Linear lag adjustment left no clear rise in Superior and Michigan-Huron monthly change correlation in 1920-2025

We tested whether a reported rise in monthly change correlation remains after linear lag adjustment. We used coordinated v2025 levels for Superior and Michigan-Huron. Separate models for 1920-1971 and 1972-2025 removed calendar-month means and three prior changes in both lakes. The month-mean-only correlation rose from 0.326 to 0.450. After lag adjustment, it rose from 0.417 to 0.436. The adjusted difference was 0.019, with a conditional 95% five-year block interval of -0.092 to +0.127. Adjustment reduced the difference by 0.105, with an interval of -0.166 to -0.040. Checks with 1, 6 and 12 lags gave similar estimates. Thus, the prior increase is sensitive to linear lag adjustment. This does not prove that memory caused the increase or that new shared inputs stayed constant. The models use fitted residuals, not measured water-budget inputs. Revised historical data, model form and block assumptions limit inference. The package gives source hashes, monthly values, code, resampling draws, a figure and independent numerical checks.

Great Lakes · monthly water levels · lag adjustment · partial correlation · block bootstrap · Lake Superior · Michigan-Huron · null result