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Fisher information in a stationary Gaussian autoregressive location model

For

X_{1} = θ + ε_{1}, X_{i} = θ (1 - γ) + γ X_{i - 1} + 1 - γ ε_{i},

where the

ε_{i}

are independent

N (0, 1)

and

0 \leq γ < 1

,

I_{n} (θ) = 1 + (n - 1) \frac{1 - γ}{1 + γ} .

The information tensorizes exactly when

γ = 0

.

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