This sounds like a standard question to me but I haven't found any answer so far, looking on a hundred sites.
We have a time series (say >100 x and y values, x equidistant) representing a smooth curve plus gaussian noise. We want to estimate a) the smooth curve and b) its first and second derivatives. Currently we apply a gaussian kernel smoother but we run into trouble at the edges, so we want to switch to a kernel with finite support.
For a) I understand that the Epanechnikov kernel is optimal in a way but biweight or triangular are not much worse.
Regarding b) we have no idea. Is there an equivalently good / robust / established solution to find smooth derivatives?