Try the Ornstein-Uhlenbeck kernel for the gaussian processes

[rlouf]

The Ornstein-Uhlenbeck kernel defines a stationary gaussian process that describes a mean-reverting stochastic process. It seems more adapted to our modeling problem than a gaussian kernel that doesn't have an interpretation in terms of stochastic processes.

[AlexAndorra]

Mmmh, the Gaussian kernel is also a stationary, mean-reverting process IIRC 🤔
What would be the difference with the OU kernel?

[rlouf]

A GP with the Ornstein-Uhlenbeck kernel is equivalent to an AR(1) process (cf Rasmussen & Williams p.212), so it is definitely worth trying if we have time.

I'd need to do the computation myself for the squared exponential kernel, but I don't think it is equivalent to anything well known in the time-series world; at least I didn't find it documented anywhere.

[AlexAndorra]

I think it's the limit of an auto-regressive process, where you learn the step of the auto-regression -- but better to check indeed. What I'm sure of is that you can compute the derivative of the Gaussian kernel an infinite number of times and that's is the limit of a lot of kernels.
In any case, I'm definitely curious to try the OU kernel one of these days!