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Modelling financial transaction price movements: a dynamic integer count data model 187
hypothesis of Diamond and Verrecchia (1987) who predict a negative correlation
between price changes and the time between transactions. Hence, one would
expect asymmetric effects on the probabilities of a certain price reaction. 14
In a similar way, the transaction rate and the transaction volume are introduced
into the model as conditioning information for the size of the price changes (2.23):
ln !i ¼ d0Di þ d1Di 1 þ v 0Vi þ v1Vi 1 þ t0Ti þ t1Ti 1 þ i: (3.3)
Note that the conditional distribution of the price change Pr Yi ¼ yijZi; F y;z
h i
ð Þ
resulting from the specifications (3.2) and (3.3) does not explicitly rest on a
structural theoretical model for the joint process of price changes, volume, and
transaction rates, which would treat each of these variables as an endogenous
quantity. Equations (3.2) and (3.3), rather, reflect ad-hoc assumptions with respect
to the distribution of the price changes conditional on volume and transaction rate
(as it could result from a joint distribution of these variables). Correspondingly,
the estimated relations cannot be interpreted as structural economic relations.
Nevertheless, the augmented ICH model can serve as an instrument for capturing
and quantifying the relationship between important marks of the trading process.
This allows us to shed light on the empirical relevance of the theoretical implications
sketched above.
Tables 3 and 4 contain the estimation results for the augmented ICH model with
the transaction rate and trading volume as additional covariates. For the two submodels,
we have chosen the same order of the process that was found to be optimal
for the pure time series specification. In the price direction model (Table 3) both log
trading volume Vi and the log time between transactions T i have a significantly
positive impact on the log–odds ratios (i.e., the probability that the transaction price
changes increases with the size of the transaction volume and the time between
transactions). Since the probability of a nonzero price change can be interpreted as
a specific measure of price volatility, it implies that low transaction rates go along
with higher price volatility. This provides empirical support for the implications of
the model proposed by Diamond and Verrecchia (1987), where no transactions
indicate bad news, which contradicts the theoretical implications of Easley and
O’Hara (1992) where no transactions indicate lack of news in the market. Our
finding that high transaction volumes are positively correlated with volatility is
consistent with the implication of the model proposed by Easley and O’Hara
(1987), where large volumes correspond to the existence of additional news in the
market. The effect of volume on the probability of a price change is partly compensated
for by the subsequent transaction. The effect of the transaction time on the
probability of a price change is asymmetric in the sense that the major reaction for
negative price change occurs immediately, while parts of the reaction on log–odds
ratio for a positive price change occurs also with the subsequent transaction. This
interesting reaction pattern holds for JBX and HAL.
Finally, the inclusion of the microstructure variables greatly improves the value
of the Schwarz criterion, but worsens the dynamic properties of the model as
indicated by the Q-statistics. Our empirical results for the direction of the price
changes are in accordance with those put forth by Rydberg and Shephard (2003) for
14 The LR-test clearly rejects the null hypothesis of symmetric price reactions.
i 1