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Order aggressiveness and order book dynamics 147
5 Empirical results
As the estimation of six-dimensional ACI processes is a challenging task requiring
the estimation of a large number of parameters, we estimate restricted ACI
specifications. In order to reduce the number of parameters, we specify the baseline
intensity functions in terms of a Weibull parameterization, where we do not allow
for interdependencies between the individual functions, i.e. pr k =1∀k ≠ r. This
restriction is motivated by the fact that the consideration of interdependencies
would require estimating 30 additional parameters without significantly improving
the model’s goodness-of-fit in terms of the BIC. Similar arguments hold for the
specification of spill-over effects in the persistence terms, where we restrict the
matrix B to be specified as a diagonal matrix. In order to account for deterministic
intra-day seasonality patterns, we specify three linear spline functions for the
processes of aggressive market orders, limit orders, and cancellations based on 1 h
nodes. 11 To ease the numerical optimization of the log-likelihood function, we
standardize the time scale by the average duration of the pooled process.
To test the economic hypotheses formulated in Sect. 2, we define several
explanatory variables to capture the state of the market. The market depth on the
ask side is measured by the (log) ratio between the current 5% ask volume quantile
and the corresponding price impact, formally given by AD=ln[0.05·avol/
(p0.05,a−mq)], where avol denotes the aggregated volume pending on the ask queue,
p 0.05,a is the limit price associated with the 5% ask volume quantile and mq denotes
the mid-quote. Correspondingly, the bid depth is given by BD=ln[0.05·bvol/(mq−
p 0.05,b)]. The choice of the 5% quantile is driven by the trade-off between a
parsimonious specification 12 and an appropriate measurement of market depth.
However, recent studies (see e.g. Pascual and Veredas 2004 or Hall and Hautsch
2004) show that traders’ order submission is dictated by the depth in the lower
sections of the book. Therefore, we presume that the impact of market depth is well
approximated by the volume–price relation over the 5% volume quantile. In order
to account not only for the volume–price ratio solely, but also for the volume level
itself, we include AV=ln(avol) and BV=ln(bvol ) as separate regressors.
Furthermore, we capture the (signed) cumulative changes in the logarithmic
aggregated ask volume (DAV), the logarithmic aggregated bid volume (DBV) as
well as in the mid-quote (MQ) process during the past 5 min. Finally, we include
the current volatility (VL), measured by the average squared mid-quote changes
during the past 5 min as well as the current bid-ask spread (SP).
In order to analyze the importance of order book dynamics and the information
provided by the open limit order book for the goodness-of-fit and the explanatory
power of the model, we estimate three different specifications. Table 4 reports the
estimation results based on an ACI model including both dynamic variables as well
as order book variables. Table 5 is based on a specification which includes order
book information, but does not account for any dynamics in the multivariate
process. Hence, in this specification, e i is set to zero. Finally, Table 6 gives the
results of a specification which accounts for dynamic structures but excludes any
order book covariates.
11 However, motivated by the results by Hall and Hautsch (2004), we assume identical seasonality
patterns on the ask and bid side.
12 Note that for each regressor six parameters have to be estimated.