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In any frequency, daily or monthly, economic and financial price-like time series $X_t$ such as settlement prices of gold futures or the US inflation has the following empirical feature.  Define return as $R_t = \Delta \log( X_t)$ and use the stochastic volatility model $R_t = exp(h_t/2) z_t$ with $z_t \sim i.i.d. N(0,1)$.  Then the autocorrelations of $V_t = h_t + \log(z_t^2)$ is significantly different from zero for many lags and an ARFIMA model will detect the fractional differencing parameter to around $d= 0.4$.  However, although $V_t$ is stationary, fitting an ARMA model to it will produce estimates that have far smoother predictions than out-of-sample values of $V_t$.
What we have found is that $\Delta V_t$ fitted by an AR(12) or AR(20) series produces coefficient series that are well described by a Mittag-Leffler function.