MSE |
_________QLIKE____ | ||
ARMA |
1.659 |
ARFIMA |
3159.2 |
ARFIMA |
1.667 |
ARMA |
3174.3 |
GARCHRV |
1.952 |
SVRV |
3222.5 |
GJRRV |
2.161 |
VIX |
3253.0 |
GJRRVG |
2.404 |
GARCHRV |
3266.6 |
VIX |
2.525 |
GJRRV |
3278.7 |
GARCH |
2.575 |
GARCH |
3472.5 |
SV |
2.730 |
GJR |
3575.7 |
GJR |
2.857 |
GJRRVG |
3700.7 |
SVRV |
4.543 |
SV_______ |
3923.0 |
Table 1: Loss function rankings for individual forecasts.
Model |
Tr |
MCS |
TSQ |
MCS |
P |
Pl |
P |
Pl | |
SVRV |
0.013 |
0.013 |
0.005 |
0.005 |
GJR |
0.016 |
0.016 |
0.005 |
0.005 |
SV |
0.016 |
0.016 |
0.002 |
0.005 |
GARCH |
0.011 |
0.016 |
0.003 |
0.005 |
VIX |
0.011 |
0.016 |
0.004 |
0.005 |
GJRRVG |
0.009 |
0.016 |
0.000 |
0.005 |
GJRRV |
0.005 |
0.016 |
0.000 |
0.005 |
GARCHRV |
0.008 |
0.016 |
0.006 |
0.006 |
ARFIMA |
0.844 |
0.844 |
0.844 |
0.844 |
ARMA |
_ |
1.000 |
_ |
1.000 |
Table 2: MCS results for individual forecasts given the MSE loss function.
The first row respresents the first model removed, down to the best performing
model in the last row.
that incorporate RV measures into the volatility equation are more accurate
out-of-sample than those that do not.
MCS results will now reveal whether the VIX is significantly inferior to
those forecasts with lower average loss.
Table 2 reports the MCS results for the individual forecasts based on the
MSE loss function. It turns out that the model with the largest T⅛ test statistic
is the SVRV model. The p-value, determined in the first reduction round is
0.013. As it is eliminated in the first round this automatically determines the
17
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