Some Novel Bayesian Model Combination Schemes: An Application to Commodities Prices
Abstract
:1. Introduction
2. Literature Review
2.1. Dynamic Model Averaging
2.2. Other Models
2.3. Commodities Prices Predictors
3. Data
4. Methodology
4.1. Dynamic Model Averaging (DMA)
4.2. Dynamic Model Selection (DMS)
4.3. Median Probability Model (MED)
4.4. Evaluation of Models
5. Results and Discussion
5.1. Descriptive Analysis of the First Results
5.2. Main Results
5.3. Further Remarks
6. Conclusions
Funding
Conflicts of Interest
Abbreviations
ARIMA | Auto ARIMA model described by Hyndman and Khandakar [71] |
BMA | Bayesian Model Averaging as a special case of DMA with forgetting factors |
BMED | Bayesian Median Probability Model as a special case of MED with forgetting factors |
BMS | Bayesian Model Selection as a special case of DMS with forgetting factors |
DM | The Diebold–Mariano test [75] |
DMA | Dynamic Model Averaging proposed by Raftery et al. [4] |
DMS | Dynamic Model Selection, i.e., model averaging in DMA replaced by selecting the model with the highest posterior probability |
MED | Median Probability Model of Barbieri and Berger [74] |
NAIVE | the naive forecast, i.e., the last observation is the one-ahead forecast |
RMSE | Root Mean Squared Error |
nRMSE | Normalized RMSE, i.e., RMSE divided by the mean value of the forecasted time-series |
TVP | Time-Varying Parameters, i.e., DMA reduced to exactly one model, i.e., the one with all predictors |
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IBEVERAGES | Beverages index includes cocoa, coffee and tea. |
---|---|
IFOOD | Food index includes fats and oils, grains and other food items. |
IFATS_OILS | Fats and oils index includes coconut oil, groundnut oil, palm oil, soybeans, soybean oil and soybean meal. |
IGRAINS | Grains index includes barley, maize, rice and wheat. |
IOTHERFOOD | Other food index includes bananas, beef, chicken meat, oranges and sugar. |
IRAW_MATERIAL | Agricultural raw materials index includes timber and other raw materials. |
ITIMBER | Timber index includes tropical hard logs and sawn wood. |
IOTHERRAWMAT | Other raw materials index includes cotton, natural rubber and tobacco. |
IAGRICULTURE | Agriculture index includes beverages, food and agricultural raw materials. |
ALUMINUM | Aluminium (LME) London Metal Exchange, unalloyed primary ingots, high grade, minimum 99.7% purity, settlement price beginning 2005; previously cash price |
BANANA_US | Bananas (Central & South America), major brands, US import price, free on truck US (f.o.t.) Gulf ports |
BARLEY | Barley (Canada), feed, Western No. 1, Winnipeg Commodity Exchange, spot, wholesale farmers’ price |
COAL_AUS | Coal (Australia), thermal, f.o.b. piers, Newcastle/Port Kembla, 6300 kcal/kg (11,340 btu/lb), less than 0.8%, sulfur 13% ash beginning January 2002; previously 6667 kcal/kg (12,000 btu/lb), less than 1.0% sulfur, 14% ash |
COCOA | Cocoa (ICCO), International Cocoa Organization daily price, average of the first three positions on the terminal markets of New York and London, nearest three future trading months. |
COCONUT_OIL | Coconut oil (Philippines/Indonesia), bulk, c.i.f. Rotterdam |
COFFEE_ARABIC | Coffee (ICO), International Coffee Organization indicator price, other mild Arabicas, average New York and Bremen/Hamburg markets, ex-dock |
COFFEE_ROBUS | Coffee (ICO), International Coffee Organization indicator price, Robustas, average New York and Le Havre/Marseilles markets, ex-dock |
COPPER | Copper (LME), grade A, minimum 99.9935% purity, cathodes and wire bar shapes, settlement price |
COPRA | Copra (Philippines/Indonesia), bulk, c.i.f. N.W. Europe |
