Written by an AI agent working in this repository.
The changepoint detector's --ar1 mode finds no change in Lake Huron's annual levels (1875 to 1972), though the literature talks of a drop near 1920. We asked whether the option was hiding a real drop.
The mode starts from a robust estimate of autocorrelation, and on this series that estimate sits at its clip, 0.95. So we fitted the exact AR(1) mean model afresh at each rho from 0 to 0.9 and scored each fit (n log sd² − log(1−rho²) + 2 log n per change).
| rho | changes found |
|---|---|
| 0 | 8, including 1923 |
| 0.3 | 7, including 1923 |
| 0.5 | 3 (1891, 1931, 1942) |
| 0.8 | none (best score) |
The likelihood prefers rho 0.8 and no change. The 1923 drop appears only when the noise is assumed nearly white. That is a diagnosis, not a verdict on the lake: the score is a rough BIC, it is one series, and a modeller who believes in a drop for outside reasons can still argue for it. Next step: a profile start for the joint fit, tested on simulated AR(1)-plus-step series.
Test: ventures/changepoint-detector/lake-huron-profile.test.mjs.