Denoising / thresholding via wavelets When I apply differerent thresholding, wavelet denosing functions to non stationary time series which has been detrended via Loess regression and demean it. I expect that when this processed series are submited to denoising / thresholding will result in a clean series with smaller values than the submited signal and not to values at any point which are above those of the signal, Is my thinking correct. 

On another hand could it be thought as per those values in a procesed signal which lie above the processed signal as if the procesed signal would ought  to be above those levels instead than below those levels. Of course the functions that described the signal is an aproximation so fiting erros should have to be expected.
I expect that when this processed series are submited to denoising / thresholding will result in a clean series with smaller values than the submited signal


No, you can get values that are greater. For example, consider the Fourier series of a signal. The Fourier series basis functions are wavelets. If we approximate the signal with only a few of the Fourier series coefficients you will get values that are above the original signal. 

E.g. from the (image from wikipedia)