I have some data acquired by an acoustic sensor with 1 Hz sampling rate. Due to some inevitable issues, I have some noise in my signal, saying 10% pollution. I'm looking for a reliable method for replacing the outliers.
In order to find a suitable approach I manipulated a clean record such that it contains 9% spurious data. I replace outliers with some different methods like Kalman Predictor, Linear Time Series Modeling, and the Local Mean.
Now, I want to compare them together with. Can you suggest criteria to show which method restores fluctuations better if compared to the clean original signal.
If the figure below shows the cross-correlation between the original signal and the restored ones, how can I interpret the large negative peak in lag19?
Furthermore, is it correct if I say: as the ACF of the signal resored by wavelet-LTS tracks that of original signal, this method could mimic the original signal better than the others?