We propose TrendSegment, a methodology for detecting multiple change-points corresponding to linear trend changes in one dimensional data. A core ingredient of TrendSegment is a new Tail-Greedy Unbalanced Wavelet transform: a conditionally orthonormal, bottom-up transformation of the data through an adaptively constructed unbalanced wavelet basis, which results in a sparse representation of the data. Due to its bottom-up nature, this multiscale decomposition focuses on local features in its early stages and on global features next which enables the detection of both long and short linear trend segments at once. To reduce the computational complexity, the proposed method merges multiple regions in a single pass over the data. We show the consistency of the estimated number and locations of change-points. The practicality of our approach is demonstrated through simulations and two real data examples, involving Iceland temperature data and sea ice extent of the Arctic and the Antarctic. Our methodology is implemented in the R package trendsegmentR, available from CRAN.
翻译:我们提议了趋势部分,这是探测与一维数据线性趋势变化相对应的多重变化点的方法。趋势部分的核心成分是一个新的尾尖Greedy 不平衡的波盘变换:通过一个适应性构建的不平衡波盘基础,以有条件的正态自下而上的方式转换数据,结果数据呈现出很少。由于这种多尺度分解具有自下而上的性质,它侧重于地方特征的早期阶段,以及下一个能够同时探测长线和短线性趋势部分的全球特征。为降低计算复杂性,拟议方法将多个区域合并成一个数据传到一个传输点。我们显示了变化点的估计数量和位置的一致性。我们的方法的实用性通过模拟和两个真实数据实例(包括冰岛温度数据以及北极和南极的海冰范围)得到证明。我们的方法在CRAN提供的R包式趋势区域中实施。