COTTON_A_INDX | Cotton (Cotton Outlook “CotlookA index”), middling 1-3/32 inch, traded in Far East, C/F beginning 2006; previously Northern Europe, c.i.f. |
CRUDE_PETRO | Crude oil, average spot price of Brent, Dubai and West Texas Intermediate, equally weighed |
CRUDE_BRENT | Crude oil, U.K. Brent 38’ API, f.o.b. U.K ports, spot price |
CRUDE_DUBAI | Crude oil, Dubai Fateh 32’ API, f.o.b. Dubai, spot price |
CRUDE_WTI | Crude oil, West Texas Intermediate (WTI) 40’ API, f.o.b. Midland Texas, spot price |
DAP | DAP (diammonium phosphate), standard size, bulk, spot, f.o.b. US Gulf |
IENERGY | Energy index, a Laspeyres Index with fixed weights based on 2002–2004 average developing countries export values, for coal, crude oil and natural gas. |
IFERTILIZERS | Fertilizers index includes natural phosphate rock, phosphate, potassium and nitrogenous products. |
FISH_MEAL | Fishmeal (any origin), 64–65%, c&f Bremen, estimates based on wholesale price, beginning 2004; previously c&f Hamburg |
GOLD | Gold (UK), 99.5% fine, London afternoon fixing, average of daily rates |
GRNUT_OIL | Groundnut oil (any origin), c.i.f. Rotterdam |
LEAD | Lead (LME), refined, 99.97% purity, settlement price |
LOGS_CMR | Logs (West Africa), sapele, high quality (loyal and marchand), 80 centimeter or more, f.o.b. Douala, Cameroon beginning January 1996; previously of unspecified dimension |
LOGS_MYS | Logs (Malaysia), meranti, Sarawak, sale price charged by importers, Tokyo beginning February 1993; previously average of Sabah and Sarawak weighted by Japanese import volumes |
MAIZE | Maize (US), no. 2, yellow, f.o.b. US Gulf ports |
BEEF | Meat, beef (Australia/New Zealand), chucks and cow forequarters, frozen boneless, 85% chemical lean, c.i.f. U.S. port (East Coast), ex-dock, beginning November 2002; previously cow forequarters |
CHICKEN | Meat, sheep (New Zealand), frozen whole carcasses Prime Medium (PM) wholesale, Smithfield, London beginning January 2006; previously Prime Light (PL) |
IMETMIN | Metals and minerals index includes aluminum, copper, iron ore, lead, nickle, tin and zinc. |
NGAS_US | Natural Gas (U.S.), spot price at Henry Hub, Louisiana |
NICKEL | Nickel (LME), cathodes, minimum 99.8% purity, settlement price beginning 2005; previously cash price |
INONFUEL | Non-energy index, a Laspeyres Index with fixed weights based on 2002–2004 average developing countries export values, for 34 commodities contain in the agriculture, fertilizer, and metals and minerals indices. |
ORANGE | Oranges (Mediterranean exporters) navel, EEC indicative import price, c.i.f. Paris |
PALM_OIL | Palm oil (Malaysia), 5% bulk, c.i.f. N. W. Europe |
PLATINUM | Platinum (UK), 99.9% refined, London afternoon fixing |
PLYWOOD | Plywood (Africa and Southeast Asia), Lauan, 3-ply, extra, 91 cm × 182 cm × 4 mm, wholesale price, spot Tokyo |
POTASH | Potassium chloride (muriate of potash), standard grade, spot, f.o.b. Vancouver |
RICE_05 | Rice (Thailand), 5% broken, white rice (WR), milled, indicative price based on weekly surveys of export transactions, government standard, f.o.b. Bangkok |
RUBBER1_MYSG | Rubber (Asia), RSS3 grade, Singapore Commodity Exchange Ltd. (SICOM) nearby contract beginning 2004; during 2000 to 2003, Singapore RSS1; previously Malaysia RSS1 |
SAWNWD_MYS | Sawnwood (Malaysia), dark red seraya/meranti, select and better quality, average 7 to 8 inches; length average 12 to 14 inches; thickness 1 to 2 inch(es); kiln dry, c. & f. UK ports, with 5% agents commission including premium for products of certified sustainable forest beginning January 2005; previously excluding the premium |
