Effects of ARMA Errors on Tests for Regression Coefficients: Comments on Vinod's Article; Improved and Additional Results

Abstract

The problem that dependent disturbances may reverse the conclusions of t or F tests of the significance of the coefficients in least squares regression has been investigated by Vinod (1976). In this comment, imperfections in Vinod's article are indicated and improved results for a more general test are presented. Bounds on the critical values of the test of a set of linear constraints, including the simple significance test, are derived and calculated for disturbances generated by ARMA stochastic processes. Further, bounds on the consequences of disregarding the dependence of the disturbances are computed.