Analysis of Financial Time Series, Third Edition

5.4 Models for Price Changes

The discreteness and concentration on “no change” make it difficult to model the intraday price changes. Campbell et al. (1997) discuss several econometric models that have been proposed in the literature. Here we mention two models that have the advantage of employing explanatory variables to study the intraday price movements. The first model is the ordered probit model used by Hauseman, Lo, and MacKinlay (1992) to study the price movements in transactions data. The second model has been considered recently by McCulloch and Tsay (2000) and is a simplified version of the model proposed by Rydberg and Shephard (2003); see also Ghysels (2000).

5.4.1 Ordered Probit Model

Let be the unobservable price change of the asset under study (i.e., ), where is the virtual price of the asset at time t. The ordered probit model assumes that is a continuous random variable and follows the model

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where xi is a p-dimensional row vector of explanatory variables available ...