility processes. Our analysis shows that the size departures are not only a small-sample effect but will also remain asymptotically because of the failure to consistently estimate cross-correlations in this Economics Letters 97 (2007) 133 – 137 www.elsevier.com/locate/econbase ⁎ Corresponding author. Tel./fax: +34 965 90 36 21. E-mail addresses: prodrig@ualg.pt (P.M.M. Rodrigues), antonio.rubia@ua.es (A. Rubia). 1 Tel.: +351 289 817 571; fax: +351 289 815 937. 0165-1765/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2007.02.032