A Sequential Test For a Unit Root in Monitoring a p-th Order Autoregressive Process
A Sequential Test For a Unit Root in Monitoring a p-th Order Autoregressive Process
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监控p阶自回归过程中单位根的序贯检验
DOI：
10.1108/s0731-90532023000045a004
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
and Junfan Tao
中科院分区：
文献类型：
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作者：
Kohtaro Hitomi;Keiji Nagai;Yoshihiko Nishiyama;and Junfan Tao
在这项研究中，作者研究了序贯分析方法，以前瞻性地测试随时间监测的 p 阶自回归 (AR) 过程中针对静止或爆炸状态的单位根的存在性。我们的顺序采样方案使用基于观察到的局部统一参数的 Fisher 信息的停止时间。与迪基-富勒 (DF) 检验统计量相反，序贯检验统计量具有渐近正态性。作者推导了检验统计量和停止时间的联合极限，可以使用由时变布朗运动驱动的 3/2 维贝塞尔过程来表征。作者获得了零值和局部替代方案下的极限联合拉普拉斯变换和密度函数。此外，通过仿真验证了理论结果的有效性。
In this study, the authors investigate methods of sequential analysis to test prospectively for the existence of a unit root against stationary or explosive states in a p-th order autoregressive (AR) process monitored over time. Our sequential sampling schemes use stopping times based on the observed Fisher information of a local-to-unity parameter. In contrast to the Dickey–Fuller (DF) test statistic, the sequential test statistic has asymptotic normality. The authors derive the joint limit of the test statistic and the stopping time, which can be characterized using a 3/2-dimensional Bessel process driven by a time-changed Brownian motion. The authors obtain their limiting joint Laplace transform and density function under the null and local alternatives. In addition, simulations are conducted to show that the theoretical results are valid.