Oscillatory unit-root diagnosis from an undamped sample autocorrelation (${\Phi }_{\mathrm{osc}}(B)=1-2\cos \omega B+B^2$)

A large, slowly damping oscillatory sample autocorrelation function suggests autoregressive zeros near a conjugate pair on the unit circle. For period $s$, the pair is near $e^{\pm 2\pi i/s}$, with minimal real filter $1-2\cos (2\pi /s)B+B^2$. Such a plot is evidence, not proof: a finite sample cannot distinguish a near-unit stationary model or a random sinusoid solely from the shape.