Introduction

In most of the models previously discussed, the dependent variable, yt, is assumed to be a continuous random variable. There are a number of situations where the continuity assumption is inappropriate and alternative classes of models must be specified to explain the time series features of discrete random variables. This chapter reviews the important class of discrete time series models commonly used in microeconometrics namely the probit, ordered probit and Poisson regression models. It also discusses some recent advances in the modelling of discrete random variables with particular emphasis on the binomial thinning model of Steutel and Van Harn (1979) and the Autoregressive Conditional Duration (ACD) model of Engle and Russell (1998), together with some of its extensions.

Motivating Examples

Recent empirical research in financial econometrics has emphasised the importance of discrete random variables. Here, data on the number of trades and the duration between trades are recorded at very high frequencies. The examples which follow all highlight the need for econometric models that deal with discrete random variables by preserving the distributional characteristics of the data.

Example 21.1 Transactions Data on Trades

Table 21.1 provides a snapshot of transactions data recorded every second, on the United States stock AMR, the parent company of American Airlines, on 1 August 2006. Three examples of discrete random variables can be obtained from the data in Table 21.1.