SHRIMP_MEX | Shrimp, (Mexico), west coast, frozen, white, No. 1, shell-on, headless, 26 to 30 count per pound, wholesale price at New York |
SILVER | Silver (Handy & Harman), 99.9% grade refined, New York |
SORGHUM | Sorghum (US), no. 2 milo yellow, f.o.b. Gulf ports |
SOYBEAN_MEAL | Soybean meal (any origin), Argentine 45/46% extraction, c.i.f. Rotterdam beginning 1990; previously US 44% |
SOYBEAN_OIL | Soybean oil (Any origin), crude, f.o.b. ex-mill Netherlands |
SOYBEANS | Soybeans (US), c.i.f. Rotterdam |
SUGAR_EU | Sugar (EU), European Union negotiated import price for raw unpackaged sugar from African, Caribbean and Pacific (ACP) under Lome Conventions, c.I.f. European ports |
SUGAR_US | Sugar (US), nearby futures contract, c.i.f. |
SUGAR_WLD | Sugar (world), International Sugar Agreement (ISA) daily price, raw, f.o.b. and stowed at greater Caribbean ports |
TEA_AVG | Tea, average three auctions, arithmetic average of quotations at Kolkata, Colombo and Mombasa/Nairobi. |
TEA_COLOMBO | Tea (Colombo auctions), Sri Lankan origin, all tea, arithmetic average of weekly quotes. |
TEA_KOLKATA | Tea (Kolkata auctions), leaf, include excise duty, arithmetic average of weekly quotes. |
TEA_MOMBASA | Tea (Mombasa/Nairobi auctions), African origin, all tea, arithmetic average of weekly quotes. |
TIN | Tin (LME), refined, 99.85% purity, settlement price |
TOBAC_US | Tobacco (any origin), unmanufactured, general import, cif, US |
TSP | TSP (triple superphosphate), up to September 2006 bulk, spot, f.o.b. US Gulf; from October 2006 onwards Tunisian, granular, f.o.b. |
UREA_EE_BULK | Urea, (Black Sea), bulk, spot, f.o.b. Black Sea (primarily Yuzhnyy) beginning July 1991; for 1985–1991 (June) f.o.b. Eastern Europe |
WHEAT_US_HRW | Wheat (US), no. 1, hard red winter, ordinary protein, export price delivered at the US Gulf port for prompt or 30 days shipment |
WHEAT_US_SRW | Wheat (US), no. 2, soft red winter, export price delivered at the US Gulf port for prompt or 30 days shipment |
WOODPULP | Woodpulp (Sweden), softwood, sulphate, bleached, air-dry weight, c.i.f. North Sea ports |
ZINC | Zinc (LME), high grade, minimum 99.95% purity, settlement price beginning April 1990; previously special high grade, minimum 99.995%, cash prices |
Variable | Mean | Standard Deviation | Min | Max | Skewness | Kurtosis |
---|---|---|---|---|---|---|
dpr | −0.0134 | 0.0035 | −0.0200 | −0.0057 | 0.2356 | −0.8496 |
str | 0.0358 | 0.0277 | 0.0001 | 0.1047 | 0.2098 | −1.0013 |
ltr | 0.0553 | 0.0263 | 0.0150 | 0.1356 | 0.5970 | −0.0447 |
ts | 0.0195 | 0.0107 | −0.0053 | 0.0376 | −0.2611 | −0.9187 |
drs | 0.0327 | 0.0126 | 0.0036 | 0.0593 | −0.2889 | −0.8796 |
cpi | 0.0022 | 0.0026 | −0.0179 | 0.0137 | −1.4017 | 11.2535 |
ip | 0.0017 | 0.0061 | −0.0440 | 0.0203 | −1.5642 | 9.4380 |
une | 0.0609 | 0.0146 | 0.0380 | 0.1000 | 0.7915 | −0.0500 |
aud | −0.0004 | 0.0332 | −0.1798 | 0.0885 | −0.7722 | 2.7502 |
inr | −0.0045 | 0.0186 | −0.1956 | 0.0594 | −3.1422 | 28.1909 |
kei | −0.0167 | 0.2709 | −1.3324 | 0.6661 | 0.0505 | 1.5030 |
op | 0.0136 | 0.0224 | −0.0727 | 0.0937 | −0.1124 | 3.4690 |
tr | 0.0010 | 0.0338 | −0.2010 | 0.1168 | −0.7119 | 4.1604 |
m | 0.0047 | 0.0083 | −0.0337 | 0.0574 | 1.5217 | 9.2340 |
IBEVERAGES | −0.0002 | 0.0462 | −0.1592 | 0.2870 | 0.8529 | 4.7751 |
IFOOD | 0.0009 | 0.0305 | −0.1877 | 0.1500 | −0.1921 | 4.6650 |
IFATS_OILS | 0.0006 | 0.0459 | −0.2540 | 0.1998 | −0.3230 | 3.6843 |
IGRAINS | 0.0005 | 0.0415 | −0.1962 | 0.1837 | 0.1331 | 2.2778 |
IOTHERFOOD | 0.0019 | 0.0336 | −0.1016 | 0.1055 | 0.1153 | 0.3257 |
IRAW_MATERIAL | 0.0012 | 0.0256 | −0.0901 | 0.1103 | 0.3225 | 2.7758 |
ITIMBER | 0.0016 | 0.0338 | −0.1317 | 0.2011 | 1.0682 | 7.1127 |
