# Prediction of $X_{n+1}$ with Yule-Walker estimate

Consider a causal AR(1) process $$X_t = \phi X_{t−1} + Z_t$$ with $$(Z_t)$$ iid with mean 0 and finite variance. I am reading in a book, that $$\phi X_n$$ is the best predictor for $$X_{n+1}$$ because it minimizes $$E[(X_{n+1}-f(X_1,\ldots,X_n))^2]$$.

But then it says that if $$\phi$$ is unknown, then $$\hat{\phi} X_n$$ (with $$\hat{\phi}$$ being the Yule-Walker estimate) is not the best predictor for $$X_{n+1}$$ in the same sense. I can't really see why this is, could someone explain?