Table 9 Results of different subgroups of Boston housing price.

From: Shapley value-driven superior subset selection algorithm for carbon price interval forecast combination

 

Subset

PICP (↑)

MPIW (↓)

CWC (↓)

IS (↓)

The best individual model

{9}

0.9509

19.5345

0.3992

23.8322

SA

{1,2,3,4,5,6,7,8,9,10}

0.9902

22.5381

0.5533

22.6950

Median

{1,2,3,4,5,6,7,8,9,10}

1

21.3760

0.4581

21.3760

IBSW

{1,2,3,4,5,6,7,8,9,10}

1

20.6668

0.4931

20.6668

IWSW

{1,2,3,4,5,6,7,8,9,10}

0.9804

21.7555

0.5419

21.9409

ICWCW

{1,2,3,4,5,6,7,8,9,10}

0.9902

25.1545

0.5354

25.6494

The proposed algorithm

{5,6,7}

1

16.4609

0.3116

16.4609

The proposed algorithm based on CWC

{1,7}

0.9706

20.0252

0.3646

34.4566

Deleting a model from the selected subset

{5,6}

0.8333

11.5499

341.9764

67.5498

{5,7}

0.9902

17.2747

0.2969

21.9414

{6,7}

1

18.1248

0.3454

18.1248

Adding a model to the selected subset

{1,5,6,7}

1

16.9744

0.3165

16.9745

{2,5,6,7}

1

17.6189

0.4162

17.6189

{3,5,6,7}

1

18.6991

0.3597

18.6991

{4,5,6,7}

1

17.1384

0.3533

17.1384

{5,6,7,8}

1

19.0728

0.3686

19.0728

{5,6,7,9}

1

16.9149

0.3138

16.9149

{5,6,7,10}

1

17.9543

0.3684

17.9543

HLN (0.15,0.25,0.35) [2]

{1,2,3,4,5,6,7,8,9,10}

1

20.6668

0.4931

20.6668

Encompassing test [7]

{1,2,4,5,7,9}

1

18.9567

0.4667

18.9567

CEI [18]

{4,9}}

0.9902

19.53

0.5044

30.3142

MI [13]

{1,9}

0.9608

18.6764

0.4553

55.5783

RRLS [14]

{1,5,7,9}

1

18.1714

0.3234

18.1714

  1. Note: Bold text highlights PICP values exceeding Pc, as well as the smallest MPIW, CWC and IS values when the PICP is greater than Pc. “↑” indicates that a higher value is better, while “↓” suggests that a lower value is preferable.