IOTHERRAWMAT | 0.0007 | 0.0347 | −0.1967 | 0.1147 | −0.5056 | 3.8493 |
IAGRICULTURE | 0.0008 | 0.0241 | −0.1591 | 0.0941 | −0.4836 | 5.1574 |
ALUMINUM | 0.0008 | 0.0561 | −0.3262 | 0.1801 | −0.5625 | 3.6371 |
BANANA_US | 0.0028 | 0.1619 | −0.4556 | 0.5934 | 0.3911 | 1.5758 |
BARLEY | 0.0015 | 0.0680 | −0.2788 | 0.2832 | −0.0479 | 2.5754 |
COAL_AUS | 0.0030 | 0.0558 | −0.3285 | 0.3637 | 0.2609 | 8.5692 |
COCOA | −0.0005 | 0.0569 | −0.1948 | 0.2309 | 0.0823 | 0.8005 |
COCONUT_OIL | 0.0010 | 0.0782 | −0.2598 | 0.3512 | 0.3355 | 1.2619 |
COFFEE_ARABIC | −0.0001 | 0.0756 | −0.3525 | 0.4227 | 0.6971 | 4.0604 |
COFFEE_ROBUS | −0.0007 | 0.0673 | −0.2498 | 0.3779 | 0.6395 | 3.4206 |
COPPER | 0.0039 | 0.0635 | −0.3501 | 0.2492 | −0.3496 | 4.1479 |
COPRA | 0.0010 | 0.0760 | −0.2128 | 0.3258 | 0.3644 | 1.3311 |
COTTON_A_INDX | −0.0003 | 0.0560 | −0.2690 | 0.2006 | −0.0479 | 2.7694 |
CRUDE_PETRO | 0.0016 | 0.0874 | −0.4388 | 0.4304 | −0.4109 | 3.7925 |
CRUDE_BRENT | 0.0017 | 0.0910 | −0.3834 | 0.4326 | −0.2648 | 2.7104 |
CRUDE_DUBAI | 0.0017 | 0.0928 | −0.5401 | 0.4910 | −0.5290 | 6.1827 |
CRUDE_WTI | 0.0014 | 0.0851 | −0.3968 | 0.3755 | −0.4118 | 2.7034 |
DAP | 0.0012 | 0.0619 | −0.4597 | 0.2551 | −0.9681 | 12.9591 |
IENERGY | 0.0015 | 0.0720 | −0.3337 | 0.3449 | −0.4010 | 2.8708 |
IFERTILIZERS | 0.0020 | 0.0461 | −0.2749 | 0.2425 | −0.3816 | 5.6836 |
FISH_MEAL | 0.0026 | 0.0433 | −0.1542 | 0.2002 | 0.2202 | 1.3521 |
GOLD | 0.0029 | 0.0356 | −0.1248 | 0.1601 | 0.3494 | 1.3229 |
GRNUT_OIL | 0.0012 | 0.0515 | −0.2102 | 0.2607 | 0.3673 | 3.9632 |
LEAD | 0.0045 | 0.0702 | −0.2933 | 0.3091 | −0.3071 | 2.6723 |
LOGS_CMR | 0.0021 | 0.0345 | −0.1743 | 0.1440 | −0.2417 | 3.5366 |
LOGS_MYS | 0.0013 | 0.0500 | −0.1931 | 0.2941 | 0.8165 | 5.0984 |
MAIZE | 0.0001 | 0.0586 | −0.2448 | 0.2975 | −0.1347 | 3.5803 |
BEEF | 0.0015 | 0.0395 | −0.1780 | 0.1432 | −0.1629 | 2.4215 |
CHICKEN | 0.0026 | 0.0205 | −0.0558 | 0.1045 | 0.8058 | 3.0832 |
IMETMIN | 0.0021 | 0.0496 | −0.3045 | 0.1585 | −0.8080 | 5.0908 |
NGAS_US | 0.0002 | 0.1241 | −0.4055 | 0.4779 | 0.0691 | 1.6753 |
NICKEL | 0.0022 | 0.0856 | −0.3824 | 0.5811 | 0.7231 | 5.7015 |
INONFUEL | 0.0012 | 0.0265 | −0.2032 | 0.1002 | −1.1311 | 9.2270 |
ORANGE | 0.0022 | 0.1233 | −0.4199 | 0.4127 | −0.2108 | 1.0353 |
PALM_OIL | 0.0001 | 0.0739 | −0.3469 | 0.2731 | −0.3735 | 2.4278 |
PLATINUM | 0.0021 | 0.0527 | −0.2929 | 0.2335 | −0.4484 | 4.7605 |
PLYWOOD | 0.0019 | 0.0393 | −0.1583 | 0.1781 | 0.8362 | 4.3207 |
POTASH | 0.0025 | 0.0403 | −0.4158 | 0.3438 | −1.0375 | 41.9405 |
RICE_05 | 0.0011 | 0.0580 | −0.2424 | 0.4233 | 1.2896 | 8.8429 |
RUBBER1_MYSG | 0.0009 | 0.0708 | −0.3904 | 0.2121 | −0.4335 | 3.1845 |
SAWNWD_MYS | 0.0018 | 0.0346 | −0.1401 | 0.2382 | 1.1335 | 10.5032 |
SHRIMP_MEX | −0.0001 | 0.0424 | −0.2432 | 0.1839 | −0.6345 | 7.0185 |
SILVER | 0.0015 | 0.0621 | −0.2143 | 0.2604 | 0.1165 | 1.6884 |
SORGHUM | 0.0006 | 0.0634 | −0.2777 | 0.3419 | −0.0446 | 3.8254 |
SOYBEAN_MEAL | 0.0008 | 0.0567 | −0.1858 | 0.2176 | 0.2146 | 1.6060 |
SOYBEAN_OIL | 0.0007 | 0.0557 | −0.2785 | 0.2611 | −0.0453 | 3.2895 |
SOYBEANS | 0.0006 | 0.0503 | −0.2561 | 0.2140 | −0.2455 | 2.9699 |
SUGAR_EU | 0.0001 | 0.0364 | −0.3052 | 0.2568 | −1.4701 | 24.9057 |
SUGAR_US | 0.0006 | 0.0314 | −0.1366 | 0.1670 | 0.0769 | 4.7483 |
SUGAR_WLD | 0.0015 | 0.0832 | −0.3080 | 0.3128 | 0.1817 | 0.7727 |
TEA_AVG | 0.0007 | 0.0524 | −0.1960 | 0.2378 | 0.2114 | 1.7555 |
TEA_COLOMBO | 0.0014 | 0.0699 | −0.4681 | 0.4046 | −0.2496 | 8.3187 |
TEA_KOLKATA | −0.0004 | 0.1224 | −0.3100 | 0.4718 | 1.1349 | 2.1171 |
TEA_MOMBASA | 0.0011 | 0.0704 | −0.4613 | 0.4550 | 0.0674 | 10.5021 |
TIN | 0.0012 | 0.0567 | −0.2517 | 0.1615 | −0.3940 | 2.5582 |
