Implications of uncorrelatedness and independence in linear regression models

Abstract

The assumption of normally distributed disturbances in the linear regression model implies that the disturbances are both uncorrelated and independent. Recently however, attention has focussed on possibly nonnonnally distributed disturbances, and in this case a distinction needs to be made between only uncorrelated disturbances and independently distributed disturbances. In this paper, general specification errors associated with misspecifying uncorrelatedness and independence for student - t distributed disturbances is examined. This class of distributions is a reasonable way of modelling tails that are fatter than those of the normal distribution which has applications to the modelling of series such as prices in financial and commodity markets, growth -curve models and astronomical data. Specification tests which test for only uncorrelatedness versus independence are also discussed.

Keywords:

• nonnormality
• student-t
• spherically-symmetric
• uncorrelated
• independence
• maximum likelihood
• ordinary least squares