I have historical data for three variables : Y, X1, X2, for example 1000 points. The distribution of future values of Y depends from X1 and X2 and can’t be expressed in deterministic way. I am trying to model the distribution of Y[n:n+20] based on distribution of X1[n-980, n] and X2[n-980, n]. I am using Markov Chain Monte Carlo for that and PyMC library. In this example I can use historical data and extract priors of X1, X2 and Y by using X1[0:980], X2[0:980], Y[980:1000]. How model in terms if PyMC will look if we can’t analytically express how X1 and X2 influence Y? If I get 1001 point, I’d like to see how Y[981:1001] (posterior) will look if we have X1 and X2 updated ([21:1001]). How it can be implemented using PyMC?
This looks related to Predicting out-of-sample for autoregressive models. The short version is that you are writing down a model for Y using X1 and X2, so you might use the parameters you learn with PyMC3 to generate samples going forward, or pad X1 and X2 with NaN's.