Two integrated stock markets are generally subjected to common shocks revealing that commonalities in fundamentals drive their underlying return processes. In such a case, volatility series should share a long-run component although their transitory components might temporary diverge. In this paper, we investigate stock market integration in East Asia by analyzing the co-persistent nature of their ex-post observed volatility. Using recent fractional cointegration techniques, we find that volatility of several markets converges in the long run to a common equilibrium. Our results reveal that a global integration process drives the most developed markets of the region, while no evidence of co-persistence appears for emerging markets.