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

Exchange rate volatility and the mixture of distribution hypothesis 23
Fig. 4 Recursive estimates of b7 in the parsimonious specifications Eqs. (16) and (17).
Computations in PcGive 10.4 with OLS and initialisation at observation number 50
(1.66−0.67=0.99) than in the realised (0.98−0.47=0.51). Both graphs appear to be
trending downward for most of the sample, the exception being towards the end in
the weekly case, and in both graphs there seems to be a distinct shift downwards as
the change to partial inflation targeting takes place in the beginning of 1999. One
should be careful however in attributing the shift to the change in regime without
further investigation. Indeed, another possible reason is the transition to the euro,
since Δqt attains both its maximum and minimum in the first weeks of 1999.
3.2 EGARCH analysis
The estimates of the three EGARCH specifications which we report have all equal
mean-specification rt=br ¼ þ et ¼ þ tzt , where rt=log(St/St−1) is the weekly
return, br ¼ 0:007615 is the sample standard deviation of the returns, and where
{z t} t=1,572 is an IID sequence. For exchange rates it is also common to include an
AR(1) term in the mean-equation in order to account for the possibility of negative
serial correlation in the returns. In our data however there are signs that this term
induces serial correlation in either the standardised residuals or in the squared
standardised residuals or in both. So we do not include it in the specifications
reported here. The three EGARCH specifications can be considered as the ARCH