We propose new methods for detecting multiple change points in time series, specifically designed for random walk processes, where stationarity and variance changes present challenges. Our approach combines two trend estimation methods: the Hodrick Prescott (HP) filter and the l1 filter. A major challenge in these methods is selecting the tuning parameter lambda, which we address by introducing two selection techniques. For the HP based change point detection, we propose a probability-based threshold to select lambda under the assumption of an exponential distribution. For the l1 based method, we suggest a selection strategy assuming normality. Additionally, we introduce a technique to estimate the maximum number of change points in time segments using the l1 based method. We validate our methods by comparing them to similar techniques, such as PELT, using simulated data. We also demonstrate the practical application of our approach to real-world SNP stock data, showcasing its effectiveness in detecting change points.

翻译：本文针对随机游走过程提出新的时间序列多重变点检测方法，该场景中非平稳性与方差变化构成显著挑战。我们的方法融合两种趋势估计技术：Hodrick-Prescott（HP）滤波与l1滤波。这些方法面临的核心挑战是调节参数lambda的选择问题，为此我们提出两种参数选择策略。对于基于HP滤波的变点检测，我们在指数分布假设下提出基于概率的阈值选择方法以确定lambda。针对基于l1滤波的方法，我们提出基于正态性假设的选择策略。此外，我们引入一种利用l1滤波方法估计时间片段内最大变点数量的技术。通过模拟数据与PELT等同类方法的对比验证了所提方法的有效性。最后，我们以实际SNP股票数据为例，展示了该方法在变点检测中的实际应用效能。