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The recent literature has proposed a (limited) number of approaches to test for time revesibility, that is one of the main hypotheses in time series. A very interesting proposal is a Gini-based framwork that, among other things, includes a test for time reversibility focussing on possible differences between backward and forward autocorrelations. This feature is indeed useful to identify models with underlying heavy tailed and non-normal innovations. In this paper we intend to shed some more light on this and investigate, via Monte Carlo simulations, ont he possibility that this test can effectively have power in detecting some form of nonlinearity.