| Anya McGuirk, Virginia Polytechnic Institute Aris Spanos, Virginia Polytechnic Institute |
| Unit Root Testing Revisited: Nested vs. Non-Nested Tests |
| Session: C-8-18 Monday 14 August 2000 by Spanos, Aris |
| The traditional account of testing for a unit root in the context of AR(1) formulation is revisited paying particular attention to the implicit statistical parameterizations. The primary aim of this paper is twofold. First, to diagnose the well-documented problem of low power associated with Dickey-Fuller type tests. It is argued that the low power is a consequence of the fact that these tests are based on models for the null and alternative hypotheses which are essentially non-nested, but the test statistics ignore this dimension of the problem. A Cox type modified LR test test is proposed and its superior finite sample power properties demonstrated. Second, to utilize an alternative (non-stationary) autoregressive model which nests the unit root hypothesis in order to derive both a Likelihood ratio (LR) and a Lagrange multiplier (LM) test. The proposed LM and LR tests are shown to have considerable power for significance in the interval [0.90,1.0). For instance, the power of the LR test is greater than 90% for significance in the interval [0.95,1.0) and n=100. |