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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?

enter image description here

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?

enter image description here

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You can compare the restored signals with mean squared error (MSE) against the original. The best method will be the one with the lower MSE. Another criterion might be the improvement in signal-to-noise ratio (SNR). – deps_stats May 24 '11 at 16:55
How about plotting cross-correlation function? or comparing ACF of the original signal with the restored ones? – K-1 May 26 '11 at 2:35
Very interesting update... Comparing the ACF or the restored signals vs the original might help to identify which method recovers the original auto-correlation structure. The large peak at lag19 is actually intriguing. I cannot say a word about that. – deps_stats May 26 '11 at 16:47
As the data is actually streamwise velocity component from a tidal estuary, I guess the peak in ACF might show the scale of strongest horizontal turbulence. But have no idea about the correlation function. – K-1 May 28 '11 at 4:52

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