I have financial price time series data and it has some noisy (probably erroneous) data and it also has gaps. As a first step I want apply a Tukey median smoother on points that do exist so I can study the residuals to decide if the point is an outlier. So far approach looks very promising on full sets of data that are noisy.
When applying smoothing to data with gaps how should I treat the points that are adjacent to the gaps. Simple approaches could be to (a) concatenate the data and treat as if no gaps (b) treat each section of data between gaps on its own and apply standard Tukey end point methods. Is there an approach that improves on these simple methods?