论文标题：Whittle-type estimation under long memory and nonstationarity

　　发表时间：2020

　　论文所有作者：Ying Lun Cheung, Uwe Hassler

　　期刊名及所属分类：AStA Advances in Statistical Analysis(国际SCI)

　　英文摘要：We consider six variants of (local) Whittle estimators of the fractional order of integration d. They follow a limiting normal distribution under stationarity as well as under (a certain degree of) nonstationarity. Experimentally, we observe a lack of continuity of the objective functions of the two fully extended versions at $$d="1/2$$" d = 1 / 2 that has not been reported before. It results in a pileup of the estimates at $$d="1/2$$" d = 1 / 2 when the true value is in a neighborhood to this half point. Consequently, studentized test statistics may be heavily oversized. The other four versions suffer from size distortions, too, although of a different pattern and to a different extent.

　　中文摘要：我们考虑积分d的分数阶(局部)惠特估计的六个变量。它们在平稳性和(一定程度)非平稳性下遵循极限正态分布。在实验上，我们观察到在SSd="1/2ss" d="1/2时两个完全扩展版本的目标函数缺乏连续性，这在以前没有报道过。在SSd=1/2Ss" d="1/2处，当真值在这个0.5点附近时，它会导致估计的堆积。因此，学习测试的统计数据可能严重超标。遭受扭曲大小,其他四个版本,尽管不同的模式和不同的延期。