Testing Self-Affinity of Stock Returns

Given the process {X(t), t in T}, the definition of self-affinity is reformulated in terms of diameter of the space of the rescaled pdf's of X(t). Two necessary conditions are deduced which contribute to discriminate uniscaling processes. Furthermore, by properly choosing the distance, the measure of self-affinity reduces itself to the Smirnov statistics. This allows to apply the well-known significance test due to Kolmogorov and Smirnov, An empirical analysis showing that uniscaling does not generally hold in financial markets completes the paper