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

Model	Tr	MCS	^TSQ	MCS
	P	∙x∙"∙4. Pl	P	∙x∙"∙4. Pl
GJRRVG	0.000	0.000	0.001	0.001
SV	0.001	0.001	0.001	0.001
GJR	0.000	0.001	0.000	0.001
GARCH	0.002	0.002	0.001	0.001
GJRRV	0.000	0.002	0.000	0.001
ALLMBF ^u	0.002	0.002	0.008	0.008
GARCHRV	0.007	0.007	0.009	0.009
SVRV	0.006	0.007	0.006	0.009
VIX	0.022	0.022	0.034	0.034
ALL^u	0.017	0.022	0.026	0.034
ARMA	0.055	0.055	0.047	0.047
ALL^r	0.082	0.082	0.091	0.091
ARMA + ARFIMA^u	0.078	0.082	0.066	0.091
ARFIMA	0.082	0.082	0.106	0.106
[ARMAiARFIMA] ^u∖ +SVRV+VIX )	0.150	0.150	0.212	0.212
ALLMBF ^r	0.827	0.827	0.795	0.795
ARMA + ARFIMA^r	0.867	0.867	0.867	0.867
(ARMA+ARFIMA∖ ^r∖ +SVRV+VIX )	_	1.000	_	1.000

Table 6: MCS results for individual forecasts given the QLIKE loss function.
The first row respresents the first model removed, down to the best performaing
model in the last row.

found to be superior to the individual mode based and VIX forecasts. In
summary, the most accurate SfcP 500 volatility forecast is obtained from a
combination of short and long memory models of realised volatility. While
previous work has found that the VIX contains no information beyond that
contained in model based forecasts. These findings indicate that, while it is
entirely plausible that the implied volatility combines information used in a
range of different model based forecasts, it is not the best possible combination
of such information. When compared to other combined forecasts, the VIX
drops out of the model confidence set.

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