The LAD test of a unit root null with fat tailed innovations

Abstract

This paper considers the least absolute deviations (LAD) test of a unit root null without drift when distributions of innovations are fat tailed. The limiting distributions of the test statistics are expressed in terms of functional of a standard Brownian motion. Percentiles are tabulated. A Monte Carlo experiment indicates that the LAD tests dominate the Dickey-Fuller tests when innovations are fat tailed, except distributions with extremely heavy tails such as Cauchy.