Fisher information in a stationary Gaussian autoregressive location model
= Fisher information in a stationary Gaussian autoregressive location model
{c}
For
$$
X_1=\theta+\varepsilon_1,\qquad
X_i=\theta(1-\sqrt\gamma)+\sqrt\gamma X_{i-1}
+\sqrt{1-\gamma}\,\varepsilon_i,
$$
where the $\varepsilon_i$ are independent $N(0,1)$ and $0\leq\gamma<1$,
$$
I_n(\theta)
=1+(n-1)\frac{1-\sqrt\gamma}{1+\sqrt\gamma}.
$$
The information tensorizes exactly when $\gamma=0$.