Switching Coefficients or Automatic Variable Selection: An Application in Forecasting Commodity Returns
Abstract
:1. Introduction
2. Methodology
- A simple AR(1) model
- A macro factor-based HMM, where and the parameters are driven by a Markov state variable;
- A macro factor-based stepwise regression, which is obtained when and the macro variables are recursively selected by backward/forward stepwise procedures;
- An HMM model that includes macro as well as asset-specific factors, which is obtained when and the parameters (, , and ) are driven by a Markov state variable;
- An HMM model that includes macro as well as aggregate (across all commodities) asset-specific factors, obtained when and and the parameters (, , and ) are driven by a Markov state variable;
- A stepwise regression model that includes macro as well as asset-specific factors, where and the parameters are recursively selected by backward/forward stepwise procedures;
- A stepwise regression model that includes macro as well as aggregate (across all commodities) asset-specific factors, where (while ) and the variables are recursively selected by backward/forward stepwise procedures;
- A stepwise regression model that includes macro- as well as aggregate and individual asset-specific factors, which is obtained when all the dummy variables are active and the variables are recursively selected by backward/forward stepwise methods.
2.1. Stepwise Regressions
2.2. Hidden Markov Models
3. Data
3.1. Commodity Futures Return Series
3.2. Macroeconomic Factors
3.3. Commodity Factors
4. The Statistical Predictive Performance
5. Asset Allocation Performance
6. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Light Crude Oil | Corn | Soybeans | Wheat | Coffee | Cocoa | Sugar | Cotton No. 2 | Gold | Silver | Platinum | Orange Juice | Lumber | Live Cattle | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Panel A | Macro Principal Components Only | |||||||||||||
Forward—Low | 0.0768 | 0.0748 | 0.0764 | 0.0825 | 0.0918 | 0.0703 | 0.0707 | 0.0698 | 0.0454 | 0.0801 | 0.0786 | 0.0842 | 0.0755 | 0.0758 |
Forward—High | 0.1142 | 0.1324 | 0.1149 | 0.1264 | 0.1006 | 0.1214 | 0.1113 | 0.1125 | 0.0655 | 0.1457 | 0.1498 | 0.1043 | 0.0973 | 0.0925 |
Backward—Low | 0.0775 | 0.0749 | 0.0762 | 0.0823 | 0.0902 | 0.0703 | 0.0709 | 0.0695 | 0.0455 | 0.0820 | 0.0785 | 0.0842 | 0.0755 | 0.0752 |
Backward—High | 0.1166 | 0.1407 | 0.1146 | 0.1286 | 0.1023 | 0.1620 | 0.1125 | 0.1139 | 0.0726 | 0.1458 | 0.1488 | 0.1057 | 0.1130 | 0.0926 |
Panel B | Macro Principal Components + Commodity-Specific Factors (Always Included) | |||||||||||||
Forward—Low | 0.0823 | 0.0741 | 0.0788 | 0.0862 | 0.0990 | 0.0791 | 0.0755 | 0.0661 | 0.0493 | 0.0905 | 0.0869 | 0.0946 | 0.0813 | 0.1039 |
Forward—High | 0.1182 | 0.1565 | 0.1140 | 0.1549 | 0.1339 | 0.1609 | 0.1180 | 0.1290 | 0.0824 | 0.1766 | 0.8282 | 0.1151 | 0.1247 | 0.1354 |
Backward—Low | 0.0822 | 0.0736 | 0.0804 | 0.0861 | 0.1003 | 0.0798 | 0.0752 | 0.0694 | 0.0481 | 0.0912 | 0.0938 | 0.0944 | 0.0801 | 0.0984 |
