Thank you all for your feedback. I was aware of the “histogram approximation” approach, but I also had problems with it in the past. I was under the impression that using the posterior predictive was a way around approximating the posterior using a custom approach (I was wrong).
About @ricardoV94 suggestion, when I have a time series problem I usually do this (i.e. resampling the whole dataset or a moving window). But in this case, I have a variable that in the first period is given (is data) and in the second I want to estimate. I don’t understand how can I build a retrieval scheme in which a variable in one period is data and for the next is to be estimated.