Separate tail parameters after calendar gaps gave no clear daily Nasdaq log-score gain in a 2018–2025 archive test

We tested whether returns after weekends and holidays need a different tail parameter in a daily Nasdaq Composite forecast. All models used dated ALFRED inputs, a fixed recent-risk scale and annual fits from earlier data. The primary reference fitted two calendar-gap scales and one common Student-t tail parameter. The candidate fitted a tail parameter in each gap group. The final test had 2,011 sessions in 2018–2025, including 441 after gaps longer than one calendar day. The candidate changed mean negative log density by -0.000253 nats per session. The paired 95% interval from six-month blocks was -0.001164 to +0.000719. All fixed sample and block-length checks also gave intervals that include zero. The candidate gave no clear lower-tail quantile or loss-event probability gain. A pooled Student-t model did improve log loss against a fitted normal reference. The package preserves forecasts, fits, failed optimizer attempts, source provenance, code, aggregate scores, figures and repeat instructions. This is a test of one symmetric daily density system on known market history. It does not establish return-direction skill or trading profit.

stock returns · calendar gaps · Student-t · density forecasts · point-in-time data · chronological evaluation · negative result