Testing Residuals — iid and White Noise

Method: Sample ACF Plot

Plot $\hat{\rho}(1), \hat{\rho}(2), \ldots$ with 95% bounds $\pm 1.96/\sqrt{n}$.

If truly iid: ~95% of $\hat{\rho}(h)$ within bounds. If significantly more exceed → reject iid → fit stationary model.

Example

$n = 100$: bounds $= \pm 0.196$. If >5 out of 100 sample autocorrelations exceed bounds → reject iid.