Modelling Irregularly Spaced Financial Data

1 Introduction.- 2 Point Processes.- 2.1 Basic Concepts of Point Processes.- 2.1.1 Fundamental Definitions.- 2.1.2 The Homogeneous Poisson Process.- 2.1.3 The Intensity Function and its Properties.- 2.1.4 Intensity-Based Inference.- 2.2 Types of Point Processes.- 2.2.1 Poisson Processes.- 2.2.2 Renewal Processes.- 2.2.3 Dynamic Point Processes.- 2.3 Non-Dynamic Point Process Models.- 2.3.1 Intensity-Based Models.- 2.3.2 Duration Models.- 2.3.3 Count Data Models.- 2.4 Censoring and Time-Varying Covariates.- 2.4.1 Censoring.- 2.4.2 Time-Varying Covariates.- 2.5 Outlook on Dynamic Extensions.- 3 Economic Implications of Financial Durations.- 3.1 Types of Financial Durations.- 3.1.1 Selection by Single Marks.- 3.1.2 Selection by Sequences of Marks.- 3.2 The Role of Trade Durations in Market Microstructure Theory.- 3.2.1 Traditional Market Microstructure Approaches.- 3.2.2 Determinants of Trade Durations.- 3.3 Risk Estimation based on Price Durations.- 3.3.1 Duration-Based Volatility Measurement.- 3.3.2 Economic Implications of Directional Change Durations.- 3.4 Liquidity Measurement.- 3.4.1 The Liquidity Concept.- 3.4.2 Volume Durations and Liquidity.- 3.4.3 The VNET Measure.- 3.4.4 Measuring (Il)liquidity Risks using Excess Volume Durations.- 4 Statistical Properties of Financial Durations.- 4.1 Data Preparation Issues.- 4.1.1 Matching Trades and Quotes.- 4.1.2 Treatment of Split-Transactions.- 4.1.3 Identification of Buyer- and Seller-Initiated Trades.- 4.2 Transaction Databases and Data Preparation.- 4.2.1 NYSE Trading.- 4.2.2 XETRA Trading.- 4.2.3 Frankfurt Floor Trading.- 4.2.4 Bund Future Trading at EUREX and LIFFE.- 4.2.5 ASX Trading.- 4.3 Statistical Properties of Trade, Limit Order and Quote Durations.- 4.4 Statistical Properties of Price Durations.- 4.5 Statistical Properties of (Excess) Volume Durations.- 4.6 Summarizing the Statistical Findings.- 5 Autoregressive Conditional Duration Models.- 5.1 ARMA Models for (Log-)Durations.- 5.2 The ACD Model.- 5.2.1 The Basic ACD Framework.- 5.2.2 QML Estimation of the ACD Model.- 5.2.3 Distributional Issues and ML Estimation of the ACD Model.- 5.2.4 Seasonalities and Explanatory Variables.- 5.3 Extensions of the ACD Framework.- 5.3.1 Augmented ACD Models.- 5.3.2 Theoretical Properties of Augmented ACD Models.- 5.3.3 Regime-Switching ACD Models.- 5.3.4 Long Memory ACD Models.- 5.3.5 Further Extensions.- 5.4 Testing the ACD Model.- 5.4.1 Simple Residual Checks.- 5.4.2 Density Forecast Evaluations.- 5.4.3 Lagrange Multiplier Tests.- 5.4.4 Conditional Moment Tests.- 5.4.5 Integrated Conditional Moment Tests.- 5.4.6 Monte Carlo Evidence.- 5.5 Applications of ACD Models.- 5.5.1 Evaluating ACD Models based on Trade and Price Durations.- 5.5.2 Modelling Trade Durations.- 5.5.3 Quantifying (Il)liquidity Risks.- 6 Semiparametric Dynamic Proportional Intensity Models.- 6.1 Dynamic Integrated Intensity Processes.- 6.2 The Semiparametric ACPI Model.- 6.3 Properties of the Semiparametric ACPI Model.- 6.3.1 Autocorrelation Structure.- 6.3.2 Evaluating the Estimation Quality.- 6.4 Extensions of the ACPI Model.- 6.4.1 Regime-Switching Dynamics.- 6.4.2 Regime-Switching Baseline Intensities.- 6.4.3 Censoring.- 6.4.4 Unobserved Heterogeneity.- 6.5 Testing the ACPI Model.- 6.6 Estimating Volatility Using the ACPI Model.- 6.6.1 The Data and the Generation of Price Events.- 6.6.2 Empirical Findings.- 7 Univariate and Multivariate Dynamic Intensity Models.- 7.1 Univariate Dynamic Intensity Models.- 7.1.1 The ACI Model.- 7.1.2 The Hawkes Model.- 7.2 Multivariate Dynamic Intensity Models.- 7.2.1 Definitions.- 7.2.2 The Multivariate ACI Model.- 7.2.3 The Multivariate Hawkes Model.- 7.3 Dynamic Latent Factor Models for Intensity Processes.- 7.3.1 The LFI Model.- 7.3.2 The Univariate LFI Model.- 7.3.3 The Multivariate LFI Model.- 7.3.4 Dynamic Properties of the LFI Model.- 7.3.5 SML Estimation of the LFI Model.- 7.3.6 Testing the LFI Model.- 7.4 Applications of Dynamic Intensity Models.- 7.4.1 Estimating Multivariate Price Intensities.- 7.4.2 Estimating Simultaneous Buy/Sell Intensities.- 7.4.3 Estimating Trading Intensities Using LFI Models.- 8 Summary and Conclusions.- A Important Distributions for Duration Data.- B List of Symbols (in Alphabetical Order).- References.