I'm trying to perform a Gaussian Process Regression on time-varying data of the form (t, x, y, z), where t is the time when sampled, x, y are physical coordinates, and z is the value being measured at those coordinates. Measurements are not always gathered at the same coordinates, and different measurements come in at different times.

Example data:

[0.0, 4.5, 5.0, 1.0]
[2.1, 6.8, 5.1, 1.1]
[2.9, 1.2, 8.3, 2.3]

While the regression works great for interpolation, it does a poor job of forecasting into the future, which I believe is because the series is not stationary. What would be the best way of making it stationary?

I've tried subtracting the rolling mean from each measurement, but this neglects that samples which are physically distant from one another will have different means. Any suggestions?


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