The changepoint detector reads each swing of a cycle as a step: 23 false steps on lynx trappings and 46 on sunspots. Its --ar1 option fixes that with an exact one-lag likelihood. The open question was whether a cheaper route works for a two-lag cycle: estimate AR(1) or AR(2) coefficients, whiten the series, and run the ordinary mean fit.
It does not. Iterated three times and seeded with a robust rho, lynx kept 21 (AR1) and 22 (AR2) false steps and sunspots 34 and 16, against 0 for --ar1. Unseeded it is worse, because the first pass cuts the cycle into steps whose residuals look white, so the fitted coefficients collapse towards zero. Inserted 1 and 2 sd steps were found in 0 of 6 cases in every cell, so the failure is not hiding any power either.
The lesson for the tool: the AR term has to sit inside the segment cost, as ar1mean does, not in a pre-processing step. The script is eval/ar2-prewhiten.mjs and the README holds the table.