Testing for Parameter Constancy in Linear Regressions: An Empirical Distribution Function Approach

This paper proposes some tests for parameter constancy in linear regression models with possible infinite variance.Both dynamic and trending regressors are allowed.The tests are based on the empirical distribution function of estimated residuals and are shown to have non-trivial local power against a wide range of alternatives.Within a certain class of alternatives including simple shifts, the tests have higher power for testing the simple shift alternatives.These tests are formulated in such a way that the limiting variables are distribution-free.The residuals may be obtained based on any root-n consistent estimator (under the null) of regression parameters.As part of these results, some weak convergence for weighted sequential empirical processes of residuals is established.