I'm trying to develop a predictive model for an angular dependent variable (on $[0,2\pi])$ using several independent measurements – also angular variables, on $[0,2\pi]$ – as predictors. Each predictor is significantly but not extremely strongly correlated with the dependent variable. How can I combine the predictors to determine a predictive model for the dependent variable that is optimal in some sense? And how can I rigorously identify the strongest predictor(s)?
For variables on Euclidean space(s), I'd employ multiple regression (or similar) and principal components analysis. But the periodicity of all variables mucks with these approaches, e.g., 0.02 must be highly correlated with 6.26, but not with 3.14. How are "the usual" procedures generalized to directional / circular statistics? Any insights or cites to useful references would be useful. (I'm already aware of the texts by N. Fisher and Mardia & Jupp, but don't have handy access to these.)