A dynamical assessment of market (in)efficiency is performed under the hypothesis that the price process follows a Multifractional Process with Random Exponent, a class of stochastic processes recently introduced to make the fractional Brownian motion more versatile in describing time nonhomogeneous dynamics. Two indicators are defined that allow to quantify the degree of (in)efficiency in absolute terms and in both positive and negative terms, once a significance level has been fixed. The application of the methodology to main stock indexes of U.S., Europe and Asia from 1990 to 2012 reveals that inefficiency is ubiquitous and the (often claimed) overall efficiency in the long run can be explained in terms of the balancing of inefficiencies of opposite sign. Furthermore, the empirical analysis shows that the less inefficient index in the considered time span is Nikkei 225, whereas Footsie 100 picks up the wooden spoon.
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