Detecting linear trend changes in data sequences

We propose TrendSegment, a methodology for detecting multiple change-points corre- sponding 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 multi- scale 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.