We advocate the use of absolute moment ratio statistics in conjunctionwith standard variance ratio statistics in order to disentangle lineardependence, non-linear dependence, and leptokurtosis in financial timeseries. Both statistics are computed for multiple return horizonssimultaneously, and the results are presented in a comprehensive wayusing a graphical device. We construct a formal joint testing procedurebased on bootstrapped and block-bootstrapped uniform confidenceintervals. The methodology is hybrid because it combines a formaltesting procedure with volatility curve pattern recognition based onexpert opinions. An application to forex data illustrates theprocedure.