Abstract
This article proposes a modified version of the Langrange Multiplier (LM) test for a unit root, which is efficient and avoids arbitrary estimation of the levels regression intercept. If required, this intercept can be estimated indirectly in the second-step autoregression. In addition to simple-hypothesis LM unit root tests, a new F-type version of the test is proposed, which is based on a joint hypothesis. Parametric augmentation is discussed in detail, and simulated new critical values are provided.
Notes
1 For analysis of the LM test with structural breaks (which is beyond the scope of this article), see Lee and Strazicich (2003).
2 See references by Dickey and Fuller (DF) (Citation1979, Citation1981), Dickey and Said (Citation1981) and Said and Dickey (Citation1984, Citation1985).
3 This recommendation is superfluous, creating excess estimation biases in the general case. Note that for a model with linear trend only, the two approaches produce identical results. In this case Δzt is a column of ones.
4 The critical values of all LM tests are invariant with respect to the initial condition under the null.
5 SP propose no joint LM test, which is proposed in this article for the first time.