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

作　　者：张守刚[1] 白智琳 金浩[1] ZHANG Shou-gang;BAI Zhi-lin;JIN Hao(School of Science,Xi＇an University of Science and Technology,Xi＇an 710054,China)

机构地区：[1]西安科技大学理学院

出　　处：《数学的实践与认识》2018年第18期158-165,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(71473194);陕西省科技厅科技基金(2013KJXX-40,2018JM1041 2017JM1042);陕西省教育厅专项基金(2016JK1500)

摘　　要：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.

关 键 词：稳定分布 单位根 尺度变点 DF检验 LÉVY过程 

分 类 号：O211.61[理学—概率论与数理统计]