Applications of state space models in finance

182 Appendix C
Table C.4: Out-of-sample mean absolute errors (100 samples).
This table reports the estimated out-of-sample MAE (×10 2 ) for the eighteen DJ Stoxx sectors.
For each sector i, figures in parentheses denote the relative rank of a model’s MAE, where the
model with the smallest MAE ranks first.
Sector β OLS
β tG
β SV
β RW
β MR
β MMR β GRW β MSM β MS
Automobiles 1.309 1.287 1.294 1.289 1.336 1.257 1.254 1.279 1.299
(8) (4) (6) (5) (9) (2) (1) (3) (7)
Banks 0.456 0.489 0.482 0.478 0.447 0.480 0.488 0.459 0.454
(3) (9) (7) (5) (1) (6) (8) (4) (2)
Basics 1.584 1.496 1.517 1.485 1.495 1.493 1.489 1.568 1.583
(9) (5) (6) (1) (4) (3) (2) (7) (8)
Chemicals 1.106 0.991 1.026 0.931 0.959 0.942 0.948 1.083 1.090
(9) (5) (6) (1) (4) (2) (3) (7) (8)
Construction 0.938 0.872 0.863 0.870 0.926 0.882 0.881 0.909 0.916
(9) (3) (1) (2) (8) (5) (4) (6) (7)
Financials 0.679 0.710 0.699 0.694 0.666 0.678 0.699 0.673 0.673
(5) (9) (8) (6) (1) (4) (7) (3) (2)
Food 0.941 0.959 0.957 0.931 FTC a
0.929 0.935 0.933 0.951
(5) (8) (7) (2) (–) (1) (4) (3) (6)
Healthcare 1.032 1.096 1.095 1.024 1.022 1.028 1.021 1.046 1.011
(6) (9) (8) (4) (3) (5) (2) (7) (1)
Industrials 0.794 0.738 0.728 0.740 0.788 0.741 0.745 0.806 0.799
(7) (2) (1) (3) (6) (4) (5) (9) (8)
Insurance 1.098 0.991 1.011 1.017 1.080 1.000 1.004 1.127 1.097
(8) (1) (4) (5) (6) (2) (3) (9) (7)
Media 0.941 1.012 1.028 0.964 0.956 0.973 0.964 0.975 1.032
(1) (7) (8) (3) (2) (5) (4) (6) (9)
Oil & Gas 1.232 1.261 1.251 1.244 1.239 1.245 1.255 1.259 1.261
(1) (8) (5) (3) (2) (4) (6) (7) (9)
Personal 0.665 0.666 0.667 0.662 0.655 0.659 0.655 0.662 0.668
(6) (7) (8) (5) (2) (3) (1) (4) (9)
Retail 1.072 1.141 1.123 1.122 1.108 1.095 1.092 1.107 1.099
(1) (9) (8) (7) (6) (3) (2) (5) (4)
Technology 1.818 1.778 1.752 1.820 1.813 1.762 1.781 1.900 1.885
(6) (3) (1) (7) (5) (2) (4) (9) (8)
Telecom 1.161 1.089 1.078 1.057 1.053 1.044 1.065 1.147 1.129
(9) (6) (5) (3) (2) (1) (4) (8) (7)
Travel 0.738 0.757 0.753 0.739 0.741 0.736 0.739 0.748 0.761
(2) (8) (7) (4) (5) (1) (3) (6) (9)
Utilities 0.833 0.838 0.824 0.846 0.843 0.842 0.849 0.902 0.831
(3) (4) (1) (7) (6) (5) (8) (9) (2)
Average MAE 1.022 1.009 1.008 0.995 1.007 0.988 0.992 1.032 1.030
Average Rank 5.44 5.94 5.39 4.06 4.24 3.22 3.94 6.22 6.28
a Failed to converge.