TOBAC_US | 0.0015 | 0.0185 | −0.0486 | 0.0997 | 0.4662 | 2.0420 |
TSP | 0.0016 | 0.0577 | −0.4652 | 0.3021 | −1.4839 | 19.0871 |
UREA_EE_BULK | 0.0020 | 0.0857 | −0.5548 | 0.2863 | −1.0811 | 7.0126 |
WHEAT_US_HRW | 0.0003 | 0.0594 | −0.2192 | 0.2291 | 0.3510 | 2.0921 |
WHEAT_US_SRW | 0.0005 | 0.0669 | −0.2604 | 0.2582 | −0.0620 | 1.7340 |
WOODPULP | 0.0017 | 0.0407 | −0.2430 | 0.1195 | −0.9021 | 4.2056 |
ZINC | 0.0033 | 0.0635 | −0.2873 | 0.2440 | −0.3777 | 1.6376 |
Variable | ADF Stat. | ADF p-Value | PP Stat. | PP p-Value | KPSS Stat. | KPSS p-Value |
---|---|---|---|---|---|---|
dpr | −2.1052 | 0.5329 | −5.7584 | 0.7880 | 3.8742 | 0.0100 |
str | −4.2431 | 0.0100 | −10.8935 | 0.5009 | 6.2736 | 0.0100 |
ltr | −5.3644 | 0.0100 | −26.3474 | 0.0187 | 7.2737 | 0.0100 |
ts | −3.7999 | 0.0192 | −16.8927 | 0.1654 | 0.2584 | 0.1000 |
drs | −3.6411 | 0.0291 | −13.1674 | 0.3737 | 0.6484 | 0.0182 |
cpi | −7.2334 | 0.0100 | −213.8512 | 0.0100 | 1.2606 | 0.0100 |
ip | −5.3868 | 0.0100 | −423.8474 | 0.0100 | 0.5108 | 0.0392 |
une | −2.7554 | 0.2583 | −4.6099 | 0.8523 | 0.6316 | 0.0198 |
aud | −7.1520 | 0.0100 | −378.7165 | 0.0100 | 0.0913 | 0.1000 |
inr | −5.7244 | 0.0100 | −299.0263 | 0.0100 | 0.5656 | 0.0269 |
kei | −2.5681 | 0.3374 | −24.2551 | 0.0280 | 0.9875 | 0.0100 |
op | −6.1213 | 0.0100 | −48.5397 | 0.0100 | 0.6558 | 0.0176 |
tr | −6.8977 | 0.0100 | −438.0874 | 0.0100 | 0.1613 | 0.1000 |
m | −4.2691 | 0.0100 | −440.1250 | 0.0100 | 0.6770 | 0.0156 |
IBEVERAGES | −7.0048 | 0.0100 | −308.1486 | 0.0100 | 0.1271 | 0.1000 |
IFOOD | −7.3267 | 0.0100 | −268.4524 | 0.0100 | 0.1037 | 0.1000 |
IFATS_OILS | −7.2873 | 0.0100 | −254.9748 | 0.0100 | 0.1066 | 0.1000 |
IGRAINS | −7.4273 | 0.0100 | −265.4955 | 0.0100 | 0.0746 | 0.1000 |
IOTHERFOOD | −8.2980 | 0.0100 | −324.5334 | 0.0100 | 0.0477 | 0.1000 |
IRAW_MATERIAL | −5.9460 | 0.0100 | −257.0040 | 0.0100 | 0.0794 | 0.1000 |
ITIMBER | −6.2504 | 0.0100 | −252.2372 | 0.0100 | 0.0952 | 0.1000 |
IOTHERRAWMAT | −6.4909 | 0.0100 | −220.2585 | 0.0100 | 0.0710 | 0.1000 |
IAGRICULTURE | −7.2953 | 0.0100 | −262.9362 | 0.0100 | 0.1247 | 0.1000 |
ALUMINUM | −7.1961 | 0.0100 | −365.2150 | 0.0100 | 0.0341 | 0.1000 |
BANANA_US | −11.9615 | 0.0100 | −386.4737 | 0.0100 | 0.0102 | 0.1000 |
BARLEY | −6.6144 | 0.0100 | −295.1878 | 0.0100 | 0.0398 | 0.1000 |
COAL_AUS | −7.2526 | 0.0100 | −300.5987 | 0.0100 | 0.0589 | 0.1000 |
COCOA | −6.9616 | 0.0100 | −328.7648 | 0.0100 | 0.1377 | 0.1000 |
COCONUT_OIL | −6.0853 | 0.0100 | −310.3757 | 0.0100 | 0.1201 | 0.1000 |
COFFEE_ARABIC | −6.9242 | 0.0100 | −303.8905 | 0.0100 | 0.0504 | 0.1000 |
COFFEE_ROBUS | −6.4421 | 0.0100 | −286.3518 | 0.0100 | 0.1332 | 0.1000 |
COPPER | −8.3053 | 0.0100 | −229.5696 | 0.0100 | 0.0559 | 0.1000 |
COPRA | −6.2123 | 0.0100 | −298.2183 | 0.0100 | 0.1291 | 0.1000 |
COTTON_A_INDX | −7.6277 | 0.0100 | −186.2706 | 0.0100 | 0.0412 | 0.1000 |
CRUDE_PETRO | −8.0039 | 0.0100 | −276.5855 | 0.0100 | 0.0738 | 0.1000 |
CRUDE_BRENT | −8.0758 | 0.0100 | −302.9128 | 0.0100 | 0.0744 | 0.1000 |
CRUDE_DUBAI | −8.1482 | 0.0100 | −272.9248 | 0.0100 | 0.0765 | 0.1000 |
CRUDE_WTI | −7.8943 | 0.0100 | −267.0152 | 0.0100 | 0.0669 | 0.1000 |
DAP | −7.8995 | 0.0100 | −154.9484 | 0.0100 | 0.0555 | 0.1000 |
IENERGY | −7.7445 | 0.0100 | −269.3615 | 0.0100 | 0.0834 | 0.1000 |
IFERTILIZERS | −6.5734 | 0.0100 | −208.0159 | 0.0100 | 0.0769 | 0.1000 |
FISH_MEAL | −7.2824 | 0.0100 | −219.0414 | 0.0100 | 0.0876 | 0.1000 |
GOLD | −6.2878 | 0.0100 | −334.6587 | 0.0100 | 0.3927 | 0.0803 |
GRNUT_OIL | −5.6487 | 0.0100 | −203.1413 | 0.0100 | 0.0450 | 0.1000 |
LEAD | −6.5034 | 0.0100 | −323.0123 | 0.0100 | 0.0610 | 0.1000 |
