Dynamics of trade-by-trade price movements: decomposition and models

In this paper we introduce a decomposition of the joint distribution of price changes of assets recorded trade--by--trade. Our decomposition means that we can model the dynamics of price changes using quite simple and interpretable models which are easily extended in a great number of directions, including using durations and volume as explanatory variables. Thus we provide an econometric basis for empirical work on market microstructure using time series of transactions data. We use maximum likelihood estimation and testing methods to assess the fit of the model to a year of IBM stock price data taken from the New York Stock Exchange.