Sample autocorrelation function ($\hat{\rho }(h)$)

The sample autocorrelation function replaces the mean and lagged covariance in $\rho (h)$ by their empirical counterparts.

A correlogram plots the estimated autocorrelation function against lag. The plot helps distinguish the finite autocorrelation cutoff of a moving-average model from the decaying dependence of a causal autoregressive model. Estimated cutoffs are diagnostics, not exact finite-sample identities.