论文标题
基于一般移动总和的时间序列的数据分割
Data Segmentation for Time Series Based on a General Moving Sum Approach
论文作者
论文摘要
在本文中，我们提出了有关数据分割的新方法，也称为多重变化点问题，在一个一般框架中，包括经典的平均变化场景，线性回归的变化以及时间序列结构的变化，例如Poisson-AutoreRoregression-Arecremission Time序列的参数。特别是，我们基于估算方程式证明了变更点数量的一致性以及变更点位置的估计量的融合速率的一般理论。更确切地说，考虑了两种不同类型的Mosum（移动总和）统计数据：基于本地估计器的差异和基于全球估计器的Mosum-Score统计量基于Mosum-Wald统计量。后者通常在计算上少于尤其是在不知道估计器的封闭形式的非线性问题中，因此需要数值方法。最后，我们通过模拟数据以及使用某些地球物理井数据数据来评估该方法。
In this paper we propose new methodology for the data segmentation, also known as multiple change point problem, in a general framework including classic mean change scenarios, changes in linear regression but also changes in the time series structure such as in the parameters of Poisson-autoregressive time series. In particular, we derive a general theory based on estimating equations proving consistency for the number of change points as well as rates of convergence for the estimators of the locations of the change points. More precisely, two different types of MOSUM (moving sum) statistics are considered: A MOSUM-Wald statistic based on differences of local estimators and a MOSUM-score statistic based on a global estimator. The latter is usually computationally less involved in particular in non-linear problems where no closed form of the estimator is known such that numerical methods are required. Finally, we evaluate the methodology by means of simulated data as well as using some geophysical well-log data.