Backward—High | 0.1197 | 0.1780 | 0.1298 | 0.1666 | 0.1244 | 0.1659 | 0.1258 | 0.1414 | 0.0849 | 0.1768 | 0.7025 | 0.1270 | 0.1523 | 0.1538 |
Panel C | Macro Principal Components + Commodity-Specific Factors | |||||||||||||
Forward—Low | 0.0707 | 0.0725 | 0.0773 | 0.0846 | 0.0917 | 0.0728 | 0.0720 | 0.0682 | 0.0472 | 0.0829 | 0.0833 | 0.0900 | 0.0797 | 0.0833 |
Forward—High | 0.0648 | 0.1526 | 0.1029 | 0.1468 | 0.1159 | 0.1898 | 0.1126 | 0.1214 | 0.0762 | 0.1510 | 0.1539 | 0.1086 | 0.1182 | 0.1117 |
Backward—Low | 0.0696 | 0.0731 | 0.0780 | 0.0841 | 0.0925 | 0.0746 | 0.0717 | 0.0693 | 0.0471 | 0.0836 | 0.0840 | 0.0946 | 0.0791 | 0.0836 |
Backward—High | 0.0634 | 0.1598 | 0.1186 | 0.1632 | 0.1248 | 0.1616 | 0.1120 | 0.1228 | 0.0825 | 0.1707 | 0.7496 | 0.1171 | 0.1448 | 0.1228 |
Panel D | Macro Principal Components + Aggregated Commodity-Specific Factors (Always Included) | |||||||||||||
Forward—Low | 0.0851 | 0.0775 | 0.0894 | 0.0877 | 0.0971 | 0.0750 | 0.0788 | 0.0759 | 0.0661 | 0.0836 | 0.0792 | 0.0964 | 0.0852 | 0.1154 |
Forward—High | 0.2179 | 0.1829 | 0.1810 | 0.2229 | 0.1574 | 0.1652 | 0.2498 | 0.1851 | 0.0958 | 0.2103 | 0.2792 | 0.1316 | 0.1854 | 0.1140 |
Backward—Low | 0.0846 | 0.0780 | 0.0786 | 0.0873 | 0.0960 | 0.0750 | 0.0793 | 0.0767 | 0.0603 | 0.0837 | 0.0792 | 0.0960 | 0.0858 | 0.0909 |
Backward—High | 0.2113 | 0.1822 | 0.1741 | 0.2233 | 0.1614 | 0.1549 | 0.2234 | 0.2726 | 0.1169 | 0.2345 | 0.2644 | 0.1312 | 0.1884 | 0.1139 |
Panel E | Macro Principal Components + Aggregated Commodity-Specific Factors | |||||||||||||
Forward—Low | 0.0789 | 0.0786 | 0.0757 | 0.0852 | 0.0929 | 0.0750 | 0.0744 | 0.0724 | 0.0448 | 0.0796 | 0.0782 | 0.0959 | 0.0807 | 0.0770 |
Forward—High | 0.1265 | 0.1593 | 0.1107 | 0.1990 | 0.1444 | 0.1374 | 0.1220 | 0.1157 | 0.0761 | 0.1428 | 0.1701 | 0.1205 | 0.1212 | 0.0969 |
Backward—Low | 0.0795 | 0.0780 | 0.0767 | 0.0864 | 0.0909 | 0.0735 | 0.0746 | 0.0734 | 0.0458 | 0.0802 | 0.0782 | 0.0951 | 0.0850 | 0.0760 |
Backward—High | 0.1221 | 0.1589 | 0.1395 | 0.2050 | 0.1529 | 0.1340 | 0.1521 | 0.1691 | 0.0813 | 0.1700 | 0.1750 | 0.1233 | 0.1307 | 0.0979 |
Panel F | Macro Principal Components + Commodity-Specific Factors + Aggregated Commodity-Specific Factors (Always Included) | |||||||||||||
Forward—Low | 0.0848 | 0.0795 | 0.0773 | 0.0945 | 0.1041 | 0.0815 | 0.0844 | 0.0746 | 0.0475 | 0.0953 | 0.0827 | 0.1038 | 0.0884 | 0.0855 |
Forward—High | 0.2278 | 0.1739 | 0.1580 | 0.2322 | 0.1471 | 0.1722 | 0.2192 | 0.2086 | 0.1152 | 0.1963 | 0.5971 | 0.1322 | 0.1962 | 0.1467 |
Backward—Low | 0.0862 | 0.0788 | 0.0801 | 0.0939 | 0.1064 | 0.0838 | 0.0850 | 0.0738 | 0.0481 | 0.1841 | 0.0821 | 0.1085 | 0.0882 | 0.0865 |
Backward—High | 0.2264 | 0.1866 | 0.1607 | 0.2233 | 0.1663 | 0.1754 | 0.2242 | 0.3524 | 0.1360 | 0.2070 | 0.5627 | 0.1742 | 0.2487 | 0.1956 |
Panel G | Benchmark AR(1) | |||||||||||||
AR(1) | 0.0856 | 0.0867 | 0.0792 | 0.0946 | 0.0882 | 0.0799 | 0.0861 | 0.0800 | 0.0522 | 0.0955 | 0.0723 | 0.0916 | 0.0799 | 0.0463 |
Light Crude Oil | Corn | Soybeans | Wheat | Coffee | Cocoa | Sugar | Cotton No.2 | Gold | Silver | Platinum | Orange Juice | Lumber | Live Cattle | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Panel A | HMM—Macro Principal Components Only | |||||||||||||
