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I have 19 currency pairs like USD.AUD, USD.CAD, etc. Also 82 cross currency pairs like AUD.CAD, EUR.AUD,EUR.CAD etc.

When I look to their graphs, most look similar, so I want to reduce number of pair and choose a few that represents the whole group. I calculate returns and create time series. I applied PCA but I am not sure how to interpret the results.

Any guidance is appreciated, is PCA is the right tool or I should look for others like cluster analysis , factor analysis, etc... For example in 82 pairs should I group them like EUR.* GBP.* ?

Below is the output of my R program , how should I interpret it ? Can I eliminate KRW.USD USD.CNH USD.HKD as their loadings are not correlated to first let's say 10 components ?

> head(returns)
             AUD.USD      EUR.USD       GBP.USD      KRW.USD      NZD.USD
2013-06-24  0.0000000000  0.000000000  0.0000000000  0.000000000  0.000000000
2013-06-25  0.0011886753 -0.003149068 -0.0008264128  0.006944472 -0.003901280
....

Importance of components:
                           Comp.1      Comp.2      Comp.3      Comp.4
Standard deviation     0.01292047 0.006641023 0.005763718 0.004634432
Proportion of Variance 0.44565430 0.117736544 0.088684302 0.057336913
Cumulative Proportion  0.44565430 0.563390849 0.652075151 0.709412064
                            Comp.5      Comp.6      Comp.7      Comp.8
Standard deviation     0.004188341 0.004066381 0.003522884 0.003427262
Proportion of Variance 0.046830128 0.044142561 0.033131261 0.031357105
Cumulative Proportion  0.756242192 0.800384752 0.833516014 0.864873118
                            Comp.9    Comp.10     Comp.11     Comp.12
Standard deviation     0.003154789 0.00295759 0.002855678 0.002798966
Proportion of Variance 0.026569419 0.02335164 0.021770068 0.020913976
Cumulative Proportion  0.891442537 0.91479418 0.936564247 0.957478223
                           Comp.13     Comp.14     Comp.15     Comp.16
Standard deviation     0.002608714 0.002233061 0.001436994 0.001043102
Proportion of Variance 0.018167468 0.013311980 0.005512535 0.002904659
Cumulative Proportion  0.975645691 0.988957670 0.994470205 0.997374864
                            Comp.17      Comp.18      Comp.19
Standard deviation     0.0009627563 1.915212e-04 1.406246e-04
Proportion of Variance 0.0024744240 9.792082e-05 5.279147e-05
Cumulative Proportion  0.9998492877 9.999472e-01 1.000000e+00
> V0$loading

Loadings:
            Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9 Comp.10
AUD.USD  0.275  0.390 -0.378        -0.142        -0.402  0.514 -0.286
    EUR.USD  0.234 -0.238                      -0.109
GBP.USD  0.178                                           -0.370 -0.632  0.553
KRW.USD         0.111                0.126 -0.327 -0.593 -0.456  0.129 -0.450
NZD.USD  0.257  0.306 -0.515         0.139 -0.453  0.549 -0.142  0.117
USD.CAD  0.149  0.123 -0.175                0.189 -0.159         0.383  0.302
USD.CHF  0.256 -0.344        -0.150                      -0.141
USD.CNH
USD.CZK  0.288 -0.271               -0.155 -0.341         0.338  0.323  0.199
USD.DKK  0.234 -0.237                      -0.107
USD.HKD
USD.HUF  0.383         0.288 -0.243 -0.178                0.197        -0.236
USD.ILS  0.137         0.107               -0.209 -0.184 -0.201         0.205
USD.JPY  0.162 -0.281 -0.458 -0.408         0.524        -0.174        -0.147
USD.MXN  0.263  0.385  0.262  0.188 -0.579  0.272  0.203 -0.339
USD.NOK  0.324                0.607  0.329  0.289 -0.149         0.256  0.213
USD.RUB  0.224  0.382  0.404 -0.444  0.584  0.121
USD.SEK  0.325 -0.169         0.350  0.283         0.139        -0.381 -0.412
USD.SGD  0.145                      -0.102        -0.128
        Comp.11 Comp.12 Comp.13 Comp.14 Comp.15 Comp.16 Comp.17 Comp.18 Comp.19
AUD.USD                  0.194   0.149  -0.133
EUR.USD                  0.131   0.370                   0.458   0.699
GBP.USD          0.221  -0.186
KRW.USD -0.131   0.169  -0.120          -0.121
NZD.USD
USD.CAD  0.304  -0.219  -0.671   0.184
USD.CHF                  0.131   0.422           0.190  -0.721
USD.CNH                                  0.344  -0.905  -0.233
USD.CZK -0.510          -0.175  -0.368
USD.DKK                  0.130   0.369                   0.432  -0.715
USD.HKD                                                                  0.999
USD.HUF  0.562   0.442          -0.205  -0.106
USD.ILS  0.350  -0.602   0.385  -0.397
USD.JPY -0.131           0.114  -0.352                   0.123
USD.MXN -0.288                          -0.106
USD.NOK  0.102   0.325   0.275
USD.RUB -0.241
USD.SEK         -0.408  -0.362  -0.133
USD.SGD                                  0.899   0.338

               Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9
SS loadings     1.000  1.000  1.000  1.000  1.000  1.000  1.000  1.000  1.000
Proportion Var  0.053  0.053  0.053  0.053  0.053  0.053  0.053  0.053  0.053
Cumulative Var  0.053  0.105  0.158  0.211  0.263  0.316  0.368  0.421  0.474
               Comp.10 Comp.11 Comp.12 Comp.13 Comp.14 Comp.15 Comp.16 Comp.17
SS loadings      1.000   1.000   1.000   1.000   1.000   1.000   1.000   1.000
Proportion Var   0.053   0.053   0.053   0.053   0.053   0.053   0.053   0.053
Cumulative Var   0.526   0.579   0.632   0.684   0.737   0.789   0.842   0.895
               Comp.18 Comp.19
SS loadings      1.000   1.000
Proportion Var   0.053   0.053
Cumulative Var   0.947   1.000
$\endgroup$
  • $\begingroup$ What are you trying to achieve? You want to reduce to a basket of pairs that are uncorrelated to each other? $\endgroup$ – Matt Oct 8 '14 at 4:59
  • $\begingroup$ He says "I want to reduce number of pair and choose a few that represents the whole group" $\endgroup$ – rupweb Oct 8 '14 at 9:15
  • $\begingroup$ Yes Matt, I want to reduce pairs and keep uncorrelated ones. $\endgroup$ – paglos Oct 8 '14 at 12:55

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