Asymptotic inference in time series regressions with a unit root and infinite variance errors

Abstract

In this paper, we study the limiting distribution of the OLS estimators and t-statistics of the null hypothesis of a unit root in various regression models when the true generating mechanism is either a driftless random walk or a random walk with drift and the distribution of the error term belongs to the normal domain of attraction of a stable law with characteristic exponent less than two. We show that in the former data generating processes (DGP) the same functional form as in the finite variance case applies with the Lévy process replacing the standard Wiener process. On the other hand, under the random walk with drift DGP, we show that different limiting distributions are obtained according to the magnitude of the maximal moment exponent α. Finally, we investigate the consequences of a “local” departure from the finite variance setup and provide simulation evidence on the robustness of the limiting distributions (derived under finite variance) to heavy tails in finite samples.