We consider trend estimation under long-range dependence using a combination of smoothing components without thresholding and nonsmooth components filtered by hard thresholding. Optimal tuning parameters are obtained using suitable asymptotic approximations. Apart from estimation, the decomposition can be used to detect departures from continuity. A bootstrap procedure is developed that allows for nonparametric testing without detailed knowledge of the underlying residual process. Asymptotic results are derived. The finite sample performance is illustrated by simulations.

Keywords: Long-range dependence; Wavelets; Nonparametric estimation; Discontinuity

Biography: The speaker is a professor at the University of Konstanz. He received his PhD in mathematics at ETH Zurich, and held faculty and visiting positions at several universities in the US before returning to Europe in 1991. One of his main, long-lasting research interests is long-range dependence.