Stochastic processes, non-normal innovations, and the use of scaling ratios

Market efficiency tests that rely on the martingale difference be-havior of returns can be based on various volatility measures. This paper argues that, to be able to differentiate between dependence and fat-tailedness. one should look simultaneously at plots based on ab-solute returns and variances. If the distribution is heavy-tailed, this shows up in the absolute moment plots, but not in the variance re-lated plots. Linear dependence. by contrast, is revealed in both plots. We provide and discuss an analytical and a simulation experiment illustrating these points.