Developments in Maximum Likelihood Unit Root Tests

TL;DR

This paper introduces a new, simpler derivation of the asymptotic distribution for the maximum likelihood unit root test, along with a fast algorithm for critical values, demonstrating superior empirical power across various distributions.

Contribution

A novel derivation of the asymptotic distribution for the MLE-based unit root test and a new algorithm for computing critical values, implemented in the R package mleur.

Findings

The new test has significantly higher power than the traditional test.

The algorithm provides accurate finite-sample critical values.

The test performs well under various innovation distributions.

Abstract

The exact maximum likelihood estimate (MLE) provides a test statistic for the unit root test that is more powerful \citep[p. 577]{Fuller96} than the usual least squares approach. In this paper a new derivation is given for the asymptotic distribution of this test statistic that is simpler and more direct than the previous method. The response surface regression method is used to obtain a fast algorithm that computes accurate finite-sample critical values. This algorithm is available in the R package {\tt mleur} that is available on CRAN. The empirical power of the new test is shown to be much better than the usual test not only in the normal case but also for innovations generated from an infinite variance stable distribution as well as for innovations generated from a GARCH$(1,1)$ process.