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

MCS р-value for SVRV to be 0.013. In the second round of elimination the
GJR model fares worst. It produces the largest Tr test statistic (р-value of
0.016) and is therefore dropped at a 5% significance level. As the р-value of
0.016 is larger than the MCS р-values of the model(s) previously dropped this
is also its MCS p-value. In fact, at a 5% significance level 6 more models are
dropped from M and only the ARFIMA and ARMA survive in the MCS
and therefore constitute Λ‰₅. As can be seen from the last two columns this
result does not change qualitatively if one considers the Tsq statistic rather
than the Tr statistic.

Therefore ARFIMA and ARMA constitute the MCS with 95% confidence
and are significantly superior to other competing models and the VIX. Results
based on the QLIKE loss function, reported in Table 3, reveals somewhat of
a different picture. At a 5% significance, the MCS contains SVRV, VIX,
ARFIMA and ARMA. Under the QLIKE loss assumption, the VIX is of
EPA but clearly not superior to the three surviving MBF. As the asymmetric
loss function admits two additional models in the MCS it can be conjectured
that the SVRV and VIX in fact avoid significantly underpredicting volatility,
as that is the mistake most heavily penalised under this loss function.

These results will motivate the combinations forecasts formed in the fol-
lowing section. The results of the following section will reveal whether the
VIX is of EPA relative to these combinations and can therefore be viewed as
a combination of various MBF.

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