含尺度变点稳定分布的单位根检验

Testing for a Unit Root Under Stable Distribution with Scale Changes

研究稳定分布噪声模型中含有尺度变点的单位根检验问题．在尺度突变的情形下，给出DF型检验统计量在原假设成立时的渐近分布．结果表明：统计量的渐近分布不仅是Lévy过程的泛函，且依赖尺度变化的位置和跳跃幅度．最后，通过Mente Carlo数值模拟证实，DF检验统计量不再稳健，尺度变点会导致单位根检验的经验水平值发生扭曲．

This paper investigates the unit root test for α stable distribution noise model with breaks in scale volatility. If the scale changes are present, the asymptotic distribution of conventional DF-type test is obtained under the null hypothesis. It is shown that it is not only the functional of Lévy process, but also depends on the location and magnitude of scale changes. Finally, Monte Carlo simulations demonstrate the empirical size has serious distortion caused by presence of scale changes.