Let's say we have a Markov process Xt, and we come up with a forecast model that takes some information from outside world and says: "value X[t+1] has probability density distribution Pt(x)". The forecasted distribution changes on every step, because it depends on some parameters from outside world that change on every step. We look at each consequtive Xt, and try to compare it to previously forecasted Pt(x) every time. How do we say that the underlying model is valid?

Let's say we have a Markov process $X_t$, and we come up with a forecast model that takes some information from outside world and says: "value $X_{t+1}$ has probability density distribution $P_t(x)$". The forecasted distribution changes on every step, because it depends on some parameters from outside world that change on every step. We look at each consequtive $X_t$, and try to compare it to previously forecasted $P_t(x)$ every time. How do we say that the underlying model is valid?