0.1014 | 0.0970 | 0.1021 | 0.1069 | 0.2446 | 0.0909 | 0.1036 | 0.0958 | 0.1088 | 0.1215 | 0.0968 | 0.1213 | 0.0857 | 0.0472 | |
Panel B | HMM—Macro Principal Components + Commodity-Specific Factors | |||||||||||||
0.0871 | 0.1025 | 0.1430 | 0.1280 | 0.1153 | 0.1151 | 0.1040 | 0.0966 | 0.0989 | 0.3136 | 0.0921 | 0.1084 | 0.1074 | 0.0515 | |
Panel C | HMM—Macro Principal Components + Aggregated Commodity-Specific Factors | |||||||||||||
0.1326 | 0.0976 | 0.0877 | 0.1192 | 0.1074 | 0.1258 | 0.1414 | 0.1192 | 0.0815 | 0.1142 | 0.0834 | 0.1089 | 0.0978 | 0.0526 | |
Panel D | Stepwise Regression—Macro Principal Components Only | |||||||||||||
Forward | 0.0830 | 0.0920 | 0.0846 | 0.0973 | 0.0925 | 0.0836 | 0.0858 | 0.0821 | 0.0516 | 0.0962 | 0.0832 | 0.0911 | 0.0824 | 0.0829 |
Backward | 0.0817 | 0.0918 | 0.0845 | 0.0976 | 0.0916 | 0.0847 | 0.0860 | 0.0820 | 0.0531 | 0.0972 | 0.0830 | 0.0913 | 0.0843 | 0.0825 |
Panel E | Stepwise Regression—Macro Principal Components + Commodity-Specific Factors (Always Included) | |||||||||||||
Forward | 0.0841 | 0.0956 | 0.0838 | 0.1019 | 0.0981 | 0.0926 | 0.0880 | 0.0824 | 0.0546 | 0.1032 | 0.2508 | 0.0975 | 0.0901 | 0.0971 |
Backward | 0.0840 | 0.0936 | 0.0867 | 0.1032 | 0.0974 | 0.0957 | 0.0887 | 0.0860 | 0.0545 | 0.1035 | 0.2128 | 0.0978 | 0.0909 | 0.0977 |
Panel F | Stepwise Regression—Macro Principal Components + Commodity-Specific Factors | |||||||||||||
Forward | 0.0733 | 0.0916 | 0.0824 | 0.1019 | 0.0938 | 0.0899 | 0.0862 | 0.0818 | 0.0546 | 0.0972 | 0.0853 | 0.0943 | 0.0883 | 0.0869 |
Backward | 0.0723 | 0.0916 | 0.0849 | 0.1023 | 0.0934 | 0.0918 | 0.0862 | 0.0830 | 0.0536 | 0.0993 | 0.2267 | 0.0973 | 0.0892 | 0.0881 |
Panel G | Stepwise Regression—Principal Components + Aggregated Commodity-Specific Factors (Always Included) | |||||||||||||
Forward | 0.0989 | 0.0982 | 0.1038 | 0.1159 | 0.0996 | 0.0871 | 0.1144 | 0.0931 | 0.0662 | 0.1144 | 0.1080 | 0.1008 | 0.1032 | 0.1051 |
Backward | 0.0980 | 0.0984 | 0.0971 | 0.1159 | 0.0996 | 0.0858 | 0.1100 | 0.1151 | 0.0696 | 0.1146 | 0.1041 | 0.1000 | 0.1036 | 0.0922 |
Panel H | Stepwise Regression—Macro Principal Components + Aggregated Commodity-Specific Factors | |||||||||||||
Forward | 0.0826 | 0.0950 | 0.0822 | 0.1131 | 0.0969 | 0.0871 | 0.0890 | 0.0824 | 0.0524 | 0.0972 | 0.0896 | 0.0994 | 0.0876 | 0.0842 |
Backward | 0.0802 | 0.0951 | 0.0887 | 0.1162 | 0.0953 | 0.0831 | 0.0944 | 0.0874 | 0.0541 | 0.0978 | 0.0891 | 0.0986 | 0.0907 | 0.0837 |
Panel I | Stepwise Regression—Principal Components + Commodity-Specific Factors + Aggregated Commodity-Specific Factors (Always Included) | |||||||||||||
Forward | 0.0986 | 0.0963 | 0.0911 | 0.1185 | 0.0987 | 0.0914 | 0.1151 | 0.0945 | 0.0590 | 0.1096 | 0.1896 | 0.1037 | 0.1062 | 0.0914 |
Backward | 0.0957 | 0.1001 | 0.0937 | 0.1193 | 0.1029 | 0.0934 | 0.1108 | 0.1347 | 0.0674 | 0.1600 | 0.1939 | 0.1116 | 0.1146 | 0.0990 |
Panel J | Benchmark AR(1) | |||||||||||||
AR(1) | 0.0856 | 0.0867 | 0.0792 | 0.0946 | 0.0882 | 0.0799 | 0.0861 | 0.0800 | 0.0522 | 0.0955 | 0.0723 | 0.0916 | 0.0799 | 0.0463 |
