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

ALLu

0.017

0.022

0.026

0.034

ARMA

0.055

0.055

0.047

0.047

ALLr

0.082

0.082

0.091

0.091

ARMA + ARFIMAu

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 + ARFIMAr

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.

24



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