Adaptive LAD-Based Bootstrap Unit Root Tests Under Unconditional Heteroscedasticity
研究了无条件异方差下基于最小绝对偏差回归的单位根检验，提出自适应块bootstrap方法计算临界值，模拟显示该方法在异方差和序列依赖下能控制检验水平，且对厚尾数据有更高检验功效。
This paper studies unit root testing based on least absolute deviations (LAD) regression under unconditional heteroskedasticity. We first derive asymptotic properties of the LAD estimator under both unit root and local-to-unity settings in the presence of unconditional heteroskedasticity 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 heteroskedasticity. To conduct feasible LAD-based unit root tests, we propose a novel adaptive block bootstrap procedure, which accommodates unconditional heteroskedasticity 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 heteroskedasticity and serial dependence, the proposed tests exhibit reasonable size control, whereas the classic LAD/quantile-based tests developed under homoskedasticity 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.