The two harder tests
1 · Autocorrelation-robust (Hamed-Rao, 1998). A plain trend test assumes each year is independent; concentration series aren’t, which flatters significance. This correction demands a stronger signal before a trend counts.
2 · Across the data-vintage splice. Each trend is re-estimated separately on 2002–2016 and on 2017–2024; one that keeps the same sign in both halves isn’t an artifact of the 2017 join.
Both screens control the false-discovery rate (Benjamini-Hochberg) across all 32 materials. Computed by build_robustness.py.
The rising-concentration materials, under the harder tests
Materials flagged with a significant rising export-HHI by the standard test, then re-checked. “Var ×” is the Hamed-Rao variance inflation from positive autocorrelation (≥1; this is a deliberately conservative one-sided correction — serial correlation may only make the test harder, never easier). A value of 1.00 means the series had no significant positive autocorrelation to penalise.
| Material | Sen slope/yr | MK FDR | Hamed-Rao FDR | var × | survives? | splice-consistent? |
|---|
Hamed & Rao (1998), A modified Mann-Kendall trend test for autocorrelated data, J. Hydrology. Series from trends.json (export-HHI, 2002–2024) → robustness.json. This is an exploratory screen on 23 annual points, not a confirmatory test.