Prediction in pyro

Good day.

I saw some example for out of sample prediction is changing the value of x and checking the output of y.

For example in the stock price prediction case, x is time while y is changes in price.

Based on my understanding, MCMC is ‘memoryless’ where future value is based on current value.

I am interested in instead of using time as x value, I want to know how to use current y value as input and check what is the predicted value.

May I know is there an example or some method to do it in Pyro or numpyro? using current y value in set_data and run the sample posterior predictive to get the predicted y_value

Thank you very much.