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In the paper "Realized kernels in practice: trades and quotes" by O. E.Bandorff-Nielsen etc. cf.

https://onlinelibrary.wiley.com/doi/full/10.1111/j.1368-423X.2008.00275.x

in the section dedicated to data cleaning the authors suggest:

Delete entries for which the mid-quote deviated by more than 10 mean absolute 
deviations from a rolling centred median (excluding the observation 
under consideration) of 50 observations (25 observations before and 25 after).

Assume that we are working with stock tick data. Assume the current point, which is under consideration, is an outlier based on MAD. The question: Should one completely delete this current point when we move the window to the next step and deciding for the next point?

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  • $\begingroup$ It depends on why you are cleaning the data and what the possible reasons are for outliers. In some circumstances this form of cleaning would be a terrible idea (imagine a time series of real estate sales where the high outliers might contribute to most of the market value) and in others it will be just fine. What application do you have in mind? $\endgroup$ – whuber Jan 30 at 16:59
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    $\begingroup$ Dear @whuber. Thank you for the comment. I have clarified in the question. I am mostly interested in financial time series. In the tick data there are a lot of outliers, which has nothing to do with real prices. The reason for this is a subject for another very big discussion. $\endgroup$ – ABK Jan 30 at 17:04

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