Adaptive LAD-Based Bootstrap Unit Root Tests Under Unconditional Heteroscedasticity

原文摘要

This paper studies unit root testing based on least absolute deviations (LAD) regression under unconditional heteroscedasticity. We first derive asymptotic properties of the LAD estimator under both unit root and local-to-unity settings in the presence of unconditional heteroscedasticity and weak dependence. The results show that the limiting distribution of the LAD estimator (and thus the derived test statistics) is closely associated with unknown heteroscedasticity. To conduct feasible LAD-based unit root tests, we propose a novel adaptive block bootstrap procedure, which accommodates unconditional heteroscedasticity and serial dependence, both of which exhibit unknown forms, to compute critical values. The asymptotic validity of the proposed bootstrap method is established. Furthermore, we extend the testing procedure to incorporate deterministic components, such as a constant term or a linear trend. Simulation results show that, in the presence of unconditional heteroscedasticity and serial dependence, the proposed tests exhibit reasonable size control, whereas the classic LAD/quantile-based tests developed under homoscedasticity exhibit severe size distortion. Additionally, compared to existing least squares based tests, our new tests show superior testing power when the data are heavy-tailed. Finally, empirical analysis based on unemployment rates is conducted to illustrate the applicability of the new tests.

摘要来源：OpenAlex