Systems of Regression Equations

Abstract

The previous chapters dealt with models for univariate financial time series. In many applications, it is desirable to model the joint behavior of multiple time series because of possible effciency gains to the joint estimation of a system of time series models. For example, there may be complex interactions between the variables and/or the error structure across models. Univariate models cannot capture these interactions whereas multivariate models can. Furthermore, many equilibrium models for asset returns, like the capital asset pricing model (CAPM) or the arbitrage price model (APT), imply parameter restrictions that are common to the model representation of all assets. Hence, the testing of equilibrium asset pricing models requires the testing of cross equation parameter constraints, and the proper estimation of these models would impose these cross equation restrictions.