Light Crude Oil | Corn | Soybeans | Wheat | Coffee | Cocoa | Sugar | Cotton No. 2 | Gold | Silver | Platinum | Orange Juice | Lumber | Live Cattle | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Panel A | Macro Principal Components Only | |||||||||||||
Forward—Low | 0.0613 | 0.0592 | 0.0547 | 0.0644 | 0.0688 | 0.0555 | 0.0583 | 0.0544 | 0.0356 | 0.0638 | 0.0653 | 0.0669 | 0.0610 | 0.0625 |
Forward—High | 0.0829 | 0.0952 | 0.0872 | 0.0932 | 0.0801 | 0.0971 | 0.0866 | 0.0842 | 0.0494 | 0.1084 | 0.0916 | 0.0874 | 0.0721 | 0.0701 |
Backward—Low | 0.0615 | 0.0597 | 0.0545 | 0.0641 | 0.0672 | 0.0555 | 0.0584 | 0.0543 | 0.0356 | 0.0645 | 0.0655 | 0.0670 | 0.0610 | 0.0618 |
Backward—High | 0.0817 | 0.1019 | 0.0869 | 0.0947 | 0.0826 | 0.1077 | 0.0894 | 0.0861 | 0.0517 | 0.1077 | 0.0890 | 0.0884 | 0.0847 | 0.0703 |
Panel B | Macro Principal Components + Commodity-Specific Factors (Always Included) | |||||||||||||
Forward—Low | 0.0644 | 0.0574 | 0.0605 | 0.0665 | 0.0791 | 0.0630 | 0.0610 | 0.0510 | 0.0378 | 0.0716 | 0.0702 | 0.0745 | 0.0659 | 0.0789 |
Forward—High | 0.0902 | 0.1192 | 0.0866 | 0.1139 | 0.0976 | 0.1139 | 0.0918 | 0.0990 | 0.0572 | 0.1378 | 0.4112 | 0.0969 | 0.0972 | 0.0984 |
Backward—Low | 0.0646 | 0.0570 | 0.0625 | 0.0660 | 0.0801 | 0.0642 | 0.0608 | 0.0542 | 0.0369 | 0.0723 | 0.0735 | 0.0741 | 0.0652 | 0.0736 |
Backward—High | 0.0923 | 0.1260 | 0.0971 | 0.1267 | 0.0923 | 0.1175 | 0.0934 | 0.1059 | 0.0587 | 0.1385 | 0.3565 | 0.1059 | 0.1162 | 0.1134 |
Panel C | Macro Principal Components + Commodity-Specific Factors | |||||||||||||
Forward—Low | 0.0563 | 0.0579 | 0.0585 | 0.0651 | 0.0682 | 0.0575 | 0.0597 | 0.0523 | 0.0369 | 0.0658 | 0.0679 | 0.0701 | 0.0650 | 0.0671 |
Forward—High | 0.0517 | 0.1089 | 0.0827 | 0.1080 | 0.0858 | 0.1129 | 0.0894 | 0.0905 | 0.0568 | 0.1214 | 0.0906 | 0.0893 | 0.0912 | 0.0868 |
Backward—Low | 0.0549 | 0.0581 | 0.0593 | 0.0644 | 0.0693 | 0.0598 | 0.0594 | 0.0523 | 0.0365 | 0.0669 | 0.0675 | 0.0745 | 0.0647 | 0.0673 |
Backward—High | 0.0507 | 0.1129 | 0.0918 | 0.1179 | 0.0930 | 0.1102 | 0.0883 | 0.0943 | 0.0586 | 0.1346 | 0.3724 | 0.0981 | 0.1083 | 0.0908 |
Panel D | Macro Principal Components + Aggregated Commodity-Specific Factors (Always Included) | |||||||||||||
Forward—Low | 0.0675 | 0.0630 | 0.0620 | 0.0691 | 0.0749 | 0.0596 | 0.0649 | 0.0589 | 0.0461 | 0.0665 | 0.0644 | 0.0761 | 0.0658 | 0.0908 |
Forward—High | 0.1292 | 0.1305 | 0.1195 | 0.1373 | 0.1172 | 0.1213 | 0.1761 | 0.1295 | 0.0708 | 0.1473 | 0.1526 | 0.1013 | 0.1174 | 0.0836 |
Backward—Low | 0.0668 | 0.0633 | 0.0585 | 0.0687 | 0.0736 | 0.0597 | 0.0651 | 0.0600 | 0.0433 | 0.0663 | 0.0645 | 0.0760 | 0.0656 | 0.0754 |
Backward—High | 0.1216 | 0.1304 | 0.1167 | 0.1394 | 0.1195 | 0.1205 | 0.1539 | 0.1517 | 0.0747 | 0.1576 | 0.1478 | 0.1014 | 0.1187 | 0.0830 |
Panel E | Macro Principal Components + Aggregated Commodity-Specific Factors | |||||||||||||
Forward—Low | 0.0625 | 0.0628 | 0.0563 | 0.0661 | 0.0686 | 0.0608 | 0.0614 | 0.0568 | 0.0350 | 0.0630 | 0.0653 | 0.0749 | 0.0631 | 0.0635 |
