International tourism demand, which is typically measured as tourist arrivals, to Australia has experienced dramatic fluctuations in recent years due to changes in the economic, financial and political environment. However, variations in tourism demand, specifically the conditional variance, or volatility, have not previously been investigated in the tourism literature. An analysis of such volatility is essential for investigating the effects of shocks in tourism demand models. This paper models the conditional mean and conditional variance of the logarithm of the monthly tourist arrival rate from the four leading tourism source countries to Australia, namely Japan, New Zealand, UK and USA, using three multivariate static or constant conditional correlation (CCC) volatility models, specifically the symmetric CCC-MGARCH model of (Rev. Econ. Stat. 72 (1990) 498), symmetric vector ARMA-GARCH model of (Econ. Theory 19 (2003) 278), and asymmetric vector ARMA-AGARCH model of (Australasian Meeting of the Econometric Society, Brisbane, Australia, 2002). Monthly data from July 1975 to 2000 are used in the empirical analysis. The results suggest the presence of interdependent effects in the conditional variances between the four leading countries, and asymmetric effects of shocks in two of the four countries. This is an important result as it emphasizes interdependencies between major tourism source countries, as well as the asymmetric effects of positive and negative shocks in tourism demand. The estimated CCC matrices for the three models are not substantially different from each other, which confirms the robustness of the estimates to alternative specifications of the multivariate conditional variance. (c) 2004 Elsevier Ltd. All rights reserved.