I just ran my first ever PCA, so please excuse any naivety on my part.
As input, I used five years worth of the following:
- S&P/ASX 200 A-REIT
- S&P/ASX 200 Consumer Discretionary
- S&P/ASX 200 Consumer Staples
- S&P/ASX 200 Energy
- S&P/ASX 200 Financial-x-A-REIT
- S&P/ASX 200 Health Care
- S&P/ASX 200 Industrials
- S&P/ASX 200 Information Technology
- S&P/ASX 200 Materials
- S&P/ASX 200 Resources
- S&P/ASX 200 Telecommunication Services
- S&P/ASX 200 Utilities
Using R, I simply ran the following commands:
arc.pca1 <- princomp(sp_sector_data, scores=TRUE, cor=TRUE) summary(arc.pca1) plot(arc.pca1) biplot(arc.pca1)
Summary
Importance of components: Comp.1 Comp.2 Comp.3 Standard deviation 2.603067 1.05203261 0.88394057 Proportion of Variance 0.564663 0.09223105 0.06511258 Cumulative Proportion 0.564663 0.65689405 0.72200662 Comp.4 Comp.5 Comp.6 Standard deviation 0.84122312 0.76978259 0.73901015 Proportion of Variance 0.05897136 0.04938044 0.04551133 Cumulative Proportion 0.78097798 0.83035842 0.87586975 Comp.7 Comp.8 Comp.9 Standard deviation 0.66409102 0.62338449 0.52003850 Proportion of Variance 0.03675141 0.03238402 0.02253667 Cumulative Proportion 0.91262116 0.94500518 0.96754185 Comp.10 Comp.11 Comp.12 Standard deviation 0.45637805 0.42371864 0.0409804189 Proportion of Variance 0.01735674 0.01496146 0.0001399496 Cumulative Proportion 0.98489859 0.99986005 1.0000000000
Loadings
Loadings: Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 RE -0.235 0.520 -0.533 -0.438 0.355 -0.150 disc -0.332 -0.125 0.294 staples -0.295 0.226 -0.211 0.554 energy -0.332 -0.251 0.172 0.176 -0.130 fin_RE -0.323 -0.118 -0.130 0.384 health -0.224 0.465 -0.124 -0.193 0.603 0.537 -0.112 ind -0.337 IT -0.224 0.145 -0.757 -0.461 -0.312 mat -0.329 -0.351 0.295 0.126 -0.116 res -0.335 -0.350 0.297 0.123 -0.133 telco -0.161 0.609 0.327 0.609 -0.311 -0.113 util -0.270 0.160 0.146 -0.256 0.234 -0.694 -0.509 Comp.8 Comp.9 Comp.10 Comp.11 Comp.12 RE -0.217 disc 0.309 0.567 0.596 staples -0.688 -0.141 energy -0.215 0.240 -0.783 -0.165 fin_RE 0.374 -0.724 0.207 health ind 0.398 0.311 -0.743 -0.221 IT -0.183 mat -0.127 0.461 -0.638 res -0.123 0.226 0.752 telco 0.116 util 0.115 Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 SS loadings 1.000 1.000 1.000 1.000 1.000 1.000 Proportion Var 0.083 0.083 0.083 0.083 0.083 0.083 Cumulative Var 0.083 0.167 0.250 0.333 0.417 0.500 Comp.7 Comp.8 Comp.9 Comp.10 Comp.11 SS loadings 1.000 1.000 1.000 1.000 1.000 Proportion Var 0.083 0.083 0.083 0.083 0.083 Cumulative Var 0.583 0.667 0.750 0.833 0.917 Comp.12 SS loadings 1.000 Proportion Var 0.083
Scree Plot
Biplot
Is this useful?
Am I right in assuming that these indices are correlated with each other?
Does the biplot show some sort of clustering?
What if anything, does any of this mean?
pca
andbiplot
. $\endgroup$