and ALLr are contained in the MCS, it may be conjectured that the role played
by the RV time series ARMA and ARFIMA forecasts is responsible for this
as no other individual forecast is included. Once again, the VIX as an in-
dividual forecast is significantly inferior to these individual and combination
forecasts. The only role played by the VIX in this case is as a constituent
of the ARM A+ARFIM A+SV RV+VIXr and ALL combinations. A similar
pattern emerges when the QLIKE results in Table 6 are examined. In this case
the MCS is narrower and does not contain the ALLr or ALLMBFr forecasts.
Once again the VIX forecast is clearly inferior to these combination forecasts.
Interestingly, the MCS based on the QLIKE loss function does not include the
individual ARMA and ARFIMA models any longer. This indicates that here,
in contrast to the case of the MSE loss function, the combination of forecasts
delivers a statistically significant advantage.
A number of interesting patterns emerge from these results. From a practical
viewpoint, it is clear that combination forecasts have the potential to produce
forecasts of superior accuracy relative to the individual forecasts. This is not
surprising as different models capture different dynamics in volatility. If the top
performing individual forecasts are combined this may lead to a dominant com-
bination forecast, superior to its individual constituents and other competing
models. In the present context, however, this is only true for the asymmetric
loss function QLIKE.
The results also shed further light on the manner in which IV estimates
(VIX in this case) are formed. These results suggest that option traders,
when forming volatility forecasts, are not taking into account the same quality
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