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