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.

[0] https://archive.org/details/creativecomputing-1980-07/page/n...

[1] https://en.wikipedia.org/wiki/Monotone_cubic_interpolation