Forward—High | 0.0896 | 0.1122 | 0.0889 | 0.1258 | 0.1076 | 0.1047 | 0.0973 | 0.0869 | 0.0536 | 0.1128 | 0.1091 | 0.0946 | 0.0950 | 0.0713 |
Backward—Low | 0.0631 | 0.0621 | 0.0582 | 0.0679 | 0.0676 | 0.0586 | 0.0618 | 0.0573 | 0.0359 | 0.0630 | 0.0654 | 0.0746 | 0.0661 | 0.0631 |
Backward—High | 0.0854 | 0.1127 | 0.0962 | 0.1322 | 0.1147 | 0.1081 | 0.1132 | 0.1123 | 0.0577 | 0.1342 | 0.1163 | 0.0985 | 0.1000 | 0.0726 |
Panel F | Macro Principal Components + Commodity-Specific Factors + Aggregated Commodity-Specific Factors (Always Included) | |||||||||||||
Forward—Low | 0.0672 | 0.0615 | 0.0602 | 0.0734 | 0.0787 | 0.0650 | 0.0700 | 0.0588 | 0.0370 | 0.0760 | 0.0658 | 0.0829 | 0.0689 | 0.0688 |
Forward—High | 0.1309 | 0.1352 | 0.1131 | 0.1714 | 0.1203 | 0.1244 | 0.1515 | 0.1536 | 0.0796 | 0.1532 | 0.3081 | 0.1029 | 0.1339 | 0.1055 |
Backward—Low | 0.0678 | 0.0595 | 0.0626 | 0.0728 | 0.0815 | 0.0662 | 0.0702 | 0.0576 | 0.0377 | 0.0893 | 0.0641 | 0.0858 | 0.0690 | 0.0698 |
Backward—High | 0.1376 | 0.1409 | 0.1157 | 0.1536 | 0.1390 | 0.1301 | 0.1587 | 0.1785 | 0.0879 | 0.1602 | 0.2736 | 0.1257 | 0.1548 | 0.1367 |
Panel G | Benchmark AR(1) | |||||||||||||
AR(1) | 0.0682 | 0.0676 | 0.0603 | 0.0711 | 0.0647 | 0.0635 | 0.0674 | 0.0610 | 0.0408 | 0.0748 | 0.0492 | 0.0727 | 0.0635 | 0.0356 |
Light Crude Oil | Corn | Soybeans | Wheat | Coffee | Cocoa | Sugar | Cotton No. 2 | Gold | Silver | Platinum | Orange Juice | Lumber | Live Cattle | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Panel A | HMM—Macro Principal Components Only | |||||||||||||
0.0691 | 0.0710 | 0.0673 | 0.0766 | 0.0899 | 0.0675 | 0.0786 | 0.0691 | 0.0511 | 0.0809 | 0.0588 | 0.0833 | 0.0656 | 0.0359 | |
Panel B | HMM—Macro Principal Components + Commodity-Specific Factors | |||||||||||||
0.0656 | 0.0718 | 0.0757 | 0.0875 | 0.0862 | 0.0767 | 0.0781 | 0.0697 | 0.0510 | 0.1198 | 0.0611 | 0.0825 | 0.0763 | 0.0409 | |
Panel C | HMM—Macro Principal Components + Aggregated Commodity-Specific Factors | |||||||||||||
0.0830 | 0.0724 | 0.0636 | 0.0861 | 0.0830 | 0.0801 | 0.0898 | 0.0783 | 0.0491 | 0.0834 | 0.0563 | 0.0877 | 0.0735 | 0.0405 | |
Panel D | Stepwise Regression—Macro Principal Components Only | |||||||||||||
Forward | 0.0653 | 0.0699 | 0.0628 | 0.0734 | 0.0700 | 0.0658 | 0.0678 | 0.0627 | 0.0404 | 0.0754 | 0.0672 | 0.0732 | 0.0645 | 0.0656 |
Backward | 0.0638 | 0.0699 | 0.0626 | 0.0735 | 0.0692 | 0.0660 | 0.0684 | 0.0628 | 0.0410 | 0.0757 | 0.0671 | 0.0733 | 0.0656 | 0.0652 |
Panel E | Stepwise Regression—Macro Principal Components + Commodity-Specific Factors (Always Included) | |||||||||||||
Forward | 0.0662 | 0.0711 | 0.0653 | 0.0759 | 0.0773 | 0.0709 | 0.0694 | 0.0619 | 0.0417 | 0.0815 | 0.1064 | 0.0781 | 0.0704 | 0.0752 |
Backward | 0.0664 | 0.0697 | 0.0676 | 0.0762 | 0.0765 | 0.0733 | 0.0696 | 0.0642 | 0.0413 | 0.0822 | 0.1009 | 0.0784 | 0.0716 | 0.0748 |
Panel F | Stepwise Regression—Macro Principal Components + Commodity-Specific Factors | |||||||||||||
Forward | 0.0585 | 0.0692 | 0.0643 | 0.0751 | 0.0705 | 0.0680 | 0.0686 | 0.0617 | 0.0421 | 0.0764 | 0.0688 | 0.0751 | 0.0693 | 0.0687 |
