This paper examines whether there is evidence of spillovers of volatility from the Chinese stock market to its neighbours and trading partners, including Australia, Hong Kong, Singapore, Japan and USA. China's increasing integration into the global market may have important consequences for investors in related markets. In order to capture these potential effects, we explore these issues using an Autoregressive Moving Average (ARMA) return equation. A univariate GARCH model is then adopted to test for the persistence of volatility in stock market returns, as represented by stock market indices. Finally, univariate GARCH, multivariate VARMA-GARCH, and multivariate VARMA-AGARCH models are used to test for constant conditional correlations and volatility spillover effects across these markets. Each model is used to calculate the conditional volatility between both the Shenzhen and Shanghai Chinese markets and several other markets around the Pacific Basin Area, including Australia, Hong Kong, Japan, Taiwan and Singapore, during four distinct periods, beginning 27 August 1991 and ending 17 November 2010. The empirical results show some evidence of volatility spillovers across these markets in the pre-GFC periods, but there is little evidence of spillover effects from China to related markets during the GFC. We undertook some additional analysis for this period featuring an exploration of whether there was any spillover effect in the mean equations as well as in the variance equations. We used a bimean equation to model the conditional mean in the individual markets plus an ARMA model to capture volatility spillovers from China to the five markets considered. This augmented model showed much greater evidence of spillovers. We also suspected that the correlations were not constant and applied a moving window of 120 days of daily observations to explore time-varying conditional and fitted correlations. There was evidence of non-constant correlations and even a period of negative correlations between the US and China at the height of the GFC. This is presumably because the GFC was initially a US phenomenon, before spreading to developed markets around the globe and it was not a Chinese phenomenon.