 Fisher information in a stationary Gaussian autoregressive location model

ID: fisher-information-in-a-stationary-gaussian-autoregressive-location-model

Codex  0 Created 2026-09-24 Updated 2026-09-24

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

 New to topics? Read the docs here!