CHANGE DETECTION OF ORDERS IN STOCK MARKETS USING A GAUSSIAN MIXTURE MODEL

• Published date: 01 July 2014
• DOI: http://doi.org/10.1002/isaf.1356
• Date: 01 July 2014
• Author: Ryo Takahashi,Kiyoshi Izumi,Fujio Toriumi,Bungo Miyazaki

CHANGE DETECTION OF ORDERS IN STOCK MARKETS USING

A GAUSSIAN MIXTURE MODEL

†

BUNGO MIYAZAKI,

a

*KIYOSHI IZUMI,

a,b

FUJIO TORIUMI

a

AND RYO TAKAHASHI

c

a

The University of Tokyo, Bunkyō-ku, Tokyo, Japan

b

CREST, JST, Chiyoda-ku, Tokyo, Japan

c

Japan Exchange Group, Inc., Chūō-ku, Tokyo, Japan

SUMMARY

Wepropose a method for detecting changes in the order balance in stock markets by applying a stochastic model to

the feature vectors extracted from the order-book data of stocks. First, the data are divided into training and test

periods. Next, a Gaussian mixture model is estimated from the feature vectors extracted from the order-book data

in the training period. Finally, the goodness of fit of the feature vectors in the test period over this model is

calculated. Using the proposed method, we found that the order balances of stocks for which insider trading was

reported were unusual. Copyright © 2014 John Wiley & Sons, Ltd.

Keywords: Gaussian mixture model; stock market; order book; insider trading; change detection

1. INTRODUCTION

Illicit trading (price manipulation, insider trading, etc.) in financial markets is an important subject

academically. Research on illicit trading can be categorized as theoretical studies and empirical studies.

Examples of theoretical studies include Kyle (1985); Glosten and Milgrom (1985); Allen and Gale

(1992); Allen and Gorton (1992) and Pirrong (1993, 1995). Using formal models, these studies

theoretically demonstrated the possibility or conditions of occurrence of illicit trading. These kinds

of theoretical studies have developed to introduce more realistic assumptions to formal models or

derive more convincing results.

On the other hand, there are also a lot of empirical studies on illicit trading. Cumming, Johan, and Li

(2011) studied trading rules of stock exchanges around the world prohibiting illicit trading and showed

differences in exchange rules significantly affect liquidity of the market. Other than studies on

regulation or trading rules of exchanges, there are also a lot of studies analysing real market data

(e.g. price and volume) to investigate whether illicit trading is detectable, whether the manipulators

have gained profit, how much their activity has had an effect on the market, and so on. This paper

can be categorized as this kind of empirical study as we tried to detect a change of order situation

when there was insider trading in the Japanese stock market.

Some examples of empirical studies on illicit trading that analysed real market data are as follows.

Merrick, Naik, and Yadav (2005) analysed the relationship between March 1998 long-term UK futures

market and its deliverable issue market, and showed that market prices were distorted by a kind of

manipulation called ‘squeeze’and those who engaged in squeeze could profit from their manipulative

* Correspondence to: Bungo Miyazaki, The University of Tokyo, Bunkyo, Tokyo,Japan. E-mail: bmiyazaki@save.sys.t.u-tokyo.ac.jp

†

It should be noted that the opinions contained herein are solely those of the authors and do not necessarily reflect those of Japan

Exchange Group, Inc.

Copyright © 2014 John Wiley & Sons, Ltd.

INTELLIGENT SYSTEMS IN ACCOUNTING, FINANCE AND MANAGEMENT

Intell. Sys. Acc. Fin. Mgmt. 21, 169–191 (2014)

Published online 24 June 2014 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/isaf.1356

trading. Ni, Pearson, and Poteshman (2005) showed that stock prices tended to converge on the strike

price of related options on expiration dates, and provided evidence that stock price manipulation by

firm proprietary traders contributed to this convergence. Comerton-Forde and Putniņš (2011) tried to

detect closing price manipulation in stock markets. Based on their empirical findings, they proposed

a closing price manipulation index that measures probability and intensity of manipulation using

logistic regression. Beneish, Press, and Vargus (2012) investigated 462 firms that experienced technical

default and observed abnormal selling 1 year before the default of the firm, which might be firm

managers’insider information-based selling.

While these studies used traditional statistical or econometric methods, there are some studies that ap-

plied data mining techniques to analyse illicit trading. Donoho (2004) tried to detectinsider trading in the

option marketbefore the news breaks, comparingthe results of detection bya decision tree, logistic regres-

sion and a neuralnet (Donoho, 2004). Öğüt, Doğanay, andAktaş(2009) used data mining techniques such

as artificial neuralnetworks and a support vectormachine to detect stock pricemanipulation in the Turkish

market, and showed that these data mining techniques performed better than multivariate statistical

techniques. Diaz, Theodoulidis, and Sampaio (2011) analysed the intraday trade price data using a

decision-treealgorithm and identified new fraud manipulation patterns. These studiesproved that the data

mining technique can be used to detect illicit trading, and we used a Gaussian mixture model, which is a

data mining technique often used as a classification and novelty detection tool introduced l ater.

These studieson illicit trading mentioned abovemainly used macro data (e.g.price and trade volume) to

detect illicittrading or unusual situations.In this study,we used order-book data,explained later, whichhas

much more information than these macro data. This is the main difference of this paper from these

previous studies, and we assume that in using these order-book data a more sophisticated detection might

be possible.

In this paper, we propose a method for measuring the uniqueness of the order balance during a

specific test period using a stochastic model estimated from the order data during the training period

before the test period. For example, if many more orders have been placed at the best selling (or buying)

price than in the training period, it is considered that the order balance of the test period is unusual. We

tested four stocks for which insider trading before the announcements of capital increase was reported.

The expectation of capital increase and the anxiety about dilution of share value may change the order-

book balance through the increase in selling orders. It may be helpful for efficiently managing the

market to understand the order-book balance in a quantitative manner. This study will be applicable

for quantitatively analysing stock markets using order books.

The outline of this paper is as follows. Section 2 discusses related studies, such as those that analysed

order books and those that used Gaussian mixture models. Section 3 explains our proposed method.

First, the entire period of data is divided into training and test periods. Next, a Gaussian mixture model

is estimated from the feature vector sequence extracted from the order-book data in the training period.

Finally,the goodness of fit of the feature vector sequence in the test period over this model is calculated.

Section 4 explains the results of this study. We analysed four stocks for which insider trading was

reported and compared them with other stocks of the same industry category and with the same stocks

of other periods. Finally, Section 5 gives the conclusions of this study.

2. PREVIOUS RESEARCH

We applied a stochastic model to the feature vector extracted from order-book data. Nishioka, Toriumi,

and Ishii (2009) took a similar approach. They extracted the orders in a certain period from order-book

170 B. MIYAZAKI ETAL.

Copyright © 2014 John Wiley & Sons, Ltd. Intell. Sys. Acc. Fin. Mgmt., 21, 169–191 (2014)

DOI: 10.1002/isaf