Least absolute deviations estimation for nonstationary vector autoregressive time series models with pure unit roots

Abstract

This paper derives the asymptotic distribution of the least absolute deviations estimator for nonstationary vector autoregressive time series models with pure unit roots under mild conditions. As this distribution has a complicated form, many commonly used bootstrap techniques cannot be directly applied. To tackle this problem, we propose a novel hybrid bootstrap method by combining the classical wild bootstrap and the method in [17]. We establish the asymptotic validity of the proposed method and further apply it to construct three bootstrapping panel unit root tests. Monte Carlo experiments support the validity of our inference procedure in finite samples. The usefulness of the proposed panel unit root tests is demonstrated via analyses of real economic and financial data sets