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，该过程因非平稳性和方差变化而带来检测挑战。我们的方法融合了两种趋势估计技术：Hodrick-Prescott（HP）滤波与l1滤波。这些方法面临的核心挑战在于调节参数lambda的选择，我们通过引入两种选择策略来解决该问题。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lambda；对于基于l1滤波的方法，我们提出基于正态性假设的选择策略。此外，我们引入了一种利用l1滤波方法估计时间片段中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，我们验证了所提方法的有效性。最后，我们将该方法应用于实际SNP股票数据，展示了其在变点检测中的实用价值。