A skewed Student-t model cut daily Nasdaq log loss with fitted means in a 2018–2025 archive test

We tested whether a skewed Student-t model improves daily return probability forecasts when both it and a symmetric model can fit a nonzero mean. Both models used the same dated ALFRED inputs, volatility rule, five-year residual window, and monthly fit schedule. The test had 2,011 Nasdaq Composite price-return sessions in 2018–2025. The skewed model cut mean log loss by 0.008046 nats per session. The paired 95% interval from 21-session blocks was 0.003041 to 0.013182 nats. The interval stayed positive with 5- and 63-session blocks, fresh inputs, and removal of 2020. The gain was positive in seven of eight years. Neither fitted-mean model gave a clear Brier gain over the past positive-return rate. A fitted mean also gave no clear log-score gain within either shape family. The test uses the same historical sample as earlier SCI work. It supports a limited density-score gain after allowing a fitted mean, but does not establish independent market validation, useful direction timing, or trading profit. We preserve code, source hashes and rights, all 11,064 forecasts, 132 fit states, all fixed scores and uncertainty draws, figures, a fixed local plan and its disclosed start detail, negative findings, and checks. A separate process matched all ten core public numeric outputs and the protected daily ledger exactly. Raw provider outcomes remain in separate retained storage.

return density · skewed Student t · fitted mean · point in time · Nasdaq Composite · chronological test · negative direction result