Detecting linear trend changes in data sequences

Abstract 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 new Tail-Greedy Unbalanced Wavelet transform: conditionally orthonormal, bottom-up transformation the data through an adaptively constructed unbalanced wavelet basis, which results sparse representation Due its nature, this multiscale decomposition focuses on local features early stages and global next enables detection both long short segments at once. To reduce computational complexity, proposed method merges regions single pass over show consistency estimated number locations change-points. The practicality our approach demonstrated simulations two real examples, involving Iceland temperature sea ice extent Arctic Antarctic. Our implemented R package , available from CRAN.