This paper proposes a new statistical model for the analysis of data which arrives 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. The model is applied to the arrival times of financial transactions 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, and examined from a market microstructure point of view.