The Econometrics of Sequential Trade Models

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.

Contenu

1 Introduction.- 2 Trading Mechanisms on Financial Markets.- 2.1 Typology of Security Markets.- 2.2 Market Participants and Institutional Setup on the NYSE.- 2.2.1 Market Participants.- 2.2.2 Handling of Orders and Execution.- 2.2.3 Order Routing and Information Systems.- 3 Sequential Trade Models.- 3.1 Market Microstructure Theory.- 3.2 Microstructure Models of the Black Box under Asymmetric Information.- 3.2.1 Sequential Trade Models.- 3.2.2 Walrasian Batch Models.- 3.2.3 Critical Assessment.- 3.3 The Basic Sequential Trade Model.- 3.4 Extensions.- 3.4.1 Trade Size Effects, No-Trading Events, and History Dependence.- 3.4.2 Discriminating Between Market and Limit Orders.- 3.4.3 Models for Dually Listed Assets.- 3.5 Estimation of Structural Models.- 3.5.1 Estimation of the Basic Model Using Information on Buys and Sells.- 3.5.2 Estimation of the Basic Model Using Information on Trades.- 3.5.3 Estimation of Related Models.- 3.6 Results of Previous Studies.- 4 Econometric Analysis of Sequential Trade Models.- 4.1 The EKOP Model and Finite Mixture Models.- 4.1.1 Motivation.- 4.1.2 An Alternative Version of the EKOP Model.- 4.1.3 A Multivariate Finite Mixture Poisson Regression Model.- 4.1.4 A Mixture Regression Model Based on the Negative Binomial Distribution.- 4.1.5 Accounting for Intraday Seasonality.- 4.1.6 Autoregressive Specification of the Conditional Mean Function.- 4.1.7 A Markov Switching Approach.- 4.2 Model Evaluation and Specification Testing.- 4.2.1 Specification Tests in Static Mixture and Markov Switching Models.- 4.2.2 Determining the Number of Regimes.- 4.2.3 A Conditional Moment Test for Goodness of Fit.- 4.2.4 Testing Parameter Restrictions.- 4.2.5 Testing for Autocorrelation.- 4.3 Mixture and Regime Switching Models in Econometrics.- 5 Empirical Results.- 5.1 The TAQ Database.- 5.2 The Trade Direction.- 5.2.1 Algorithms for the Determination of the Trade Direction.- 5.2.2 Empirical Evidence on the Accuracy of Classification.- 5.2.3 Classification of Trades.- 5.3 Descriptive Statistics.- 5.4 Estimation Results.- 5.4.1 Model Selection.- 5.4.2 Parameter Estimates.- 5.4.3 Specification Tests.- 5.4.4 Classification of Regimes.- 5.4.5 Testing Parameter Restrictions.- 6 Conclusions.- A.l The Poisson Process.- A.2 Maximum Likelihood Estimation of a Multivariate Poisson Mixture Model.- A.3 The EM-Algorithm.- A.4 The Poisson Regression Model.- A.5 The Negative Binomial Regression Model.- A.6 Moments of Mixture Distributions.- A.7 Unobserved Individual Variation of Trade Arrival Rates.- A.8 Markov Chains.- A.9 The Smoothing Algorithm.- A.1O Estimation of Transition Probabilities in the Markov Switching Model.- A.11 Moments of the Dependent Variable in a Markov Switching Model.- References.- List of Figures.- List of Tables.