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on stock market data, such as the price return,
volume and volatility.
into sequences and then use sequential pattern
mining techniques (Agrawal & Srikant 1995) to
find normal sequential patterns and exceptional
sequential patterns in stock markets.At first, every
time series is discretized into a sequence of “1”
and “0” or a sequence of digits or symbols (e.g.,
“up” and “down”). Then techniques for sequential
pattern mining are used to find frequent sequential
patterns P1.After that, we can use sequential patter
mining to find sequential patterns (P2) highly as-
sociated with known illegal trades, such as insider
trading and market manipulation. By comparing
P1 and P2, we can find which sequential patterns
are truly associated with exceptional trading and
which are associated with them by chance. The
above sequential pattern mining can be done to
find the sequential patterns in a single long time
series. It can also be done on multiple time series
of the same measure of many stocks. Moreover, it
is also interesting to mine for sequential patterns
on the multiple time series of a single stock on
multiple measures, such as price, volume, spread,
index, etc.
Statistical-Based Analysis
The statistical analysis is also possible to iden-
tify exception patterns on multiple time series. A
combination of counts, frequency, or distribution
of data may be a potential way of identifying the
exceptions. It is also challenging to define the
statistical measures on proper time slides. For
example, marking the close is a typical manipu-
lation in most stock exchanges. The manipulator
normally places a lot of small orders just near the
close of the market in order to influence the clos-
ing price change. Therefore, a possible method of
identifying this type of manipulation is to analyze
the combination of frequency of order, the price
change and times slide by statistical methods.
There are many complex relationships between
elements in stock market. It is more challeng-
ing to identify the abnormal behaviors hidden
in these elements. The Bayesian Networks or
Markov Chains are possible tools to discover the
relationship between multiple time series data on
stock markets.
concluSIon
Sequential Pattern Mining
for exception detection
Exception mining is very important for stock mar-
ket surveillance. This chapter has summarized the
literature of technologies which have been used or
researched for stock market surveillance. These
include the simplest rule-based approaches, basic
statistic approaches, outlier detections, graph clus-
tering, C4.5, logistic regression, neural networks,
etc. We also have presented our OMM (Outlier
Mining on Multiple time series) model, which im-
proves the accuracy of outlier mining by integrating
multiple time series. The proposed P-BOMM and
V-BOMM are proved to perform better than the
outlier mining on single time series.
There are still many open issues in this area. We
pointed out several potential research directions in
stock market surveillance. The financial knowledge,
in particular, the market microstructure theory, is
The traditional outliers in time series are statisti-
cally based and an outlier is a specific data point
corresponding to a specific time. For example,
one point is significantly different from the rest
of data. However, the exceptions in stock mar-
ket often spans over a period of time, and their
impacts on the stock prices, volumes, indexes,
etc., are also shown over a time span, instead
of at a single time point. For example, when an
insider trading happens, the price may change
abnormally over a long period of time. Therefore,
it would be more effective to detect exceptions
by analyzing the changing of time series over a
period of time. The idea is to convert time series
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