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

hlarket efficiency tests that rely on the martingale difference behavior 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 absolute returns and variances. If the distribution is heavy-tailed, this shows up in the absolute moment plots, but not in the variance related plots. Linear dependence. by contrast, is revealed in both plots. We provide and discuss an analytical and a simulation experime illustrating these points.