A New Test for Nonstationarity Against the Stable Alternative
Posted: 22 Jan 2012
Date Written: January 21, 2012
It was recently shown (Abadir, K. M. ,1993, On the asymptotic power of unit root tests. Econometric Theory, 9, 189-221) that nonstationarity causes the limiting distributions of the Wald (W) and Lagrange multiplier (LM) statistics to become different from each other. This paper demonstrates that such a divergence between the two distributions can be used as an indicator of the presence of a unit root. A test based on this idea is devised by modifying the normalized autocorrelation coefficient (NAC). It is then shown to be an improvement on NAC in large samples and an improvement on other existing tests in large effective samples. The paper also investigates the effect of nonstationarity on the well-known inequality W ≥ LR ≥ LM.
Suggested Citation: Suggested Citation