I need to find the covariance matrix of two given estimates of an AR(1) model $$X_t = \phi X_{t-1} + Z_t$$ to find its best linear predictor of $X_2$, given $X_1$ and $X_3$.

Let W = ($X_1, X_3$)'

How could I calculate the covariance matrix of W? Cov(X1, X1), Cov(X1, X3), etc.

Thank you


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