  We study a method for detecting the origins of anomalous diffusion, when it
is observed in an ensemble of times-series, generated experimentally or
numerically, without having knowledge about the exact underlying dynamics. The
reasons for anomalous diffusive scaling of the mean-squared displacement are
decomposed into three root causes: increment correlations are expressed by the
"Joseph effect" [Mandelbrot 1968], fat-tails of the increment probability
density lead to a "Noah effect" [Mandelbrot 1968], and non-stationarity, to the
"Moses effect" [Chen et al. 2017]. After appropriate rescaling, based on the
quantification of these effects, the increment distribution converges at
increasing times to a time-invariant asymptotic shape. For different processes,
this asymptotic limit can be an equilibrium state, an infinite-invariant, or an
infinite-covariant density. We use numerical methods of time-series analysis to
quantify the three effects in a model of a non-linearly coupled L\'evy walk,
compare our results to theoretical predictions, and discuss the generality of
the method.
