Bootstrap tests for unit roots based on lad estimation

Abstract

In this paper we propose a new bootstrap test for unit roots in first order autoregressive models based on least absolute deviation (LAD) estimators. It is known that the behaviour of this estimator when the distribution is heavy tailed is very good compared with least squares estimation. The innovations distribution dependence of the LAD asymptotic law is overcome using bootstrap, which automatically approaches the target distribution. We provide the bootstrap functional limit theory necessary to prove the asymptotic validity of the procedure. Our strategy avoids the usual problem of estimating the variance matrix and the density in zero, and the construction of distribution free statistics through linear combinations with the least squares estimator. Moreover, a large simulation study shows that our test has very good power behaviour compared with others proposed in the literature.