recent developments in high frequency financial ... - Index of
recent developments in high frequency financial ... - Index of
recent developments in high frequency financial ... - Index of
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188<br />
Table 3 ML estimates <strong>of</strong> the logistic ACM-ARMA model with microstructure variables and nonsymmetric<br />
response coefficients*<br />
Par. JBX HAL<br />
Estimate Std. dev. Estimate Std. dev.<br />
μ1 −0.5443 0.2146 −0.0684 0.0079<br />
μ2 −0.6294 0.2470 −0.0806 0.0087<br />
(1)<br />
c1 0.8319 0.0628 1.1283 0.0277<br />
(2)<br />
c1 −0.1738 0.0275<br />
a11<br />
(1)<br />
0.1494 0.0366 0.1157 0.0148<br />
a12<br />
(1)<br />
0.0561 0.0269 0.1648 0.0138<br />
(1)<br />
a21 0.1798 0.0442 0.3795 0.0137<br />
(1)<br />
a22 0.1075 0.0233 0.0431 0.0146<br />
a11<br />
(2)<br />
−0.0047 0.0153<br />
a12<br />
(2)<br />
−0.1053 0.0139<br />
(2)<br />
a21 −0.2967 0.0139<br />
(2)<br />
a22 0.0653 0.0150<br />
gv1<br />
(0)<br />
0.1969 0.0316 0.1073 0.0111<br />
gv2<br />
(0)<br />
0.2259 0.0312 0.1960 0.0112<br />
(0)<br />
gt1 0.3499 0.0251 0.2599 0.0132<br />
(0)<br />
gt2 0.3289 0.0253 0.1546 0.0133<br />
gv1<br />
(1)<br />
−0.0792 0.0327 −0.0761 0.0112<br />
gv2<br />
(1)<br />
−0.0262 0.0316 −0.0949 0.0114<br />
(1)<br />
gt1 (1)<br />
−0.0001 0.0238 −0.0106 0.0132<br />
g t2<br />
0.0546 0.0234 0.0298 0.0132<br />
Log-lik. −0.885792 −0.990106<br />
SIC 0.897808 0.993094<br />
Q(30) 125.6 (0.106) 169.9 (0.000)<br />
Q(50) 211.1 (0.109) 269.3 (0.001)<br />
Res. mean (−0.003, −0.001) (0.001, −0.002)<br />
Res. var. 0:898 0:035<br />
0:035 1:092<br />
0:886 0:044<br />
0:044 1:141<br />
*Dependent variable is the direction <strong>of</strong> the price changes, D i, p-values <strong>in</strong> brackets<br />
R. Liesenfeld et al.<br />
IBM transaction prices. In particular, they also f<strong>in</strong>d a positive impact <strong>of</strong> transaction<br />
volume and time between transactions on the activity <strong>of</strong> transaction prices.<br />
Table 4 reports the estimation results <strong>of</strong> the augmented GLARMA model for<br />
the absolute (non-zero) price changes. We f<strong>in</strong>d no evidence for a strong leverage<br />
effect when account<strong>in</strong>g for lagged effects. For both shares the contemporaneous<br />
effect <strong>of</strong> Di on the volatility measure S i is negative, support<strong>in</strong>g the hypothesis <strong>of</strong> a<br />
leverage effect. But this effect is completely over-compensated for <strong>in</strong> JBX and<br />
nearly compensated for <strong>in</strong> HAL by the positive effect <strong>of</strong> D i−1. This result stands <strong>in</strong><br />
contrast to the f<strong>in</strong>d<strong>in</strong>gs by Rydberg and Shephard (2003) who f<strong>in</strong>d a leverage effect<br />
for transaction prices <strong>of</strong> the IBM share traded at the NYSE. Aga<strong>in</strong>, volume and<br />
transaction rate have a positive impact on the size <strong>of</strong> the price changes. S<strong>in</strong>ce the<br />
size <strong>of</strong> the price changes as well as the probability <strong>of</strong> a non-zero price change are<br />
volatility measures, our previous conclusions based upon the ACM component
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