The Econometrics of Sequential Trade Models: Theory and Applications Using High Frequency Data

197 Pages·2004·5.068 MB·English

by  Stefan Kokot (auth.)

Lecture Notes in Economics
and Mathematical Systems 538
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Stefan Kokot
The Econometrics
of Sequential Trade Models
Theory and Applications
Using High Frequency Data
Springer
Author
Stefan Kokot
Am Schlagsbach 13
63303 Dreieich
Germany
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ISSN 0075-8442
ISBN 978-3-540-20814-3 ISBN 978-3-642-17115-4 (eBook)
DOI 10.1007/978-3-642-17115-4
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It does take maturity to realize that models are to be used but
not to be believed.
- Henri Theil!
1 Theil (1971), p. vi.
Preface
The present study has been accepted as a doctoral thesis by the Depart
ment of Economics of the Johann Wolfgang Goethe-University in Frankfurt
am Main. It grew out from my five year long participation in two research
projects, "Econometric analysis of transaction intensity and volatility on fi
nancial markets", and "Microstructure on financial markets", that were both
conducted by the chair of Statistics and Econometrics (Empirical Economic
Research) at the Department of Economics and Business Administration, Jo
hann Wolfgang Goethe-University in Frankfurt am Main and financed by the
state of Hessen.
During this time I have benefitted from many people. First and foremost
I would like to thank my thesis supervisor, Prof. Dr. Reinhard Hujer, for
initiating and supporting my studies with great encouragement. I am also
very grateful to Prof. Dr. Christian Schlag for acting as the second thesis
supervisor. Furthermore, I wish to thank Prof. Dr. Joachim Grammig who
introduced me to the topics covered in this study in the first place and helped
me to sharpen my views on econometrics and financial market microstructure
theory through many discussions and also through his willingness to work
with me on several related studies.
I also want to thank my former colleagues at the chair of Statistics and
Econometrics Dr. Kai-Oliver Maurer and Dr. Marc Wellner. I have worked
with both of them on several working papers and have greatly benefitted from
their outstanding wisdom and experience. The same holds true for my present
colleagues, especially for Sandra Vuletic, who worked with me on a paper that
is most intimately related to the topics of the present study. In addition, I have
to thank her and Dr. Marc Wellner for proof reading the whole manuscript
with great care. Thanks also go to Marco Caliendo, Dubravko Radic, Stephan
Thomsen, Christopher Zeiss, Irene Kisters-Ostheimer, who sadly passed away,
and Birgit Andres-Kreiner for providing me an environment, in which I was
able to work hard, live fast, and sometimes laugh until coffee came running
out my nose.
VIn Preface
Furthermore I want to thank all our student assistants at the chair, espe
cially Filiz Polat, Paulo Rodrigues, Daniel Ueberall, and Oliver Wiinsche, who
lend me a hand for many rather unpleasant tasks ("Oh no, not your *#!&7
graphics again ... "). Before I started to work on my doctoral thesis, I had the
great pleasure to participate on a research project entitled " Long-Term Care
in the EU" , financed by the Volkswagenstiftung and conducted by the chair of
Economic Policy and Labor Economics, and I want to thank Prof. Dr. Roland
Eisen, and Hans-Christian Mager for their close cooperation.
Finally, I wish to express my deepest gratitude to the whole Kokot-clan
(German section) for always supporting me enthusiastically, even though I
started to behave somewhat strange during the course of this project. I am
especially indebted to my mother Tereza, my father Dragutin, my sister Irene,
and to Thaja Kokot for their love and guidance throughout my whole life.
Without you, none of this would have been possible.
Dreieich, November 2003 Stefan Kokot
Contents
Contents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. IX
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1
2 Trading Mechanisms on Financial Markets. . . . . . . . . . . . . . . .. 5
2.1 Typology of Security Markets. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5
2.2 Market Participants and Institutional Setup on the NYSE . . .. 9
2.2.1 Market Participants ............................... 9
2.2.2 Handling of Orders and Execution. . . . . . . . . . . . . . . . . .. 10
2.2.3 Order Routing and Information Systems ............. 13
3 Sequential Trade Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 15
3.1 Market Microstructure Theory. . . . . . . . . . . . . . . . . . . . . . . . . . .. 15
