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Modelling financial transaction price movements: a dynamic integer count data model 185
for HAL a richer GLARMA(2,2) yields the best goodness of fit in terms of the
Schwarz criterion.
For all estimates, the dispersion parameter κ −1/2 is significantly different from
zero so that we have to reject the null of a truncated-at-zero Poisson distribution in
favor of a Negbin distribution. The parameters for the ARMA components are
significant as well. For JBX the estimates for the roots of the AR components
are 0.8753 (plain model) and 0.9275 (flexible model), so that stationarity is
guaranteed. For HAL the implicit estimates for the two roots 11 of the AR components
are 0.8452 and −0.4631 (plain model) and 0.9649 and 0.5409 (flexible
model), so that stationarity is guaranteed as well. Since for both stocks roots are
close to one, the GLARMA model predicts a strong persistence in the non-zero
absolute price changes.
For both data sets the specification allowing for more flexible news impacts are
superior to the ones with standard news impact curves. The coefficients on ∣ɛi−1∣
are significantly positive, but also the fit of the observed dynamics improves over
the specification ignoring the possibility of the additional news impact component.
For HAL the effect is considerably lowered by a negative effect on ∣ɛ i − 2∣.
The value of Ljung-Box Q-statistics for the standardized residuals e i reported in
Table 2 indicate that the GLARMA(1,1)-dynamics chosen for the JBX absolute
price changes does not remove autocorrelation in the residuals completely. However,
based on the Q(50)-statistic for the flexible GLARMA(2,2)-specification for
HAL the null of no serial correlation in the residuals cannot be rejected at the 1%
level.
3 Transaction price dynamics and market microstructure
One of the fundamental questions of the market microstructure theory of financial
markets is concerned with the determinants of the price process and the specific
role of the institutional set-up. 12 Generally, the goal is to figure out how new price
relevant information affects the price process. Approaches based on the rational
expectation hypothesis typically assume some kind of heterogeneity among the
market participants with respect to their level of information. The corresponding
transaction process generally leads to successive revelations of price information.
This leads to empirically testable hypotheses about the joint process of transaction
price changes and other marks of the trading process, such as transaction intensities
and transaction volume.
Provided that short-selling is infeasible, Diamond and Verrecchia (1987) infer
that longer times between transactions can be taken as a signal for the existence
of bad news implying negative price reactions. The absence of a short selling
mechanism prevents market participants from profiting by exploiting the negative
information through corresponding transactions. Therefore, one can expect that
low transaction rates (longer times between transactions) are associated with
higher volatility in the transaction price process and vice versa.
11 Computed as z1;2 ¼ 1
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 2
2 2 1 þ 4 p
2:
12 See O’Hara (1995) for a comprehensive survey on the theoretical literature on market
microstructure.