LOGS_CMR | −7.6097 | 0.0100 | −326.3537 | 0.0100 | 0.0915 | 0.1000 |
LOGS_MYS | −7.1826 | 0.0100 | −221.0901 | 0.0100 | 0.0356 | 0.1000 |
MAIZE | −7.6758 | 0.0100 | −293.5180 | 0.0100 | 0.0667 | 0.1000 |
BEEF | −7.8711 | 0.0100 | −259.0861 | 0.0100 | 0.0854 | 0.1000 |
CHICKEN | −9.1732 | 0.0100 | −200.7275 | 0.0100 | 0.0144 | 0.1000 |
IMETMIN | −6.9904 | 0.0100 | −293.4994 | 0.0100 | 0.0556 | 0.1000 |
NGAS_US | −8.7317 | 0.0100 | −322.0952 | 0.0100 | 0.0427 | 0.1000 |
NICKEL | −6.1845 | 0.0100 | −270.5022 | 0.0100 | 0.0612 | 0.1000 |
INONFUEL | −7.5280 | 0.0100 | −256.6703 | 0.0100 | 0.1051 | 0.1000 |
ORANGE | −12.8775 | 0.0100 | −249.7639 | 0.0100 | 0.0119 | 0.1000 |
PALM_OIL | −7.2318 | 0.0100 | −271.7718 | 0.0100 | 0.0825 | 0.1000 |
PLATINUM | −7.7853 | 0.0100 | −301.4866 | 0.0100 | 0.0889 | 0.1000 |
PLYWOOD | −6.8155 | 0.0100 | −244.4742 | 0.0100 | 0.1393 | 0.1000 |
POTASH | −4.5756 | 0.0100 | −268.4068 | 0.0100 | 0.1228 | 0.1000 |
RICE_05 | −8.8139 | 0.0100 | −224.9817 | 0.0100 | 0.0445 | 0.1000 |
RUBBER1_MYSG | −6.1189 | 0.0100 | −302.8696 | 0.0100 | 0.0737 | 0.1000 |
SAWNWD_MYS | −6.2102 | 0.0100 | −304.1856 | 0.0100 | 0.1167 | 0.1000 |
SHRIMP_MEX | −6.9083 | 0.0100 | −313.0972 | 0.0100 | 0.0290 | 0.1000 |
SILVER | −7.1789 | 0.0100 | −320.0327 | 0.0100 | 0.2318 | 0.1000 |
SORGHUM | −8.6741 | 0.0100 | −306.9272 | 0.0100 | 0.0551 | 0.1000 |
SOYBEAN_MEAL | −7.5551 | 0.0100 | −281.1673 | 0.0100 | 0.0679 | 0.1000 |
SOYBEAN_OIL | −6.6635 | 0.0100 | −261.9871 | 0.0100 | 0.0884 | 0.1000 |
SOYBEANS | −7.7068 | 0.0100 | −305.9913 | 0.0100 | 0.0751 | 0.1000 |
SUGAR_EU | −7.8297 | 0.0100 | −392.6856 | 0.0100 | 0.2977 | 0.1000 |
SUGAR_US | −6.6006 | 0.0100 | −263.9091 | 0.0100 | 0.0360 | 0.1000 |
SUGAR_WLD | −7.5119 | 0.0100 | −264.4007 | 0.0100 | 0.0352 | 0.1000 |
TEA_AVG | −7.9940 | 0.0100 | −407.1172 | 0.0100 | 0.1510 | 0.1000 |
TEA_COLOMBO | −7.7583 | 0.0100 | −340.4424 | 0.0100 | 0.1450 | 0.1000 |
TEA_KOLKATA | −12.4679 | 0.0100 | −318.4301 | 0.0100 | 0.0345 | 0.1000 |
TEA_MOMBASA | −7.1334 | 0.0100 | −331.5262 | 0.0100 | 0.0468 | 0.1000 |
TIN | −7.4442 | 0.0100 | −309.7754 | 0.0100 | 0.2339 | 0.1000 |
TOBAC_US | −5.6608 | 0.0100 | −297.5882 | 0.0100 | 0.1241 | 0.1000 |
TSP | −7.2420 | 0.0100 | −173.8512 | 0.0100 | 0.0468 | 0.1000 |
UREA_EE_BULK | −7.2560 | 0.0100 | −221.0777 | 0.0100 | 0.0428 | 0.1000 |
WHEAT_US_HRW | −7.6825 | 0.0100 | −291.1223 | 0.0100 | 0.0479 | 0.1000 |
WHEAT_US_SRW | −8.5903 | 0.0100 | −304.0612 | 0.0100 | 0.0382 | 0.1000 |
WOODPULP | −6.6187 | 0.0100 | −230.4387 | 0.0100 | 0.0332 | 0.1000 |
ZINC | −6.3500 | 0.0100 | −291.2258 | 0.0100 | 0.0578 | 0.1000 |
COMMODITY | DMA | DMS | MED | TVP | ARIMA | NAIVE |
---|---|---|---|---|---|---|
IBEVERAGES | 0.0464 | 0.0483 | 0.0463 | 0.0477 | 0.0473 | 0.0475 |
IFOOD | 0.0316 | 0.0314 | 0.0315 | 0.0318 | 0.0334 | 0.0353 |
IFATS_OILS | 0.0461 | 0.0461 | 0.0470 | 0.0465 | 0.0487 | 0.0510 |
IGRAINS | 0.0479 | 0.0483 | 0.0481 | 0.0481 | 0.0493 | 0.0514 |
IOTHERFOOD | 0.0306 | 0.0305 | 0.0314 | 0.0320 | 0.0318 | 0.0313 |
IRAW_MATERIAL | 0.0255 | 0.0258 | 0.0258 | 0.0259 | 0.0255 | 0.0272 |
ITIMBER | 0.0279 | 0.0285 | 0.0286 | 0.0287 | 0.0271 | 0.0286 |
IOTHERRAWMAT | 0.0462 | 0.0461 | 0.0456 | 0.0465 | 0.0476 | 0.0507 |
IAGRICULTURE | 0.0249 | 0.0248 | 0.0247 | 0.0250 | 0.0273 | 0.0283 |
ALUMINUM | 0.0479 | 0.0492 | 0.0478 | 0.0497 | 0.0531 | 0.0526 |
BANANA_US | 0.1235 | 0.1231 | 0.1225 | 0.1324 | 0.1176 | 0.1223 |
BARLEY | 0.0626 | 0.0631 | 0.0631 | 0.0633 | 0.0632 | 0.0654 |
COAL_AUS | 0.0920 | 0.0928 | 0.0926 | 0.0937 | 0.1188 | 0.0981 |
COCOA | 0.0573 | 0.0571 | 0.0571 | 0.0597 | 0.0580 | 0.0578 |
COCONUT_OIL | 0.0854 | 0.0841 | 0.0839 | 0.0872 | 0.0902 | 0.0884 |
