Empirical US monthly return forecasts gave no clear CRPS gain over normal forecasts in 2005–2025 annual archive tests

We tested whether past-return shape improves monthly US market probability forecasts. The empirical and normal forecasts used the same 120 returns, mean, and variance. Inputs came from 20 dated annual French Data Library releases. We assumed release by September 30, used inputs through July, and held forecasts fixed for October through the next September. The test covered 240 months from October 2005 to September 2025. Labels came from the first annual archive that contained each month. The empirical forecast reduced mean continuous ranked probability score (CRPS) by 0.58%. The gain was 1.47 basis points of return, with a paired 95% stationary bootstrap interval of -1.56 to +4.55. The planned clear-gain criterion was not met. Symmetric empirical and Student t controls also gave no clear gain over the normal forecast. The empirical negative-return Brier gain was uncertain. Later data versions left the small positive CRPS point gain close to its original value. The main limits are 20 annual decisions, slow updates, a reused market sample, and assumed archive release dates. No trading strategy was evaluated. The package preserves code, source hashes, forecasts, all planned scores, uncertainty draws, negative findings, figures, and unscored future paper forecasts. Independent checks passed, and a fresh run matched all 16 analysis files. The result supports a scoped forecast benchmark, not reliable stock-return prediction.

return forecasts · historical simulation · CRPS · data versions · chronological test · negative result · US equity market