The aim of this work is to capture common stochastic trends in weekly volatilities of the Dow Jones, Nikkei, Hang Seng and Strait Times index using a multivariate stochastic volatility (SV) model. The results suggest a very high correlation among the volatility innovations, so that it is examined whether the four series share any common stochastic trends. A Principal Component Analysis and a Factor Analysis in the state space setting reveal that two common stochastic trends can be found to underlie the volatility series. The resulting linear combinations of the volatility series no more exhibit any stochastic trend but are stationary in the state space framework. Thus, it can be concluded that volatilities of the four stock indexes are in essence co-persistent.