Before revision:  We relax this standard assumption of linear correlation to a nonlinear generalization in order to capture the complex nature of this effect using a newly developed Bayesian sequential computation method that is fast, efficient, and on-line  . Examining 615 stocks that comprise the S  P500 and Nikkei 225, we find nearly all of the stocks to exhibit leverage effects, of which many would have been lost under the standard linear assumption. We further the analysis by exploring whether there are clear traits that characterize the complexity of the leverage effect and find that different countries and certain sectors to have tendencies for more complex leverage effects.
After revision:  We relax this standard assumption of linear correlation to a nonlinear generalization in order to capture the complex nature of this effect using a newly developed Bayesian sequential computation method that is fast, efficient, and on-line . Examining 615 stocks that comprise the S P500 and Nikkei 225, we find that 89