Neumann, Michael H.Michael H.NeumannLeucht, AnneAnneLeucht2025-02-172025-02-172025https://fis.uni-bamberg.de/handle/uniba/106371For time series data observed at non-random and possibly nonequidistant time points, we estimate the trend function nonparametrically. Under the assumption of a bounded total variation of the function and low-order moment conditions on the errors we propose a nonlinear wavelet estimator which uses a Haar-type basis adapted to a possibly non-dyadic sample size. An appropriate thresholding scheme for sparse signals with an additive polynomial-tailed noise is frst derived in an abstract framework and then applied to the problem of trend estimation.engtime seriestrend estimationwavelet thresholdingpreprint10.48550/arxiv.2502.082802502.08280