Moses, Noah and Joseph effects in Lévy walks

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