Are combination forecasts of S&P 500 volatility statistically superior?

Table 4: Loss function rankings for individual and combination forecasts.

tion forecasts based on the MCS of individual forecasts, the regression based
combinations of ARMA+ARFIMA and ARMA+ARFIMA+SV RV+VIX.
The equally weighted combinations of these also rank relatively highly, along
with individual ARMA and ARFIMA forecasts. As an individual forecast,
the VIX does not perform particularly well. This represents a preliminary
indication that the VIX, as an IV estimate, does not seem to incorporate in-
formation relevant to future volatility of the same quality as that contained in
the top performing combinations. The issue of whether the VIX is significantly
inferior will now be considered.

Tables 5 and 6 contain the MCS results given the MSE and QLIKE loss
functions respectively. Assuming a level of significance of 5%, the MSE MCS
contains predominantly ARMA and ARFIMA based forecasts. While ALLMBF^r

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