High-dimensional trend segmentation
14th May 2021, 3:00 pm – 4:00 pm
Abstract: We propose a new methodology for detecting trend changes in high-dimensional time series data which is referred to as High-dimensional Trend Segmentation (HiTS). Two scenarios investigated by our methodology include change-points in piecewise-constant and piecewise-linear signals. Our methodology is invented to be robust in estimating the number and locations of change-points especially when a sparse subset of coordinates undergo changes in trend. The key ingredient of HiTS is a new High-dimensional Tail-Greedy Unbalanced Wavelet transform: a conditionally orthonormal, bottom-up transformation of the high-dimensional panel data through an adaptively constructed unbalanced wavelet basis. We show the consistency of the estimated number and locations of change-points under two scenarios considered. The HiTS procedure is easy to implement and rapidly computed even in the case of large number of coordinates. The usefulness of HiTS is demonstrated through numerical studies and two real data examples, South Africa temperature data and sea ice extent of the Arctic and Antarctic. Our methodology is implemented in our GitHub repository.