|
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 |
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 |
_ |
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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