Testing for Unit Roots: 2 - Evans, G. B. A.; Savin, N. E. (Econometrica, 1984)
[This paper investigates the exact sampling distribution of the least squares estimator of β in the model y"t = @m + @by"t"-"1 + @u"t where the @u"t are independently N(0, @s extasciicircum2). The distribution is calculated for the case where y"0 is a known constant and where y"0 is a random variable. Given y"0 is a constant we prove a small @s asymptotic result and compute the exact powers of nonsimilar tests of the random-walk hypothesis β = 1 and of the stability hypothesis β = 0.9. The exact powers of a test of the stability hypothesis are calculated for the case where y"0 is random. The accuracy of the standard normal approximation is examined for both start-up regimes.]