Modification of the LM unit root test

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) (1979, 1981), Dickey and Said (1981) and Said and Dickey (1984, 1985).

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 Δz_t 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.