This paper introduces a method based on the use of various linear and nonlinear state space models that uses non-synchronous data to extract global stochastic financial trends (GST). These models are specifically constructed to take advantage of the intraday arrival of closing information coming from different international markets in order to improve the quality of volatility description and forecasting performances. A set of three major asynchronous international stock market indices is used in order to empirically show that this forecasting scheme is capable of significant performance improvements when compared with those obtained with standard models like the dynamic conditional correlation (DCC) family.