In this paper, we propose a nonparametric approach that can be used in envelope extraction, peak-burst detection and clustering in time series. Our problem formalization results in a naturally defined splitting/forking of the time series. With a possibly hierarchical implementation, it can be used for various applications in machine learning, signal processing and mathematical finance. From an incoming input signal, our iterative procedure sequentially creates two signals (one upper bounding and one lower bounding signal) by minimizing the cumulative $L_1$ drift. We show that a solution can be efficiently calculated by use of a Viterbi-like path tracking algorithm together with an optimal elimination rule. We consider many interesting settings, where our algorithm has near-linear time complexities.

翻译：在本文中,我们提出一种非参数方法,可用于信封提取、峰值爆破探测和时间序列中的集聚。我们的问题正规化导致对时间序列进行自然定义的分解/叉。如果可能执行等级分化,它可以用于机器学习、信号处理和数学融资方面的各种应用。通过输入信号,我们的迭代程序通过尽可能减少累积的1美元流出量而连续生成两个信号(一个上层和一个下层信号 ) 。我们表明,通过使用类似维泰比的路径跟踪算法和最佳消除规则,可以有效地计算出一种解决办法。我们考虑到许多有趣的环境,我们的算法在其中具有近线性的时间复杂性。