Commodities Factor Analysis

9 Variables: Iron Wheat Coffee Soybeans Beef Cotton Corn Copper Crude
Simple Statistics
Variable

N

Mean

Std Dev

Sum

Minimum

Maximum

Iron

432

35.78048

44.08919

15457

10.51000

187.18000

Wheat

432

166.35586

55.41891

71866

88.55224

403.81290

Coffee

432

86.44818

35.18481

37346

21.26174

182.95285

Soybeans

432

278.51582

104.64574

120319

158.31226

622.91355

Beef

432

119.03491

35.75092

51423

74.26190

272.29545

Cotton

432

73.60856

22.65506

31799

37.03000

229.66739

Corn

432

136.72270

57.54684

59064

65.35123

332.94730

Copper

432

3442

2387

1487021

1272

9881

Crude

432

41.13443

28.24933

17770

11.31000

133.93000

Pearson Correlation Coefficients, N = 432
Prob > |r| under H0: Rho=0

Iron

Wheat

Coffee

Soybeans

Beef

Cotton

Corn

Copper

Crude

Iron

1.00000

0.70718
<.0001

0.17291
0.0003

0.83702
<.0001

0.75269
<.0001

0.57005
<.0001

0.84258
<.0001

0.86057
<.0001

0.83769
<.0001

Wheat

0.70718
<.0001

1.00000

0.35826
<.0001

0.88131
<.0001

0.61609
<.0001

0.54400
<.0001

0.88888
<.0001

0.79636
<.0001

0.79189
<.0001

Coffee

0.17291
0.0003

0.35826
<.0001

1.00000

0.28492
<.0001

0.19428
<.0001

0.40259
<.0001

0.30844
<.0001

0.14843
0.0020

0.16154
0.0008

Soybeans

0.83702
<.0001

0.88131
<.0001

0.28492
<.0001

1.00000

0.72612
<.0001

0.54083
<.0001

0.93226
<.0001

0.81561
<.0001

0.83725
<.0001

Beef

0.75269
<.0001

0.61609
<.0001

0.19428
<.0001

0.72612
<.0001

1.00000

0.40908
<.0001

0.68439
<.0001

0.72983
<.0001

0.71183
<.0001

Cotton

0.57005
<.0001

0.54400
<.0001

0.40259
<.0001

0.54083
<.0001

0.40908
<.0001

1.00000

0.59708
<.0001

0.45676
<.0001

0.39767
<.0001

Corn

0.84258
<.0001

0.88888
<.0001

0.30844
<.0001

0.93226
<.0001

0.68439
<.0001

0.59708
<.0001

1.00000

0.81103
<.0001

0.81076
<.0001

Copper

0.86057
<.0001

0.79636
<.0001

0.14843
0.0020

0.81561
<.0001

0.72983
<.0001

0.45676
<.0001

0.81103
<.0001

1.00000

0.91190
<.0001

Crude

0.83769
<.0001

0.79189
<.0001

0.16154
0.0008

0.83725
<.0001

0.71183
<.0001

0.39767
<.0001

0.81076
<.0001

0.91190
<.0001

1.00000

The following chart shows the correction between commodities: All commodities are highly correlated except Coffee and Cotton.

The prices of coffee and cotton do not move with other commodities.

Correlation Matrix

Iron

Wheat

Coffee

Soybeans

Beef

Cotton

Corn

Copper

Crude

Iron

1.0000

0.7072

0.1729

0.8370

0.7527

0.5700

0.8426

0.8606

0.8377

Wheat

0.7072

1.0000

0.3583

0.8813

0.6161

0.5440

0.8889

0.7964

0.7919

Coffee

0.1729

0.3583

1.0000

0.2849

0.1943

0.4026

0.3084

0.1484

0.1615

Soybeans

0.8370

0.8813

0.2849

1.0000

0.7261

0.5408

0.9323

0.8156

0.8372

Beef

0.7527

0.6161

0.1943

0.7261

1.0000

0.4091

0.6844

0.7298

0.7118

Cotton

0.5700

0.5440

0.4026

0.5408

0.4091

1.0000

0.5971

0.4568

0.3977

Corn

0.8426

0.8889

0.3084

0.9323

0.6844

0.5971

1.0000

0.8110

0.8108

Copper

0.8606

0.7964

0.1484

0.8156

0.7298

0.4568

0.8110

1.0000

0.9119

Crude

0.8377

0.7919

0.1615

0.8372

0.7118

0.3977

0.8108

0.9119

1.0000

The following chart shows that two principal components are only matter where eigenvalue is greater than 1.

Eigenvalues of the Correlation Matrix
Eigenvalue Difference Proportion Cumulative
1 6.24488213 5.12506410 0.6939 0.6939
2 1.11981804 0.56744747 0.1244 0.8183
3 0.55237056 0.11922482 0.0614 0.8797
4 0.43314574 0.17178834 0.0481 0.9278
5 0.26135741 0.08079623 0.0290 0.9568
6 0.18056118 0.08877333 0.0201 0.9769
7 0.09178785 0.03246670 0.0102 0.9871
8 0.05932114 0.00256520 0.0066 0.9937
9 0.05675595 0.0063 1.0000

Only two factors will be retained by the mineigen criterion.

The following chart shows that the first factor highly effects on all commodities except coffee and cotton and the second factor effects positively on coffee and cotton while negatively effects on iron, soybeans, beef, copper and crude.

Factor Pattern

Factor1

Factor2

Iron

0.91379

-0.14311

Wheat

0.90047

0.09010

Coffee

0.33077

0.85318

Soybeans

0.94623

-0.02316

Beef

0.80294

-0.15500

Cotton

0.63410

0.47904

Corn

0.94521

0.03455

Copper

0.91365

-0.22659

Crude

0.90515

-0.23819

The following chart shows that two factors explain 83% of variance.

 

The following chart shows that Iron and Copper and rude move together, Beef and soybeans move together, wheat and corn move together.

Source: https://research.stlouisfed.org/fred2/graph/?graph_id=287369&category_id=

https://sites.google.com/site/econometricsacademy/econometrics-models/principal-component-analysis?pageId=103335352115747405657

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