  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.
