Modelling Irregularly Spaced Financial Data: Theory and Practice of Dynamic Duration Models

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.