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It is useful to get a sense of the empirical long-memory effects observed for log return-squared for a sampling of commodity ETFs.  If we are interested in volatility prediction, this should provide us with the correctness of using ARFIMA or fractional Brownian motions to predict volatility.  Here is a table for calculating the fractional integration parameter $d = H - 1/2$ where $H$ is the Hurst exponent.  It’s clear that all of these return series have long memory (since $d>0$).