Intraday Duration Models

Abstract

In Chapter 2 we have defined different types of durations that are of interest for the analysis of stock market intraday activity from the viewpoint of characterizing the trading frequency, the volatility, and the liquidity of a market. We also highlighted the main stylized facts of durations: a regular intraday seasonality, and after correcting the data for this pattern, clustering and overdispersion (underdispersion for volume durations). The object of this chapter is to set out econometric models that are compatible with the stylized facts. In Section 2, we introduce some basic statistical concepts relevant to the analysis of durations and make briefly the link with point processes, i.e. collections of points randomly distributed along a time axis. In Section 3, we introduce the class of autoregressive conditional duration models and their logarithmic versions. The models are carefully defined, and their properties are investigated, using a mix of analytical and numerical methods. The estimation of these models by the maximum likelihood method is briefly reviewed, and tools for testing the specification of a model are developed. In Section 4, we provide empirical results that illustrate the estimation and testing procedures. The illustration is done on trade, price, and volume durations of several stocks listed on the NYSE. Applications of the same models to test microstructure effects are pursued in Chapter 4.