COFFEE_ARABIC | 0.0850 | 0.0856 | 0.0857 | 0.0878 | 0.0881 | 0.0858 |
COFFEE_ROBUS | 0.0782 | 0.0789 | 0.0779 | 0.0786 | 0.0801 | 0.0788 |
COPPER | 0.0738 | 0.0734 | 0.0738 | 0.0736 | 0.0793 | 0.0786 |
COPRA | 0.0895 | 0.0877 | 0.0877 | 0.0918 | 0.0984 | 0.0910 |
COTTON_A_INDX | 0.0694 | 0.0677 | 0.0690 | 0.0696 | 0.0689 | 0.0808 |
CRUDE_PETRO | 0.0811 | 0.0813 | 0.0812 | 0.0879 | 0.0867 | 0.0919 |
CRUDE_BRENT | 0.0841 | 0.0841 | 0.0834 | 0.0914 | 0.0908 | 0.0942 |
CRUDE_DUBAI | 0.0789 | 0.0795 | 0.0791 | 0.0858 | 0.0846 | 0.0924 |
CRUDE_WTI | 0.0866 | 0.0864 | 0.0858 | 0.0926 | 0.0892 | 0.0947 |
DAP | 0.0774 | 0.0743 | 0.0763 | 0.0810 | 0.0864 | 0.1104 |
IENERGY | 0.0710 | 0.0706 | 0.0710 | 0.0775 | 0.0793 | 0.0814 |
IFERTILIZERS | 0.0681 | 0.0647 | 0.0656 | 0.0691 | 0.0779 | 0.0904 |
FISH_MEAL | 0.0450 | 0.0448 | 0.0448 | 0.0461 | 0.0447 | 0.0475 |
GOLD | 0.0432 | 0.0424 | 0.0449 | 0.0447 | 0.0473 | 0.0454 |
GRNUT_OIL | 0.0437 | 0.0442 | 0.0450 | 0.0462 | 0.0467 | 0.0540 |
LEAD | 0.0949 | 0.0969 | 0.0964 | 0.0979 | 0.1015 | 0.0960 |
LOGS_CMR | 0.0337 | 0.0341 | 0.0341 | 0.0345 | 0.0339 | 0.0351 |
LOGS_MYS | 0.0499 | 0.0492 | 0.0494 | 0.0499 | 0.0511 | 0.0542 |
MAIZE | 0.0696 | 0.0701 | 0.0703 | 0.0721 | 0.0714 | 0.0717 |
BEEF | 0.0446 | 0.0438 | 0.0441 | 0.0455 | 0.0451 | 0.0474 |
CHICKEN | 0.0135 | 0.0132 | 0.0131 | 0.0134 | 0.0128 | 0.0159 |
IMETMIN | 0.0541 | 0.0543 | 0.0541 | 0.0560 | 0.0592 | 0.0602 |
NGAS_US | 0.1804 | 0.1822 | 0.1810 | 0.1817 | 0.1920 | 0.1794 |
NICKEL | 0.1116 | 0.1097 | 0.1100 | 0.1128 | 0.1177 | 0.1182 |
INONFUEL | 0.0275 | 0.0274 | 0.0273 | 0.0277 | 0.0306 | 0.0331 |
ORANGE | 0.1204 | 0.1196 | 0.1197 | 0.1272 | 0.1141 | 0.1210 |
PALM_OIL | 0.0649 | 0.0646 | 0.0642 | 0.0674 | 0.0682 | 0.0707 |
PLATINUM | 0.0628 | 0.0624 | 0.0635 | 0.0635 | 0.0681 | 0.0683 |
PLYWOOD | 0.0320 | 0.0324 | 0.0328 | 0.0329 | 0.0310 | 0.0336 |
POTASH | 0.0829 | 0.0836 | 0.0843 | 0.0847 | 0.1010 | 0.0891 |
RICE_05 | 0.0836 | 0.0828 | 0.0828 | 0.0824 | 0.0858 | 0.0805 |
RUBBER1_MYSG | 0.1007 | 0.1000 | 0.0998 | 0.1031 | 0.1080 | 0.1046 |
SAWNWD_MYS | 0.0292 | 0.0349 | 0.0337 | 0.0304 | 0.0283 | 0.0291 |
SHRIMP_MEX | 0.0389 | 0.0394 | 0.0392 | 0.0399 | 0.0389 | 0.0399 |
SILVER | 0.0910 | 0.0913 | 0.0895 | 0.0991 | 0.1039 | 0.0982 |
SORGHUM | 0.0700 | 0.0705 | 0.0714 | 0.0719 | 0.0709 | 0.0714 |
SOYBEAN_MEAL | 0.0631 | 0.0620 | 0.0625 | 0.0665 | 0.0639 | 0.0658 |
SOYBEAN_OIL | 0.0513 | 0.0504 | 0.0511 | 0.0531 | 0.0550 | 0.0565 |
SOYBEANS | 0.0588 | 0.0589 | 0.0589 | 0.0600 | 0.0600 | 0.0605 |
SUGAR_EU | 0.0323 | 0.0325 | 0.0321 | 0.0332 | 0.0322 | 0.0322 |
SUGAR_US | 0.0393 | 0.0390 | 0.0388 | 0.0400 | 0.0398 | 0.0406 |
SUGAR_WLD | 0.0799 | 0.0795 | 0.0794 | 0.0824 | 0.0784 | 0.0822 |
TEA_AVG | 0.0486 | 0.0486 | 0.0486 | 0.0509 | 0.0490 | 0.0483 |
TEA_COLOMBO | 0.0535 | 0.0530 | 0.0530 | 0.0584 | 0.0527 | 0.0529 |
TEA_KOLKATA | 0.1222 | 0.1224 | 0.1215 | 0.1261 | 0.1147 | 0.1207 |
TEA_MOMBASA | 0.0695 | 0.0689 | 0.0691 | 0.0729 | 0.0687 | 0.0678 |
TIN | 0.0748 | 0.0759 | 0.0758 | 0.0754 | 0.0820 | 0.0789 |
TOBAC_US | 0.0189 | 0.0224 | 0.0192 | 0.0196 | 0.0192 | 0.0192 |
TSP | 0.0918 | 0.0924 | 0.0915 | 0.0941 | 0.1035 | 0.1251 |
UREA_EE_BULK | 0.1327 | 0.1297 | 0.1301 | 0.1242 | 0.1393 | 0.1406 |
WHEAT_US_HRW | 0.0748 | 0.0749 | 0.0747 | 0.0769 | 0.0772 | 0.0768 |
WHEAT_US_SRW | 0.0853 | 0.0853 | 0.0852 | 0.0873 | 0.0880 | 0.0860 |
WOODPULP | 0.0330 | 0.0330 | 0.0331 | 0.0345 | 0.0331 | 0.0378 |
ZINC | 0.0778 | 0.0780 | 0.0787 | 0.0811 | 0.0789 | 0.0815 |
COMMODITY | DMA < NAIVE | DMA < ARIMA | DMA > NAIVE | DMA > ARIMA | BEST | DM p-Value |
---|---|---|---|---|---|---|
