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

Table 3: MCS results for individual forecasts given the QLIKE loss function.
The first row respresents the first model removed, down to the best performing
model in the last row.

4.2 Combination forecasts

Based on the MCS results for the individual forecasts, the first set of com-
bination forecasts are chosen. Therefore combinations of ARMA+ARFIMA
and ARMA+ARFIMA+SVRV+VIX were formed given the MSE and QLIKE
results reported above. The final two sets of combinations are natural to con-
sider, a combination of all MBF and all forecasts, denoted as ALLMBF and
ALL in this section respectively. As discussed in Section 3, the combination
forecasts are constructed using both a simple average or regression weighted
function of the constituent forecasts. Both of these approaches are applied to
each of the combinations described here with the simple average and regression
based combinations indicated by и and r superscripts respectively. In total, the
performance of 19 forecasts are compared in this section, 11 individual and 8
combination forecasts.

Table 4 ranks all 19 forecasts based on both loss functions. It is evident that
the most accurate forecasts, irrespective of the loss function are the combina-

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