Backward | 0.0571 | 0.0691 | 0.0657 | 0.0748 | 0.0705 | 0.0696 | 0.0689 | 0.0624 | 0.0416 | 0.0782 | 0.1003 | 0.0784 | 0.0701 | 0.0696 |
Panel G | Stepwise Regression—Macro Principal Components + Aggregated Commodity-Specific Factors (Always Included) | |||||||||||||
Forward | 0.0706 | 0.0733 | 0.0715 | 0.0793 | 0.0740 | 0.0681 | 0.0839 | 0.0685 | 0.0485 | 0.0818 | 0.0748 | 0.0791 | 0.0732 | 0.0814 |
Backward | 0.0696 | 0.0735 | 0.0689 | 0.0792 | 0.0739 | 0.0683 | 0.0813 | 0.0729 | 0.0482 | 0.0814 | 0.0736 | 0.0787 | 0.0731 | 0.0731 |
Panel H | Stepwise Regression—Macro Principal Components + Aggregated Commodity-Specific Factors | |||||||||||||
Forward | 0.0650 | 0.0721 | 0.0631 | 0.0783 | 0.0716 | 0.0694 | 0.0704 | 0.0636 | 0.0404 | 0.0756 | 0.0696 | 0.0782 | 0.0681 | 0.0662 |
Backward | 0.0642 | 0.0719 | 0.0660 | 0.0808 | 0.0706 | 0.0669 | 0.0732 | 0.0656 | 0.0417 | 0.0755 | 0.0707 | 0.0780 | 0.0701 | 0.0660 |
Panel I | Stepwise Regression—Macro Principal Components + Commodity-Specific Factors + Aggregated Commodity-Specific Factors (Always Included) | |||||||||||||
Forward | 0.0711 | 0.0730 | 0.0674 | 0.0857 | 0.0743 | 0.0719 | 0.0863 | 0.0697 | 0.0434 | 0.0856 | 0.0928 | 0.0824 | 0.0754 | 0.0706 |
Backward | 0.0696 | 0.0735 | 0.0701 | 0.0833 | 0.0789 | 0.0732 | 0.0848 | 0.0732 | 0.0449 | 0.0928 | 0.0896 | 0.0860 | 0.0791 | 0.0750 |
Panel J | Benchmark AR(1) | |||||||||||||
AR(1) | 0.0682 | 0.0676 | 0.0603 | 0.0711 | 0.0647 | 0.0635 | 0.0674 | 0.0610 | 0.0408 | 0.0748 | 0.0492 | 0.0727 | 0.0635 | 0.0356 |
Light Crude Oil | Corn | Soybeans | Wheat | Coffee | Cocoa | Sugar | Cotton No. 2 | Gold | Silver | Platinum | Orange Juice | Lumber | Live Cattle | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Panel A | HMM | |||||||||||||
0.0936 | 0.1039 | 0.1136 | 0.1170 | 0.1485 | 0.1036 | 0.1000 | 0.0960 | 0.0916 | 0.1754 | 0.1141 | 0.1119 | 0.0914 | 0.0673 | |
Panel B | Stepwise Regression Models | |||||||||||||
0.0860 | 0.0949 | 0.0886 | 0.1086 | 0.0966 | 0.0889 | 0.0962 | 0.0920 | 0.0576 | 0.1075 | 0.1430 | 0.0986 | 0.0943 | 0.0909 | |
Panel C | Benchmark AR(1) | |||||||||||||
AR(1) | 0.0856 | 0.0867 | 0.0792 | 0.0946 | 0.0882 | 0.0799 | 0.0861 | 0.0800 | 0.0522 | 0.0955 | 0.0723 | 0.0916 | 0.0799 | 0.0463 |
Light Crude Oil | Corn | Soybeans | Wheat | Coffee | Cocoa | Sugar | Cotton No. 2 | Gold | Silver | Platinum | Orange Juice | Lumber | Live Cattle | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Panel A | HMM | |||||||||||||
0.7530 | 0.0669 | 0.0646 | 0.0834 | 0.0801 | 0.0774 | 0.0762 | 0.0672 | 0.0488 | 0.0891 | 0.0606 | 0.0787 | 0.0718 | 0.0391 | |
Panel B | Stepwise Regression Models | |||||||||||||
0.0656 | 0.0713 | 0.0663 | 0.0780 | 0.0731 | 0.0693 | 0.0744 | 0.0658 | 0.0429 | 0.0802 | 0.0818 | 0.0782 | 0.0709 | 0.0709 | |
Panel C | Benchmark AR(1) | |||||||||||||
AR(1) | 0.0682 | 0.0676 | 0.0603 | 0.0711 | 0.0647 | 0.0635 | 0.0674 | 0.0610 | 0.0408 | 0.0748 | 0.0492 | 0.0727 | 0.0635 | 0.0356 |
= 0.1 | = 0.25 | = 0.5 | ||||||||||
Mean Return | Std. Dev. | Sharpe Ratio | Realized MV | Mean Return | Std. Dev. | Sharpe Ratio | Realized MV | Mean Return | Std. Dev. | Sharpe Ratio | Realized MV | |
