单位根原假设下的持久性变点检验  

A Test for a Change in Persistence Against the Null Hypothesis of Unit Root

作　　者：秦瑞兵[1] 王文华 QIN Ruibing;WANG Wenhua(School of Mathematical Sciences,Sharixi University,TaiyuaJi 030006,China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《山西大学学报（自然科学版）》2020年第3期479-484,共6页Journal of Shanxi University(Natural Science Edition)

基　　金：山西省自然科学基金(201801D121005);青海省自然科学基金(2019-ZJ-920)。

摘　　要：针对原假设为单位根的持久性变点检验问题,基于残差提出了比率统计量,在原假设下得到了其渐近分布,在备择假设下证明了一致性。数值模拟结果表明,与已有方法相比,该检验犯第一类错误的概率与选定的显著水平0.05更接近,同时,该检验在有限样本下有更高的势,且随着样本容量的增加趋近于1,并且在过程为平稳时拒绝原假设的概率也控制在0.05左右。This paper develops a new approach to test for a change in persistence under the null hypothesis of unit root.The ratio statistic is proposed based on regression residuals,its asymptotic property under the null hypothesis is derived,and the consistency of the test is established under the alternative hypothesis.The numerical simulations show that compared with the existing methods,the new test has the empirical sizes closer to the selected significant level at 0.05.Simultaneously,the new test is more powerful under the finite samples and corresponding power converges to 1 as the sample size n increases.Remarkably,the proposed test rejects the null hypothesis of stationarity with a probability 0.05,which means that the proposed test can distinguish a stationary series or a series with a unit root from a series with a change in persistence more efficiently.

关 键 词：持久性变点 单位根过程 平稳过程 

分 类 号：O212[理学—概率论与数理统计]