Multi-step time series forecasting, with approximation methods for uncertainty propagation

[rhagenbuch]

Hello everyone. First, I want to thank you for providing this great tool.

I would like to do time-series forecasting and make predictions y(t+1), using the preceding predictions y(t), y(t-1), y(t-2) as a new input. Since there is an uncertainty associated with the new inputs, I would like to propagate this through the model to get a prediction, which isn't to overconfident. During my search for a solution I stumbled upon a Q&A Discussion (#2278), which addresses pretty much the same topic. As it's already marked as answered, I considered initiating a fresh discussion. I hope thats alright.

As far as I understand the answer from the other Q&A Discussion suggests using the Monte Carlo approach by sampling from the posterior, which appears to yield promising results. However, I was wondering if there is also a way to use approximation methods, as discussed in the thesis of Agathe Girard, when working with GPyTorch? Since we don't have to generate predictions for numerous samples, I believe that the approximation methods might offer computational advantages?

Thesis of Agathe Girard: https://www.dcs.gla.ac.uk/~rod/publications/Gir04.pdf

Thank you very much for your help.