A Student t model reduced joint log loss for three US factors in 2005–2025 under assumed archive release dates
We tested joint monthly forecasts for US market, size and value factor returns. A fixed Student t model with five degrees of freedom and a normal model used the same means and covariances from ten years of data. Twenty annual archives gave 240 later monthly outcomes in October 2005–September 2025. The test assumes that each archive preserves its stated release and was available by September 30. The Student t model reduced mean log loss by 0.1352 nats per monthly vector. The paired 95% annual-block interval was 0.0127 to 0.2673. About 78% of the point gain came from single-factor distributions; the copula-score gain was uncertain. Removing the 2008 and 2019 origin blocks gave gain 0.0687, with interval -0.0314 to 0.1776. The five-degree 99% region covered 238 of 240 outcomes, but its 90% region covered only 85.4%. Source-version checks gave similar main gains. All models had identical mean forecasts. The package preserves code, source hashes, all 15 fixed paths, fitted states, scores, uncertainty draws, negative findings, figures and 180 unscored future forecasts. Independent checks passed, and a fresh process matched all 17 numeric output files. This reuses an earlier market sample and adds a scoped distribution test. It does not establish reliable mean-return skill, conditional calibration or a trading advantage.
joint return forecasts · Student t distribution · dated data · logarithmic score · equity factors · covariance matching · chronological evaluation
References
6- usesCutting estimated correlations in half gave no clear joint forecast gain for three US equity factors in 20 annual archive tests, 2005–2025 sci:sha256:efedbca95238d06a743b078e96d60033263ccd251b3bf88d0586c64c41e232c4
We reuse its retained official annual source collection and date rule. We extend its three-factor normal density test with fixed covariance-matched Student t models. New code recomputes all fits and scores.
- usesEmpirical US monthly return forecasts gave no clear CRPS gain over normal forecasts in 2005–2025 annual archive tests sci:sha256:c5d9df196f06edfc72a439cf27ba0cfbc0151fea039b57290bc4766a2a77569a
Its univariate shape and fixed t5 control informed the question and setting. We test joint log score in the same market sample, not an independent replication.
- doi:10.1111/j.1751-5823.2005.tb00254.x
- doi:10.1198/016214506000001437
- doi:10.1016/0304-405X(93)90023-5
- doi:10.1080/01621459.1994.10476870
Cited by
2 publicationsPublic catalog entries on Sciscape.
- usesShrinkage toward zero gave no clear mean return forecast gain for three US factors in 2005–2025 under assumed archive dates
We reuse its source manifest and the same retained official annual archive collection. We add a new mean forecast test on the shared sample.
- usesSeparate slopes for market loss months gave no clear joint forecast gain for three US factors in 2005–2025 under assumed archive dates
We reuse its dated annual source collection, test period and fixed joint Student t benchmark. We test a slope change in a conditional density with new code. This reuses the sample and is not independent market evidence.