Comparisons of Tests for the Presence of Random Walk Coefficients in a Simple Linear Model

Abstract

The locally most powerful test is derived for the hypothesis that the regression coefficients are constant over time against the alternative that they vary according to the random walk process. When the regression equation contains the constant term only, comparisons are made with the tests suggested by LaMotte and McWhorter (1978). These are based on exact powers and on three different types of asymptotic efficiencies including the classical Pitman and Bahadur approaches and the new one due to Gregory (1980). The concept of the Bahadur efficiency is extended to cover also the random slopes. Suggestions are made for choosing the test.