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

MSE	____________QLIKE_______
ARMA + ARFIMA^r	1.477	∕ARMA+ARFIMA∖^rI +SVRV+VIX )	3042.5
fARMA+ARFIMA∖ ^r∖ +SVRV+VIX J	1.502	ARMA + ARFIMA^r	3043.8
ALL^r	1.509	(ARMA+ARFIMA∖ ^u∖ +SVRV+VIX )	3102.4
ALLMBF ^r	1.549	ARFIMA	3159.2
ARMA + ARFIMA^u	1.648	ARMA + ARFIMA^u	3161.6
ARMA	1.659	ARMA	3174.3
ARFIMA	1.667	ALL	3205.2
GARCHRV	1.952	SVRV	3222.5
(ARMA+ARFIMA∖ ^u∖ +SVRV+VIX )	1.969	VIX	3253.0
ALL^u	2.001	ALLMBF ^u	3266.1
ALLMBF ^u	2.014	GARCHRV	3266.6
GJRRV	2.161	GJRRV	3278.7
GJRRVG	2.404	ALLMBF ^r	3447.5
VIX	2.525	GARCH	3472.5
GARCH	2.575	GJR	3575.7
SV	2.730	GJRRVG	3700.7
GJR	2.857	SV	3923.0
SVRV_________	4.543	ALL_________	5796.9

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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