Denoising / thresholding via wavelets
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)