Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data

TLDR

The paper introduces the autoregressive conditional duration (ACD) model to analyze irregularly spaced transaction data. The ACD model treats inter‑event durations as a stochastic process with a conditional intensity that depends on past durations, extending self‑exciting point processes and enabling estimation of quasi‑maximum likelihood parameters and application to trade arrivals, price changes, and volatility. Empirical analysis of financial transaction data shows strong duration clustering, with both deterministic time‑of‑day and stochastic effects playing significant roles.

Abstract

This paper proposes a new statistical model for the analysis of data which arrive at irregular intervals. The model treats the time between events as a stochastic process and proposes a new class of point processes with dependent arrival rates. The conditional intensity is developed and compared with other self-exciting processes. Because the model focuses on the expected duration between events, it is called the autoregressive conditional duration (ACD) model. Asymptotic properties of the quasi maximum likelihood estimator are developed as a corollary to ARCH model results. Strong evidence is provided for duration clustering for the financial transaction data analyzed; both deterministic time-of-day effects and stochastic effects are important. The model is applied to the arrival times of trades and therefore is a model of transaction volume, and also to the arrival of other events such as price changes. Models for the volatility of prices are estimated with price-based durations, and examined from a market microstructure point of view.