HMM Macro Factors | 0.0006 | 0.0198 | 0.0962 | 0.0005 | 0.0001 | 0.0190 | 0.0258 | 0.0001 | 0.0002 | 0.0182 | 0.0328 | 0.0001 |
HMM Macro and Commodity-Specific Factors | 0.0020 | 0.0388 | 0.1813 | 0.0020 | −0.0002 | 0.0351 | −0.0246 | −0.0004 | 0.0019 | 0.0268 | 0.2446 | 0.0017 |
HMM Macro and Aggregate Commodity Factors | 0.0026 | 0.0429 | 0.2095 | 0.0025 | 0.0020 | 0.0185 | 0.3660 | 0.0019 | 0.0012 | 0.0213 | 0.1977 | 0.0011 |
Stepwise PCs—Forward | 0.0001 | 0.0181 | 0.0035 | 0.0001 | −0.0001 | 0.0183 | −0.0109 | −0.0001 | 0.0002 | 0.0166 | 0.0318 | 0.0001 |
Stepwise PCs—Backward | −0.0003 | 0.0220 | −0.0409 | −0.0003 | −0.0002 | 0.0202 | −0.0339 | −0.0002 | 0.0002 | 0.0182 | 0.0291 | 0.0001 |
Stepwise PCs and Commodity-Specific Factors (always incl.)—Forward | 0.0032 | 0.0376 | 0.2932 | 0.0031 | 0.0032 | 0.0369 | 0.3000 | 0.0030 | 0.0037 | 0.0361 | 0.3548 | 0.0034 |
Stepwise PCs and Commodity-Specific Factors (always incl.)—Backward | −0.0025 | 0.0388 | −0.2229 | −0.0026 | −0.0024 | 0.0379 | −0.2198 | −0.0026 | −0.0027 | 0.0381 | −0.2442 | −0.0030 |
Stepwise PCs and Commodity-Specific Factors—Forward | −0.0021 | 0.0291 | −0.2505 | −0.0021 | −0.0005 | 0.0312 | −0.0527 | −0.0006 | 0.0011 | 0.0246 | 0.1578 | 0.0010 |
Stepwise PCs and Commodity-Specific Factors—Backward | −0.0016 | 0.0274 | −0.1975 | −0.0016 | −0.0016 | 0.0271 | −0.1988 | −0.0016 | −0.0017 | 0.0253 | −0.2266 | −0.0018 |
Stepwise PCs and Aggregate Commodity Factors (always incl.)—Forward | −0.0030 | 0.0334 | −0.3088 | −0.0030 | −0.0024 | 0.0322 | −0.2582 | −0.0025 | −0.0024 | 0.0322 | −0.2577 | −0.0026 |
Stepwise PCs and Aggregate Commodity Factors (always incl.)—Backward | −0.0020 | 0.0329 | −0.2129 | −0.0021 | −0.0020 | 0.0361 | −0.1890 | −0.0021 | −0.0007 | 0.0322 | −0.0796 | −0.0010 |
Stepwise PCs and Aggregate Commodity Factors—Forward | −0.0010 | 0.0179 | −0.2020 | −0.0011 | −0.0007 | 0.0184 | −0.1408 | −0.0008 | −0.0008 | 0.0183 | −0.1520 | −0.0009 |
Stepwise PCs and Aggregate Commodity Factors—Backward | 0.0002 | 0.0319 | 0.0259 | 0.0002 | 0.0002 | 0.0319 | 0.0203 | 0.0001 | −0.0005 | 0.0320 | −0.0594 | −0.0008 |
Stepwise PCs and Aggregate Commodity- Specific Factors (always incl.)—Forward | 0.0019 | 0.0427 | 0.1550 | 0.0018 | 0.0005 | 0.0417 | 0.0400 | 0.0003 | 0.0011 | 0.0337 | 0.1151 | 0.0008 |
Stepwise PCs and Aggregate Commodity- Specific Factors (always incl.)—Backward | −0.0073 | 0.1213 | −0.2095 | −0.0081 | 0.0026 | 0.0370 | 0.2408 | 0.0024 | 0.0009 | 0.0341 | 0.0881 | 0.0006 |
AR(1) Benchmark | −0.0001 | 0.0154 | −0.0296 | −0.0001 | −0.0001 | 0.0154 | −0.0298 | −0.0002 | −0.0001 | 0.0154 | −0.0302 | −0.0002 |
= 0.1 | = 0.25 | = 0.5 | ||||||||||
Mean Return | Std. Dev. | Sharpe Ratio | Realized MV | Mean Return | Std. Dev. | Sharpe Ratio | Realized MV | Mean Return | Std. Dev. | Sharpe Ratio | Realized MV | |
HMM Macro Factors | 0.0002 | 0.0193 | 0.0330 | 0.0002 | −0.0020 | 0.0218 | −0.3101 | −0.0020 | −0.0016 | 0.0214 | −0.2637 | −0.0017 |