3.2 Microstructure Models of the Black Box under Asymmetric
Information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17
3.2.1 Sequential Trade Models . . . . . . . . . . . . . . . . . . . . . . . . . .. 17
3.2.2 Walrasian Batch Models. . . . . . . . . . . . . . . . . . . . . . . . . . .. 20
3.2.3 Critical Assessment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 22
3.3 The Basic Sequential Trade Model. . . . . . . . . . . . . . . . . . . . . . . .. 24
3.4 Extensions ............................................. 27
3.4.1 Trade Size Effects, No-Trading Events, and History
Dependence ...................................... 27
3.4.2 Discriminating Between Market and Limit Orders. . . .. 33
3.4.3 Models for Dually Listed Assets. . . . . . . . . . . . . . . . . . . .. 37
3.5 Estimation of Structural Models .......................... 43
3.5.1 Estimation of the Basic Model Using Information on
Buys and Sells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 43
3.5.2 Estimation of the Basic Model Using Information on
Trades ........................................... 44
3.5.3 Estimation of Related Models. . . . . . . . . . . . . . . . . . . . . .. 47
X CONTENTS
3.6 Results of Previous Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 50
4 Econometric Analysis of Sequential Trade Models ......... 61
4.1 The EKOP Model and Finite Mixture Models ............... 61
4.1.1 Motivation ....................................... 61
4.1.2 An Alternative Version of the EKOP Model .......... 64
4.1.3 A Multivariate Finite Mixture Poisson Regression Model 67
4.1.4 A Mixture Regression Model Based on the Negative
Binomial Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 71
4.1.5 Accounting for Intraday Seasonality ................. 73
4.1.6 Autoregressive Specification of the Conditional Mean
Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 74
4.1.7 A Markov Switching Approach ...................... 76
4.2 Model Evaluation and Specification Testing. . . . . . . . . . . . . . . .. 82
4.2.1 Specification Tests in Static Mixture and Markov
Switching Models ................................. 82
4.2.2 Determining the Number of Regimes ................. 84
4.2.3 A Conditional Moment Test for Goodness of Fit. . . . . .. 86
4.2.4 Testing Parameter Restrictions. . . . . . . . . . . . . . . . . . . . .. 87
4.2.5 Testing for Autocorrelation. . . . . . . . . . . . . . . . . . . . . . . .. 89
4.3 Mixture and Regime Switching Models in Econometrics .. . . .. 91
5 Empirical Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 93
5.1 The TAQ Database ...................................... 93
5.2 The Trade Direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 96
5.2.1 Algorithms for the Determination of the Trade Direction 96
5.2.2 Empirical Evidence on the Accuracy of Classification .. 98
5.2.3 Classification of Trades ............................. 103
5.3 Descriptive Statistics ..................................... 106
5.4 Estimation Results ...................................... 112
5.4.1 Model Selection ................................... 112
5.4.2 Parameter Estimates ............................... 120
5.4.3 Specification Tests ................................. 129
5.4.4 Classification of Regimes ........................... 135
5.4.5 Testing Parameter Restrictions ...................... 142
6 Conclusions ................................................ 145
Appendix ...................................................... 147
A.l The Poisson Process ..................................... 149
A.2 Maximum Likelihood Estimation of a Multivariate Poisson
Mixture Model .......................................... 151
A.3 The EM-Algorithm ...................................... 153
A.4 The Poisson Regression Model ............................ 156
A.5 The Negative Binomial Regression Model ................... 157
CONTENTS XI
A.6 Moments of Mixture Distributions ......................... 160
A.7 Unobserved Individual Variation of Trade Arrival Rates ...... 167
A.8 Markov Chains .......................................... 169
A.9 The Smoothing Algorithm ................................ 172
A.I0 Estimation of Transition Probabilities in the Markov
Switching Model ........................................ 173
A.ll Moments of the Dependent Variable in a Markov Switching
Model .................................................. 174
References ..................................................... 177
List of Figures ................................................. 189
List of Tables .................................................. 191