Take Bitcoin into your portfolio: a novel ensemble portfolio optimization framework for broad commodity assets

Financial Innovation

Table 3 Robustness test with different hyperparameters

Dimension	LR	RMSE	MAE	DA
Stock market
11	0.1	0.00746	0.00617	0.76316
11	0.01	0.00683	0.00512	0.85955
11	0.001	0.00734	0.00545	0.76003
22	0.1	0.00711	0.00587	0.80214
22	0.01	0.00718	0.00553	0.84403
22	0.001	0.00713	0.00565	0.79469
33	0.1	0.00723	0.00573	0.83708
33	0.01	0.00699	0.00542	0.85697
33	0.001	0.00703	0.00556	0.82905
Wheat market
11	0.1	0.00911	0.00697	0.87057
11	0.01	0.00851	0.00657	0.94101
11	0.001	0.00869	0.00780	0.92607
22	0.1	0.00887	0.00757	0.88559
22	0.01	0.00878	0.00770	0.91746
22	0.001	0.00897	0.00765	0.85845
33	0.1	0.00971	0.00689	0.90955
33	0.01	0.00954	0.00678	0.91205
33	0.001	0.00884	0.00701	0.83208
Crude oil market
11	0.1	0.02272	0.01368	0.90702
11	0.01	0.01543	0.01144	0.94662
11	0.001	0.01783	0.01555	0.90035
22	0.1	0.02749	0.01491	0.91657
22	0.01	0.02798	0.01734	0.86432
22	0.001	0.02282	0.01395	0.87529
33	0.1	0.01971	0.01984	0.86621
33	0.01	0.02448	0.01664	0.91731
33	0.001	0.02178	0.01489	0.91466
Gold market
11	0.1	0.00486	0.00394	0.89441
11	0.01	0.00452	0.00362	0.92977
11	0.001	0.00518	0.00424	0.89826
22	0.1	0.00615	0.00528	0.86571
22	0.01	0.00661	0.00511	0.86957
22	0.001	0.00526	0.00593	0.87646
33	0.1	0.00576	0.00452	0.83258
33	0.01	0.00505	0.00384	0.82749
33	0.001	0.00489	0.00389	0.82021
Bitcoin market
11	0.1	0.03622	0.03106	0.81149
11	0.01	0.03464	0.02608	0.85393
11	0.001	0.03926	0.02807	0.81113
22	0.1	0.03666	0.03356	0.80768
22	0.01	0.03842	0.03121	0.76592
22	0.001	0.04158	0.03298	0.81942
33	0.1	0.03513	0.03050	0.82017
33	0.01	0.03957	0.03164	0.81856
33	0.001	0.03931	0.03818	0.78171