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

Exchange rate volatility and the mixture of distribution hypothesis 19
Table 5 Regressions of log of realised NOK/EUR volatility
(3) (14) (15)
Est. Pval. Est. Pval. Est. Pval.
Const. −1.012 0.00 −1.690 0.00 −1.916 0.02
r
vt−1 0.405 0.05 0.643 0.00 0.483 0.00
r
vt−2
0.078 0.29 0.014 0.81 0.047 0.36
r
vt−3
0.104 0.04 0.086 0.07 0.085 0.05
r
vt−4 −0.059 0.25 −0.065 0.16 −0.050 0.28
r
vt−5 0.122 0.00 0.087 0.03 0.069 0.08
qt 0.139 0.03 0.173 0.02
Δ qt 0.876 0.00 0.725 0.00
r
mt 0.194 0.00
r
ot −0.021 0.62
xt r
0.070 0.08
ut r
−0.007 0.85
a
ft −0.256 0.63
b
ft 1.403 0.00
id 4.275 0.00 3.777 0.00 3.985 0.00
sdt 0.659 0.00 0.382 0.00 0.532 0.00
et−1 −0.130 0.53 −0.380 0.00 −0.238 0.03
R 2
0.53 0.57 0.60
AR1−10 0.86 0.57 1.17 0.31 0.81 0.62
ARCH1−10 0.44 0.93 1.34 0.20 1.15 0.32
Het. 6.16 0.91 10.91 0.82 33.69 0.21
Hetero. 30.94 0.27 50.15 0.24 128.63 0.10
JB 3.15 0.52 0.44 0.80 0.47 0.79
Obs. 568 568 568
See Table 4 for details
support the idea that exchange rate variability increases with the number of information
events, and the results suggest the impact is higher for weekly than for
realised volatility. There might be a small caveat in the realised case though. The
MA(1) term e t−1 is needed in Eqs. (14) and (15) in order to account for residual
serial correlation at lag 1 induced by the inclusion of Δq t. We have been unsuccessful
so far in identifying why Δq t induces this serial correlation, and excluding
Δq t from (15) also removes the signs of heteroscedasticity indicated by
White’s (1980) test with cross products in the sense that the p-value increases from
10% to 24%.
2. Number of traders. The hypothesised effect of an increase in the number of
traders as measured by qt is negative, but in all the four specifications in which it is
included it comes out positive. Moreover, it is significantly positive at 5% in
both realised specifications. Figure 3 aims at throwing light on why we obtain these
unanticipated results and contains recursive OLS estimates of the impact of q t with
approximate 95% confidence bands. In the weekly case the value starts out negative,
but then turns positive and stays so for the rest of the sample. However, it
descends steadily towards the end. In the realised case, the value is positive all the