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

MSE	_________QLIKE____
ARMA	1.659	ARFIMA	3159.2
ARFIMA	1.667	ARMA	3174.3
GARCHRV	1.952	SVRV	3222.5
GJRRV	2.161	VIX	3253.0
GJRRVG	2.404	GARCHRV	3266.6
VIX	2.525	GJRRV	3278.7
GARCH	2.575	GARCH	3472.5
SV	2.730	GJR	3575.7
GJR	2.857	GJRRVG	3700.7
SVRV	4.543	SV_______	3923.0

Table 1: Loss function rankings for individual forecasts.

Model	T_r	MCS	^TSQ	MCS
	P	Pl	P	Pl
SVRV	0.013	0.013	0.005	0.005
GJR	0.016	0.016	0.005	0.005
SV	0.016	0.016	0.002	0.005
GARCH	0.011	0.016	0.003	0.005
VIX	0.011	0.016	0.004	0.005
GJRRVG	0.009	0.016	0.000	0.005
GJRRV	0.005	0.016	0.000	0.005
GARCHRV	0.008	0.016	0.006	0.006
ARFIMA	0.844	0.844	0.844	0.844
ARMA	_	1.000	_	1.000

Table 2: MCS results for individual forecasts given the MSE loss function.
The first row respresents the first model removed, down to the best performing
model in the last row.

that incorporate RV measures into the volatility equation are more accurate
out-of-sample than those that do not.

MCS results will now reveal whether the VIX is significantly inferior to
those forecasts with lower average loss.

Table 2 reports the MCS results for the individual forecasts based on the
MSE loss function. It turns out that the model with the largest T⅛ test statistic
is the SVRV model. The p-value, determined in the first reduction round is
0.013. As it is eliminated in the first round this automatically determines the

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