If you take a look at the smoothened spectral density of volatility jumps, you can see that it is something that is clearly a parametric form that in fact can be fit well by a cubic polynomial.
Here is the cubic polynomial fit.
Now the ARFIMA model residual spectral density is a bit tighter than the ARMA fit.
But neither of these residuals is nearly as tight as the spectral density of white noise.
(the vertical axis is what you should compare. In this example the vertical axis is very tight for the white noise between 0.98 and 1.02 while the residuals for both ARMA and ARFIMA are much more wide. The ARFIMA residual spectrum is between 0.6 and 0.72 while the ARMA residual spectrum is between around 0.01 and 1.00 at least visually). But neither ARMA nor ARFIMA models give us a result that seems to match what we would expect from the nice parametric form of the volatility jump spectral density at the top which can be fit by a polynomial. This is an important problem because there is a missing exact science of finance which is wholly buried in the volatility models still not recovered.