A comparison of the accuracy of asymptotic approximations in the dynamic regression model using Kullback-Leibler information

Abstract

This paper illustrates the use of the Kullback-Leibler Information (KU) measure for assessing the relative quality of two approximations to an unknown distribution from which we can obtain simple random drawings. The illustration involves comparing the large-sample and small-disturbance asymptotic distributions under the null hypothesis of a t statistic from the dynamic linear regression model. We find very clear evidence in favour of the use of p-values and critical values from the small-disturbance Student's t distribution rather than from the large-sample standard normal distribution in this case.