HMM Macro and Commodity-Specific Factors | 0.0029 | 0.0333 | 0.3007 | 0.0028 | 0.0011 | 0.0211 | 0.1764 | 0.0010 | 0.0012 | 0.0213 | 0.1977 | 0.0012 |
HMM Macro and Aggregate Commodity Factors | 0.0024 | 0.0473 | 0.1727 | 0.0022 | 0.0027 | 0.0277 | 0.3362 | 0.0026 | 0.0021 | 0.0194 | 0.3697 | 0.0020 |
Stepwise PCs—Forward | 0.0027 | 0.0306 | 0.3008 | 0.0026 | 0.0022 | 0.0306 | 0.2445 | 0.0020 | 0.0021 | 0.0304 | 0.2447 | 0.0019 |
Stepwise PCs—Backward | 0.0026 | 0.0363 | 0.2506 | 0.0026 | 0.0025 | 0.0360 | 0.2388 | 0.0023 | 0.0029 | 0.0346 | 0.2923 | 0.0026 |
Stepwise PCs and Commodity-Specific Factors (always incl.)—Forward | 0.0022 | 0.0541 | 0.1378 | 0.0020 | 0.0030 | 0.0530 | 0.1942 | 0.0026 | 0.0015 | 0.0506 | 0.1035 | 0.0009 |
Stepwise PCs and Commodity-Specific Factors (always incl.)—Backward | −0.0015 | 0.0352 | −0.1495 | −0.0016 | −0.0010 | 0.0341 | −0.1051 | −0.0012 | −0.0004 | 0.0347 | −0.0373 | −0.0007 |
Stepwise PCs and Commodity-Specific Factors—Forward | 0.0011 | 0.0089 | 0.4356 | 0.0011 | 0.0010 | 0.0082 | 0.4170 | 0.0010 | 0.0010 | 0.0083 | 0.4304 | 0.0010 |
Stepwise PCs and Commodity-Specific Factors—Backward | 0.0017 | 0.0248 | 0.2440 | 0.0017 | 0.0029 | 0.0214 | 0.4731 | 0.0029 | 0.0011 | 0.0217 | 0.1726 | 0.0010 |
Stepwise PCs and Aggregate Commodity Factors (always incl.)—Forward | 0.0013 | 0.0213 | 0.2140 | 0.0013 | 0.0009 | 0.0240 | 0.1344 | 0.0009 | 0.0009 | 0.0240 | 0.1266 | 0.0007 |
Stepwise PCs and Aggregate Commodity Factors (always incl.)—Backward | −0.0003 | 0.0219 | −0.0431 | −0.0003 | −0.0003 | 0.0218 | −0.0408 | −0.0003 | 0.0002 | 0.0238 | 0.0262 | 0.0000 |
Stepwise PCs and Aggregate Commodity Factors—Forward | 0.0011 | 0.0198 | 0.1996 | 0.0011 | 0.0010 | 0.0194 | 0.1774 | 0.0009 | 0.0008 | 0.0169 | 0.1577 | 0.0007 |
Stepwise PCs and Aggregate Commodity Factors—Backward | −0.0023 | 0.0447 | −0.1746 | −0.0024 | −0.0022 | 0.0446 | −0.1690 | −0.0024 | 0.0012 | 0.0164 | 0.2497 | 0.0011 |
Stepwise PCs and Aggregate Commodity- Specific Factors (always incl.)—Forward | 0.0066 | 0.0410 | 0.5590 | 0.0065 | 0.0065 | 0.0337 | 0.6651 | 0.0063 | 0.0063 | 0.0338 | 0.6452 | 0.0060 |
Stepwise PCs and Aggregate Commodity- Specific Factors (always incl.)—Backward | 0.0066 | 0.0410 | 0.5590 | 0.0065 | 0.0065 | 0.0337 | 0.6651 | 0.0063 | 0.0073 | 0.0325 | 0.7738 | 0.0070 |
AR(1) Benchmark | 0.0011 | 0.0133 | 0.2958 | 0.0011 | 0.0011 | 0.0133 | 0.2962 | 0.0011 | 0.0011 | 0.0132 | 0.2975 | 0.0011 |
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Guidolin, M.; Pedio, M. Switching Coefficients or Automatic Variable Selection: An Application in Forecasting Commodity Returns. Forecasting 2022, 4, 275-306. https://doi.org/10.3390/forecast4010016
Guidolin M, Pedio M. Switching Coefficients or Automatic Variable Selection: An Application in Forecasting Commodity Returns. Forecasting. 2022; 4(1):275-306. https://doi.org/10.3390/forecast4010016
Chicago/Turabian StyleGuidolin, Massimo, and Manuela Pedio. 2022. "Switching Coefficients or Automatic Variable Selection: An Application in Forecasting Commodity Returns" Forecasting 4, no. 1: 275-306. https://doi.org/10.3390/forecast4010016