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

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JBX HAL
Fig. 1 Histograms of the transaction price changes for Jack in the Box Inc. (JBX) and Halliburton
Company (HAL). The smallest possible price change is 0.01 US-Dollar
$17.5 billion) and considerable trade intensity, while JBX may be seen as representative
for a share with lower market capitalization (about US$2.5 billion) and
less trade intensity.
Figure 1 depicts the histograms for the transaction price changes for JBX and
HAL. Rather typical for transaction data is the large fraction of zero price changes
(around 60%). The remaining observations are proportioned between positive
(around 25%) and negative price changes (around 15%). With a significantly
higher frequency of positive one and two tick price jumps in comparison to the
negative one and two tick price changes, the distributions for both stocks turn out to
be somewhat skewed. Finally, we can observe price jumps of more than ±5 ticks for
11% (JBX) and 6% (HAL) of the transactions, which supports our view that both
modelling transaction returns as a continuous random variable and quantal response
representation, are too crude to pick up the true nature of the dependent
variable, and neglect valuable information about the true data generating process.
For JBX (HAL) the mean price change is given by 0.009 (−0.009) ticks, with
corresponding standard deviation of 3.367 (2.743) ticks. Figures 2 and 3 display
the autocorrelation functions of the price changes and the squared price changes for
both stocks. Considering the price changes, the few positive first autocorrelation
coefficients for JBX can be related to feedback trading and the first negative first
order autocorrelation coefficient for HAL can be related to the bid-ask bounce. The
bid-ask bounce refers to the fact that the transaction prices often bounce back and
forth between the ask and bid prices creating a negative autocorrelation in the
transaction price changes. 2 Figure 3 shows that the second moments for both
stocks are subject to positive serial dependence, which represents an expression of
volatility clustering in the transaction price changes.
2 See, for example, Campbell et al. (1997), Chap. 3.2.
R. Liesenfeld et al.