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.
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 is implemented to estimate this effect in a practical, 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.