21

Autoregressive Conditional Duration

Models

1

Ruey S. Tsay

Abstract

This chapter studies the autoregressive conditional duration model. It discusses properties and
statistical inference of the model. It also considers some extensions to handle nonlinear durations
and interventions. For applications, we apply the model to daily range of the log price of Apple
stock and find that adopting the decimal system for the US stock price on January 29, 2001,
significantly reduces price volatility.

21.1 Introduction 1004
21.2 Duration models 1005
21.2.1 Properties of the EACD model 1006
21.2.2 Estimation of EACD models 1008
21.2.3 Additional ACD models 1008
21.2.4 Quasi-maximum likelihood estimates 1010
21.2.5 Model checking 1010
21.3 Some simple examples 1010
21.4 The diurnal pattern 1015
21.5 Nonlinear duration models 1019
21.5.1 The threshold autoregressive duration model 1019
21.5.2 Example 1020
21.6 The use of explanatory variables 1021
21.7 Conclusion 1024

21.1 Introduction

The autoregressive conditional duration (ACD) model was proposed by Engle and
Russell (1998) to model irregularly spaced financial transaction data. It has attracted
much interest among researchers and practitioners ever since, and has found many
applications outside of modeling transaction data. Duration is commonly defined
as the time interval between consecutive events, e.g., the time interval between
two transactions of a stock on the New York Stock Exchange or the difference
between arrival times of two customers at a service station. The duration between
two consecutive transactions in finance is important, for it may signal the arrival

1004