Rainfall downscaling in time: theoretical and empirical comparison between multifractal and Hurst-Kolmogorov discrete random cascades

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Just two moments! A cautionary note against use of high-order moments in multifractal models in hydrology (2013, methodology): “To show that in the model by Lombardo et al. (2012) the theoretical moment scaling function is given by Eq.”
Generalized binomial multiplicative cascade processes and asymmetrical multifractal distributions (2014, background): “…and asymmetry of multifractal distributions, other types of properties of multifractal distribution such as spatiotemporal stationarity (Lombardo et al., 2012, 2013), lacunarity (Mandelbrot, 1983; Plotnick et al., 1993; Cheng, 1997b) and variability (autocorrelation and variogram)…”
Generic and parsimonious stochastic modelling for hydrology and beyond (2016, background): “This is not quite easy as the transformation cannot be invariant with respect to the time scale (Lombardo et al. 2012).”