This paper explores testing unit roots based on least absolute deviations (LAD) regression under unconditional heteroskedasticity. We first derive the asymptotic properties of the LAD estimator for a first-order autoregressive process with the coefficient (local to) unity under unconditional heteroskedasticity and weak dependence, revealing that the limiting distribution of the LAD estimator (consequently the derived test statistics) is closely associated with unknown time-varying variances. To conduct feasible LAD-based unit root tests under heteroskedasticity and serial dependence, we develop an adaptive block bootstrap procedure, which accommodates time-varying volatility and serial dependence, both of unknown forms, to compute critical values for LAD-based tests. The asymptotic validity is established. We then extend the testing procedure to allow for deterministic components. Simulation results indicate that, in the presence of unconditional heteroskedasticity and serial dependence, the classic LAD-based tests demonstrate severe size distortion, whereas the proposed LAD-based bootstrap tests exhibit good size-control capability. Additionally, the newly developed tests show superior testing power in heavy-tailed distributed cases compared to considered benchmarks. Finally, empirical analysis of real effective exchange rates of 16 EU countries is conducted to illustrate the applicability of the newly proposed tests.

翻译：本文探讨在无条件异方差下基于最小绝对偏差（LAD）回归的单位根检验问题。首先推导了无条件异方差与弱相依条件下，一阶自回归过程（其系数局部趋近于1）的LAD估计量的渐近性质，结果表明LAD估计量（及由此构建的检验统计量）的极限分布与未知的时变方差密切相关。为在异方差与序列相依条件下构建可行的LAD单位根检验，我们提出了一种自适应分块自助法程序，该方法能够适应形式未知的时变波动性与序列相依性，从而计算LAD类检验的临界值。我们证明了该方法的渐近有效性，并将检验程序扩展至包含确定性分量的情形。模拟实验表明：在存在无条件异方差与序列相依时，经典LAD检验存在严重的尺寸扭曲，而本文提出的LAD自助法检验展现出良好的尺寸控制能力。此外，在厚尾分布情形下，新构建的检验相较于现有基准方法表现出更优越的检验功效。最后，通过对16个欧盟国家实际有效汇率的实证分析，展示了新提出检验方法的适用性。