recent developments in high frequency financial ... - Index of

306 V. Voev
ACF
ACF
ACF
0.5
0.5
0.5
EK GE.AA GE.MO
0.4
0.4
0.4
Autocorrelation
0.1 0.2 0.3
Autocorrelation
0.1 0.2 0.3
Autocorrelation
0.1 0.2 0.3
0.0
0.0
0.0
20 24 28 32 36
0 4 8 12 16
lag
−0.1
20 24 28 32 36
0 4 8 12 16
lag
−0.1
20 24 28 32 36
0 4 8 12 16
lag
−0.1
ACF
ACF
ACF
0.5
0.5
0.5
GE.AXP GE.BA GE.CAT
0.4
0.4
0.4
Autocorrelation
0.1 0.2 0.3
Autocorrelation
0.1 0.2 0.3
Autocorrelation
0.1 0.2 0.3
0.0
0.0
0.0
20 24 28 32 36
0 4 8 12 16
lag
−0.1
20 24 28 32 36
0 4 8 12 16
lag
20 24 28 32 36
0 4 8 12 16
lag
−0.1
ACF
ACF
0.5
0.5
0.4
0.4
Autocorrelation
0.1 0.2 0.3
Autocorrelation
0.1 0.2 0.3
Autocorrelation
0.1 0.2 0.3
Fig. 2 Autocorrelation functions of the realized variance and covariance series.
to the forecast will produce a good forecast of the initial series. So there is a
trade-off between the possibility of including more information in the forecast and
obtaining positive definite matrices on the one hand, and the distortions caused by
the non-linearity of the transformation on the other. It turns out that in our case
the beneficial effects outweigh the negative ones. Figure 3 shows the drc− Chol
and the RiskMetrics TM forecast for the same nine variance and covariance series.
From the figure it is evident that the dynamic forecasts track the true series much
closer than the RiskMetrics TM forecasts, especially at the end of the period when the
(co)volatilities were more volatile. The dsrc − Chol forecast looks quite similar
ACF
0.5
GE.KO GE.EK GE
0.4
0.0
0.0
0.0
20 24 28 32 36
0 4 8 12 16
lag
−0.1
20 24 28 32 36
0 4 8 12 16
lag
−0.1
20 24 28 32 36
0 4 8 12 16
lag
−0.1