A normal mixture cut daily Nasdaq log loss against a normal model with the same variance in 2018–2025

We tested a fixed equal mixture of fast and slow normal return forecasts against one normal forecast with the same mean and variance. The final test used 2,011 Nasdaq Composite sessions in 2018–2025. Inputs used earlier ALFRED data versions. Outcomes used the first version with both endpoint prices. The mixture cut mean negative log density by 0.01233 nats per session. The paired 95% 21-session block interval for mixture minus normal was −0.02157 to −0.00548. The gain remained without 2020, with fresh inputs, and with longer blocks. However, a fixed Student t forecast with five degrees of freedom had 0.02544 nats less loss than the mixture. The mixture gave no clear CRPS or lower 5% quantile gain over the matched normal. Both models have identical variance loss and give probability 0.5 to a rise. This is a limited distribution-shape result on a known historical sample. It does not establish direction skill or trading profit. The package preserves code, source records, all forecasts, annual fits, aggregate scores, resampling draws, figures, a local plan, checks and an exact replay. Protected source outcomes remain in separate retained research data.

return density · normal mixture · volatility forecasts · point-in-time data · Nasdaq · chronological evaluation