Stineman interpolation [0] is an alternative that is quick and "dirty" imputer for missing values. Of course there are monotonic-preserving versions [1] of splines that are excellent as well.
For my uses, cubic interpolation is simply not of value when I have noisy points and/or unpredictable behaviour between points --- Kalman smoothers or Gaussian process/Kriging gives me both a good mean estimate between points and a sense of the error associated with the interpolation.
I second this. In quantitative finance cubic splines are often, simply, out of the question. However, we end up using montonic cubic splines quite often.
For my uses, cubic interpolation is simply not of value when I have noisy points and/or unpredictable behaviour between points --- Kalman smoothers or Gaussian process/Kriging gives me both a good mean estimate between points and a sense of the error associated with the interpolation.
[0] https://archive.org/details/creativecomputing-1980-07/page/n...
[1] https://en.wikipedia.org/wiki/Monotone_cubic_interpolation