I have a time series of log prices that looks like a random walk. I want to denoise this series using wavelet denoising.
I care about predicting future returns (so predicting the difference in the series).
So far I've found it's possible to denoise the prices (not the differences), and then from that denoised series predict differences. However, I'm wondering how that compares to denoising the differences (which look like white noise).
What's the common practice?
Thanks!