|
Model |
Tr |
MCS |
TSQ |
MCS |
|
P |
Pl |
P |
Pi | |
|
GJR |
0.033 |
0.033 |
0.003 |
0.003 |
|
SV |
0.033 |
0.033 |
0.011 |
0.011 |
|
VIX |
0.022 |
0.033 |
0.010 |
0.011 |
|
SVRV |
0.023 |
0.033 |
0.004 |
0.011 |
|
GARCH |
0.023 |
0.033 |
0.010 |
0.011 |
|
GJRRV |
0.018 |
0.033 |
0.018 |
0.018 |
|
GJRRVG |
0.016 |
0.033 |
0.019 |
0.019 |
|
ALLMBF u |
0.017 |
0.033 |
0.020 |
0.020 |
|
ALL1 |
0.025 |
0.033 |
0.035 |
0.035 |
|
(ARMA+ARFIMA∖ u |
0.022 |
0.033 |
0.066 |
0.066 |
|
GARCHRV |
0.023 |
0.033 |
0.113 |
0.113 |
|
ARMA |
0.548 |
0.548 |
0.513 |
0.513 |
|
ARFIMA |
0.519 |
0.548 |
0.487 |
0.513 |
|
ARMA + ARFIMAu |
0.541 |
0.548 |
0.624 |
0.624 |
|
ALLMBF r |
0.882 |
0.882 |
0.803 |
0.803 |
|
(ARMA+AR,FIMA∖ r |
0.818 |
0.882 |
0.851 |
0.851 |
|
ALLr |
0.767 |
0.882 |
0.767 |
0.851 |
|
ARMA + ARFIMAr |
_ |
1.000 |
_ |
1.000 |
Table 5: MCS results for individual forecasts given the MSE loss function. The
first row respresents the first model removed, down to the best performaing
model in the last row.
model based volatility forecasts. This paper has readdressed this question in the
context of SfcP 500 implied volatility, the VIX index. The forecast performance
of the VIX index has been compared to a range of model based forecasts and
combination forecasts. In doing so, further light is shed on the nature of the
information reflected in the VIX forecast.
In practical terms the VIX index produces forecasts that are inferior to
a number of competing model based forecasts, namely time series models of
realised volatility. The significance of these differences has been evaluated using
the model confidence set technology by Hansen et al. (2003, 2005). As it turns
out the VIX is not significantly inferior when an asymmetric loss function is
used. When the best model based volatility forecasts are combined they are
23