This is a cross-post (on recommendation) from CV.
My problem is very simple.
I currently intend on using Kriging (Gaussian process regression) to perform regression between the trajectories marked with red dots on the below plot, where a simple linear-regression surface has been superimposed as well.
As you can see there is a strong correlation in a particular direction of the four time-series.
Through long and very interestind discussion with @DeltaIV, we started consdering other methods such as harmonic regression. The latter would have been very elegant except the example time-series in the above plot have different periods (fundamental frequencies) thus HR will not work.
Hence I would like to ask you excellent people what you would recommend for either regression or interpolation between quasi-periodic time-series such as the above? I should not that the above plot shows only one period, that approximately repeats itself but not quite (hence 'quasi').
Alas currently (in order of preference):
- Multivariate splines (recommendations here welcome too)
- Gaussian process regression (with complex kernel choice)
- Some magical way of making harmonic regression work with time-series with different periodicity
Here is another image, showing the periodicity of ONE of the signals annotated by the red dots above. Thus, this time-series shows the periodicity of the time-series over a longer period of recorded time. Again, this is just ONE of the above four time-series, recorded at a certain regime.