IBEVERAGES | 0.00 | 0.00 | MED | 0.00 | ||
IFOOD | 0.00 | 0.00 | DMS | 0.10 | ||
IFATS_OILS | 0.00 | 0.00 | DMA | 0.02 | ||
IGRAINS | 0.00 | 0.00 | DMA | 0.17 | ||
IOTHERFOOD | 0.00 | 0.00 | DMS | 0.00 | ||
IRAW_MATERIAL | 0.00 | 1.00 | ARIMA | 1.00 | ||
ITIMBER | 0.00 | 1.00 | ARIMA | 1.00 | ||
IOTHERRAWMAT | 0.00 | 0.00 | MED | 0.00 | ||
IAGRICULTURE | 0.00 | 0.00 | MED | 0.03 | ||
ALUMINUM | 0.00 | 0.00 | MED | 0.08 | ||
BANANA_US | 0.00 | 0.00 | ARIMA | 0.00 | ||
BARLEY | 0.00 | 0.00 | DMA | 0.00 | ||
COAL_AUS | 0.00 | 0.00 | DMA | 0.00 | ||
COCOA | 0.00 | 0.00 | MED | 0.00 | ||
COCONUT_OIL | 0.00 | 0.00 | MED | 0.01 | ||
COFFEE_ARABIC | 0.00 | 0.00 | DMA | 0.00 | ||
COFFEE_ROBUS | 0.00 | 0.00 | MED | 0.36 | ||
COPPER | 0.00 | 0.00 | DMS | 0.07 | ||
COPRA | 0.00 | 0.00 | DMS | 0.00 | ||
COTTON_A_INDX | 0.00 | 1.00 | DMS | 0.00 | ||
CRUDE_PETRO | 0.00 | 0.00 | DMA | 0.00 | ||
CRUDE_BRENT | 0.00 | 0.00 | MED | 0.00 | ||
CRUDE_DUBAI | 0.00 | 0.00 | DMA | 0.00 | ||
CRUDE_WTI | 0.00 | 0.00 | MED | 0.00 | ||
DAP | 0.00 | 0.00 | DMS | 0.08 | ||
IENERGY | 0.00 | 0.00 | DMS | 0.00 | ||
IFERTILIZERS | 0.00 | 0.00 | DMS | 0.38 | ||
FISH_MEAL | 0.00 | 1.00 | ARIMA | 1.00 | ||
GOLD | 0.00 | 0.00 | DMS | 0.18 | ||
GRNUT_OIL | 0.00 | 0.00 | DMA | 0.00 | ||
LEAD | 0.00 | 0.00 | DMA | 0.00 | ||
LOGS_CMR | 0.00 | 0.00 | DMA | 0.00 | ||
LOGS_MYS | 0.00 | 0.00 | DMS | 0.17 | ||
MAIZE | 0.00 | 0.00 | DMA | 0.00 | ||
BEEF | 0.00 | 0.00 | DMS | 0.00 | ||
CHICKEN | 0.00 | 1.00 | ARIMA | 1.00 | ||
IMETMIN | 0.00 | 0.00 | MED | 0.02 | ||
NGAS_US | 0.00 | 1.00 | NAIVE | 1.00 | ||
NICKEL | 0.00 | 0.00 | DMS | 0.03 | ||
INONFUEL | 0.00 | 0.00 | MED | 0.10 | ||
ORANGE | 1.00 | 0.00 | ARIMA | 0.00 | ||
PALM_OIL | 0.00 | 0.00 | MED | 0.02 | ||
PLATINUM | 0.00 | 0.00 | DMS | 0.11 | ||
PLYWOOD | 0.00 | 1.00 | ARIMA | 1.00 | ||
POTASH | 0.01 | 0.00 | DMA | 0.18 | ||
RICE_05 | 0.00 | 0.99 | NAIVE | 0.99 | ||
RUBBER1_MYSG | 0.00 | 0.00 | MED | 0.76 | ||
SAWNWD_MYS | 1.00 | 1.00 | ARIMA | 1.00 | ||
SHRIMP_MEX | 0.00 | 0.00 | DMA | 0.00 | ||
SILVER | 0.00 | 0.00 | MED | 0.00 | ||
SORGHUM | 0.00 | 0.00 | DMA | 0.00 | ||
SOYBEAN_MEAL | 0.00 | 0.00 | DMS | 0.00 | ||
SOYBEAN_OIL | 0.00 | 0.00 | DMS | 0.01 | ||
SOYBEANS | 0.00 | 0.00 | DMA | 0.00 | ||
SUGAR_EU | 0.00 | 0.00 | MED | 1.00 | ||
SUGAR_US | 1.00 | 1.00 | MED | 1.00 | ||
SUGAR_WLD | 1.00 | 0.00 | ARIMA | 0.00 | ||
TEA_AVG | 0.00 | 1.00 | NAIVE | 1.00 | ||
TEA_COLOMBO | 1.00 | 1.00 | ARIMA | 1.00 | ||
TEA_KOLKATA | 1.00 | 1.00 | ARIMA | 1.00 | ||
TEA_MOMBASA | 1.00 | 1.00 | NAIVE | 1.00 | ||
TIN | 0.00 | 0.00 | DMA | 0.08 | ||
TOBAC_US | 0.00 | 0.00 | DMA | 0.00 | ||
TSP | 0.01 | 0.00 | MED | 0.08 | ||
UREA_EE_BULK | 0.00 | 0.00 | TVP | 0.89 | ||
WHEAT_US_HRW | 0.00 | 0.00 | MED | 0.00 | ||
WHEAT_US_SRW | 0.00 | 0.00 | MED | 0.00 | ||
WOODPULP | 0.00 | 0.00 | DMS | 0.00 | ||
ZINC | 0.00 | 0.00 | DMA | 0.00 |
MODEL | FREQ. BEST | FREQ. SIGN. BEST |
---|---|---|
DMA | 26% | 22% |
DMS | 23% | 13% |
MED | 28% | 17% |
TVP | 1% | 0% |
ARIMA | 16% | 4% |
NAIVE | 6% | 0% |
BMA | 0% | 0% |
BMS | 0% | 0% |
BMED | 0% | 0% |
© 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Drachal, K. Some Novel Bayesian Model Combination Schemes: An Application to Commodities Prices. Sustainability 2018, 10, 2801. https://doi.org/10.3390/su10082801
Drachal K. Some Novel Bayesian Model Combination Schemes: An Application to Commodities Prices. Sustainability. 2018; 10(8):2801. https://doi.org/10.3390/su10082801
Chicago/Turabian StyleDrachal, Krzysztof. 2018. "Some Novel Bayesian Model Combination Schemes: An Application to Commodities Prices" Sustainability 10, no. 8: 2801. https://doi.org/10.3390/su10082801