Asymptotic Theory of LAD Estimation in a Unit Root Process with Finite Variance Errors

Abstract

In this paper we derive the asymptotic distribution of the least absolute deviations (LAD) estimator of the autoregressive parameter under the unit root hypothesis, when the errors are assumed to have finite variances, and present LAD-based unit root tests, which, under heavy-tailed errors, are expected to be more powerful than tests based on least squares. The limiting distribution of the LAD estimator is that of a functional of a bivariate Brownian motion, similar to those encountered in cointegrating regressions. By appropriately correcting for serial correlation and other distributional parameters, the test statistics introduced here are found to have either conditional or unconditional normal limiting distributions. The results of the paper complement similar ones obtained by Knight (1991, Canadian Journal of Statistics 17, 261-278) for infinite variance errors. A simulation study is conducted to investigate the finite sample properties of our tests.