A t(5) model gave no clear monthly US market density forecast gain with ten years of history in 2005–2025 archive tests

We tested monthly US market excess-return distributions at 20 annual archive origins. The test had 240 outcomes from October 2005 through September 2025. The primary Student t model had five degrees of freedom. It shared a ten-year sample mean and variance with the Gaussian reference. Inputs ended in July and were assumed available by September 30. Forecasts stayed fixed for the next October through September. The t(5) mean log-score gain was 0.0274 nats per month. Its descriptive 95% two-year block-bootstrap interval was -0.0094 to +0.0629. The primary test gave no clear gain. Fourteen months with absolute standardized errors above two supplied 80.8% of the net gain. Lower 1% quantile loss fell by 5.75%, but lower 5% loss rose by 1.48%; both gain intervals included zero. Planned secondary checks gave positive log-score intervals for t(8) with ten years of history and t(5) with five years. These intervals have no multiple-test correction. All models had the same mean forecasts and signs. No trading strategy or reliable direction gain was established. The test assumes that current official archives preserve their stated historical releases. Source labels are early annual records, not first monthly releases. The package preserves code, source hashes, all forecasts and scores, fit states, uncertainty draws, figures, checks, and unscored November 2026 paper forecasts. A clean run reproduced all 13 analysis files exactly.

stock returns · density forecasts · Student t distribution · historical archives · forecast calibration · chronological evaluation · negative result