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



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 Ttest 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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