Volume and Return Relationships in the Stock Market

J. Guillermo Llorente-Alvarez and J. del Hoyo - Universidad Autonoma de Madrid

Most models of asset pricing in financial economics are developed by dynamic optimization over time. Their solutions are usually non linear in nature, linearization is a common practice. Linearization implies linear around some point, that is "local linearity". But the local propety can change over time. The avoidance of high order terms is supposed not to be a great problem. The data bases employed for testing these models tend to be huge enough to be able to claim the usefulness of asymptotic results, leading to forget the information any observation or group of observations can add to the estimation results, even if they have important insights. Moreover, there is also an increasing evidence about the time evolving nature of some relationships: changing risk premium, changes in expected returns, etc.

There are some issues in the development of the theoretical models that receive few or none attention in their empirical implementation. We refer, for example, to transformations made to achieve linear aproximations, hypothesis about permanence through time of the derived structures, constancy of the coefficients, etc. Though some of these problems are treated in some way in most empirical work, we believe there is still room for more research.

In this paper we study how some of these problems appear in testing and forecasting implementations of the theoretical financial economic models. We study a model that represents the price volume relationships through time. We show how most of the specification problems get reflected in a changing parameter structure through time. These changes can be associated to several causes, weakeness of the model ({\it i.e.\/} omitted variables, structural changes, local validity,...) all of them related to specification errors.

Scheduled for Session 5.2 Asset Markets