统计研究 ›› 2013, Vol. 30 ›› Issue (3): 93-100.

• 论文 • 上一篇    下一篇

有限样本平稳序列与单位根序列的不可区分性

吴明华 周爱民   

  • 出版日期:2013-03-15 发布日期:2013-03-13

The Indistinguishability of Stationary Series and Unit Root Sequences Based on Finite Samples

Wu Minghua & Zhou Aimin   

  • Online:2013-03-15 Published:2013-03-13

摘要: 本文应用依分布收敛相关理论,给出有限样本下,平稳序列与单位根序列不可精确区分这一结论的新证明。结合蒙特卡洛模拟实验,解释了有限样本下单位根检验出现水平扭曲或功效偏低现象的合理性。本文还在相同的理论框架下证明,根据有限序列所得的参数估计值、相应统计量及样本外一期预测值的依分布收敛性,从而说明针对有限样本的单位根检验尽管不完美,但仍是有意义的。

关键词: 有限样本, 平稳序列, 单位根序列, 不可区分性

Abstract: Applying the theory of convergence in distribution, the paper gave new evidence that, stationary series and unit root sequences are indistinguishable based on finite samples. Combining with Monte Carlo simulation, this paper explained the reasonability of the level distortion or low power in unit root test with finite samples. Under the same theoretical framework, this paper proved the convergence in distribution of parameter estimators, the corresponding statistics and the first out-of-sample forecast values. This part also pointed out that unit root test with finite samples is not perfect but still meaningful.

Key words: Finite Samples, Stationary Series, Unit Root Sequences, Indistinguishability