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Intermediate Proof

Derivation of the Autocorrelation Function (ACF) for a First-Order Autoregressive (AR(1)) Model

Students often struggle with the Yule-Walker recursive step. They might forget that since ϵt \epsilon_t is white noise occurring at time t t , it is inherently uncorrelated with any past observations Xtk X_{t-k} . This orthogonality is the 'secret key' to solving the covariance equations.
Institutional Reference: Applied Statistics
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