In the modeling of biological phenomena, in living organisms whether the measurements are of blood pressure, enzyme levels, biomechanical movements or heartbeats, etc., one of the important aspects is time variation in the data. Thus, the recovery of a "smooth" regression or trend function from noisy time--varying sampled data becomes a problem of particular interest. Here we use non--linear wavelet thresholding to estimate a regression or a trend function in the presence of additive noise which, in contrast to most existing models, does not need to be stationary. (Here, nonstationarity means that the spectral behaviour of the noise is allowed to change slowly over time). We develop a procedure to adapt existing threshold rules to such situations, e.g., that of a time--varying variance in the errors. Moreover, in the model of curve estimation for functions belonging to a Besov class with locally stationary errors, we derive a near--optimal rate for the L 2 --risk between the unknown fu..
