平稳性检验的加权Dickey-Fuller过程
Weighted Dickey-Fuller Processes for Detecting Stationarity
摘要：
为了对时间序列进行监测，尽快发现平稳性，本文介绍了基于核加权序贯Dickey-Fuller（DF）过程及其相关的停时的监测方法，称之为加权Dickey-Fuller控制图。在较弱的假设条件下，在单位根原假设和局部-单位替换下，建立了（泛函）中心极限定理.对于一般相依和异质新息序列，极限过程依赖于一个冗余参数.在这种具有实际意义的情况下，可以使用从估计的渐进定律获得的估计控制限。另一种简单易用的方法是对DF过程进行变换，以获得对干扰参数不变的极限定律。我们为这两种方法提供了渐近理论，并通过模拟比较了它们在有限样本中的统计行为。
英文摘要：
Aiming at monitoring a time series to detect stationarity as soon as possible, we introduce monitoring procedures based on kernel-weighted sequential Dickey-Fuller (DF) processes, and related stopping times, which may be called weighted Dickey-Fuller control charts. Under rather weak assumptions, (functional) central limit theorems are established under the unit root null hypothesis and local-to-unity alternatives. For gen- eral dependent and heterogeneous innovation sequences the limit processes depend on a nuisance parameter. In this case of practical interest, one can use estimated control limits obtained from the estimated asymptotic law. Another easy-to-use approach is to transform the DF processes to obtain limit laws which are invariant with respect to the nuisance pa- rameter. We provide asymptotic theory for both approaches and compare their statistical behavior in finite samples by simulation.
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