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?