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What would be an appropriate interpolation method that does some smoothing (similar to splines), allows for unknown (relatively big) discontinuities, can be run on a dataset in an irregular grid and with an equally irregular density of points (ie: if X is the date, we can have 20 points on one day and only 5 or even none on the next day).

Solutions such as a simple spline do not work very well, as the discontinuities really affect in a bad way the interpolation (Splines on interpolation with discontinuities).

Total variation based interpolation may be a good solution, but I have the feeling that random googling will not give me the optimal solution of my problem: an expert opinion would be more efficient than the hours I have spent looking at interpolation research that does not exactly fit my problem.

Cheers

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  • $\begingroup$ Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. $\endgroup$ – José Carlos Santos Dec 4 '17 at 14:24
  • $\begingroup$ Hi Jose Carlos. I have added a bit more of detail to the answer. As I state there, I have already spent several hours looking for a good answer, but without expert guidance, it is a blind search as I have no way of knowing if the interpolation methods I find are the best fit for my problem. $\endgroup$ – Fidel Dec 4 '17 at 14:52
  • $\begingroup$ It looks better now. $\endgroup$ – José Carlos Santos Dec 4 '17 at 14:53

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