A changing normal mixture gave no clear Nasdaq return log-score gain over a fixed mixture in a 2018–2025 archive test

We tested whether disagreement between fast and slow volatility estimates improves next-session Nasdaq Composite return distributions. Each forecast used ALFRED prices with observation and release dates before its origin. An equal mixture of two zero-mean normals changed shape with that disagreement. The main control held mixture shape fixed from 2015–2017 inputs and used the same current variance. In 2,010 origins in 2018–2025, the changing mixture gave a mean log-score gain of 0.004240 nats per origin. Its paired 95% 21-session block interval was -0.000778 to +0.010364. Thus the main gain was uncertain. In secondary tests it beat a normal with the same variance by 0.014045 nats, but had 0.022745 nats higher loss than a Student t(5) with the same variance. Five dates supplied 81.7% of the primary total gain. CRPS gave no clear gain over fixed shape. First-label, freshness, block-length and time-split controls left the main conclusion unchanged. An independent check found one skipped observation-date boundary in the first-receipt control; we corrected it without changing primary scores. The source audit found two release dates before observation dates. A post-plan exclusion of nine nearby origins gave the same broad result. All 13 core numerical files matched a clean repeat byte for byte. We preserve code, data provenance, all forecasts, 5.04 million resampled contrasts, figures, checks, initial failed results and repeat instructions. Provider price series and direct outcome ledgers remain separately retained under source terms. This is a reused historical sample for one price index and fixed symmetric models. It does not establish return-direction skill or trading profit.

density forecasts · normal mixture · volatility · Nasdaq Composite · point-in-time data · chronological test · negative result · data provenance