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江海峰,初子靖. 递归趋势调整单位根检验与功效提升研究[J]. 安徽工业大学学报(自然科学版),2024,41(3):342-349. doi: 10.12415/j.issn.1671-7872.23010
引用本文: 江海峰,初子靖. 递归趋势调整单位根检验与功效提升研究[J]. 安徽工业大学学报(自然科学版),2024,41(3):342-349. doi: 10.12415/j.issn.1671-7872.23010
JIANG Haifeng, CHU Zijing. Research on Recursive Trend Adjustment and Power Enhancement for Unit Root Test[J]. Journal of Anhui University of Technology(Natural Science), 2024, 41(3): 342-349. DOI: 10.12415/j.issn.1671-7872.23010
Citation: JIANG Haifeng, CHU Zijing. Research on Recursive Trend Adjustment and Power Enhancement for Unit Root Test[J]. Journal of Anhui University of Technology(Natural Science), 2024, 41(3): 342-349. DOI: 10.12415/j.issn.1671-7872.23010

递归趋势调整单位根检验与功效提升研究

Research on Recursive Trend Adjustment and Power Enhancement for Unit Root Test

  • 摘要: 提出2种新递归趋势调整方法,并构建引理;利用引理推论推导4种递归趋势调整模式下单位根检验量的极限分布,使用蒙特卡洛模拟方法获取检验量分位数;选取2019年1月2日至2023年2月16日上证综合指数收盘价共1 000个观测值对递归趋势调整检验量进行实证研究。理论推导表明:和已有调整方法相同,新调整后变量不再含未知参数,可用于构造单位根检验量;基于递归趋势调整检验量在大样本下收敛于维纳过程的泛函,但与已有分布不同,需使用蒙特卡洛模拟方法重新获取分位数。模拟研究表明:第一种和第三种检验量分位数随样本容量增大而上升,第二种和第四种检验量分位数随样本容量增大而下降,但均呈现收敛趋势;和经典DF检验相比,在具有满意检验水平同时,递归趋势调整方法不但能够显著降低估计偏差,还能明显提高检验功效。实证结果表明:无论是上证综合指数对数收盘价序列还是收益率序列,递归趋势调整检验模式都能得到正确的检验结论。

     

    Abstract: Two new recursive trend adjustment methods were proposed, and the lemma was constructed. The limit distributions of the unit root test statistics under the 4 recursive trend adjustment modes were deduced with the inferences from the lemma, and the quantiles of the test statistics were obtained with Monte Carlo simulation. An empirical study was conducted on the trend adjustment test using a total of 1 000 observations of the closing price of the Shanghai composite index from January 2, 2019 to February 16, 2023. The theoretical research shows that as with existing adjustment methods, the newly adjusted variables no longer contain unknown parameters, and can be used to construct unit root test statistics. The recursive trend-based adjustment of the test statistics converges to the generalised function of the Wiener process for large samples. But unlike the pre-existing distribution, the quantiles should be obtained through Monte Carlo simulation method. The simulation shows that though the first and third test statistics increase while the second and fourth test statistics decrease when the sample size increases, but all quantiles show a convergence trend. Compared with the classical DF test, the recursive trend adjustment method can not only significantly reduce the estimation bias, but also improve the test power while having a satisfactory test size. The empirical results indicate that the recursive trend adjustment test model can obtain correct test conclusions for both the logarithmic closing price series and the yield series of the Shanghai composite index.

     

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