Homework 1
Problem 1
UNIVERSIDAD DE LOS ANDES Pedro Alexander Díaz Quiroga Cod: 201410616
Data
mydata <- import.csv('C:/Users/pdiazq/Desktop/TareaAI/SP500_close_price.csv')
mydata <- mydata[, -1]
date <- as.Date(mydata[, 1])
myzoo <- zoo(mydata[,-1], date )
myzoo <- na.locf(myzoo) #impute missing values
prices2returns <- function(x) 100*diff(log(x)) #function to covert from price to return
log.return.zoo <- prices2returns(myzoo)
log.return.data <- coredata(log.return.zoo) #Data
log.return.date <- time(log.return.zoo) #dateThe following is a curve that represents the first 10 stock prices that the initial data frame contains (just the first of the total data frame), where some trends could be seen
plot(myzoo[, 1:5])
The following is a representaion of the input Data, after aplying a function to covert the input to “price to return” (A meaning of the return when investing in that stock. Again the same 10 first stocks below.
plot(log.return.zoo[, 1:5])
- Fit a PCA model to log returns derived from stock price data. The code for deriving log returns is provided in the template file. Please use data frame named log.return.data as input to your PCA model. Having built the model, please do the following:
- Plot a scree plot which shows the distribution of variance contained in subsequent principal components sorted by their eigenvalues.
Now we are gonna aply PCA (Principal Component Analysis) to this input data
# apply PCA - scale. = TRUE is highly
# advisable, but default is FALSE.
zoo.pca <- prcomp(log.return.data,
center = TRUE,
scale. = TRUE)
#print (zoo.pca)
screeplot(zoo.pca, type = "l")
Create a second plot showing cumulative variance retained if top N components are kept after dimensionality reduction (i.e. the horizontal axis will show the number of components kept, the vertical axis will show the cumulative percentage of variance retained).
The following plot shows the cumulative variance as asked before. Vertical axis shows the cumulative variance with a max value of 1. Horizontal axis shows the 471 components of PCA.
s <- summary(prcomp(log.return.data))
plot (s$importance[3, ])
summary(zoo.pca)## Importance of components%s:
## PC1 PC2 PC3 PC4 PC5 PC6
## Standard deviation 13.6101 3.83252 2.9915 2.53438 2.14994 2.0241
## Proportion of Variance 0.3933 0.03119 0.0190 0.01364 0.00981 0.0087
## Cumulative Proportion 0.3933 0.42446 0.4435 0.45710 0.46691 0.4756
## PC7 PC8 PC9 PC10 PC11 PC12
## Standard deviation 1.89665 1.7901 1.7367 1.64954 1.61697 1.58928
## Proportion of Variance 0.00764 0.0068 0.0064 0.00578 0.00555 0.00536
## Cumulative Proportion 0.48325 0.4900 0.4965 0.50223 0.50778 0.51315
## PC13 PC14 PC15 PC16 PC17 PC18
## Standard deviation 1.53551 1.49585 1.46860 1.44101 1.42991 1.41189
## Proportion of Variance 0.00501 0.00475 0.00458 0.00441 0.00434 0.00423
## Cumulative Proportion 0.51815 0.52290 0.52748 0.53189 0.53623 0.54046
## PC19 PC20 PC21 PC22 PC23 PC24
## Standard deviation 1.38238 1.36995 1.35110 1.34027 1.32325 1.31581
## Proportion of Variance 0.00406 0.00398 0.00388 0.00381 0.00372 0.00368
## Cumulative Proportion 0.54452 0.54851 0.55238 0.55620 0.55991 0.56359
## PC25 PC26 PC27 PC28 PC29 PC30
## Standard deviation 1.30876 1.30059 1.28651 1.2647 1.25992 1.25226
## Proportion of Variance 0.00364 0.00359 0.00351 0.0034 0.00337 0.00333
## Cumulative Proportion 0.56723 0.57082 0.57433 0.5777 0.58110 0.58443
## PC31 PC32 PC33 PC34 PC35 PC36
## Standard deviation 1.24845 1.23610 1.22212 1.21833 1.20734 1.19755
## Proportion of Variance 0.00331 0.00324 0.00317 0.00315 0.00309 0.00304
## Cumulative Proportion 0.58774 0.59098 0.59415 0.59730 0.60040 0.60344
## PC37 PC38 PC39 PC40 PC41 PC42
## Standard deviation 1.19267 1.18708 1.18326 1.17986 1.17238 1.16458
## Proportion of Variance 0.00302 0.00299 0.00297 0.00296 0.00292 0.00288
## Cumulative Proportion 0.60646 0.60946 0.61243 0.61538 0.61830 0.62118
## PC43 PC44 PC45 PC46 PC47 PC48
## Standard deviation 1.16302 1.15823 1.15300 1.15048 1.13866 1.13568
## Proportion of Variance 0.00287 0.00285 0.00282 0.00281 0.00275 0.00274
## Cumulative Proportion 0.62405 0.62690 0.62972 0.63253 0.63529 0.63802
## PC49 PC50 PC51 PC52 PC53 PC54
## Standard deviation 1.12993 1.12555 1.11943 1.11324 1.1067 1.10216
## Proportion of Variance 0.00271 0.00269 0.00266 0.00263 0.0026 0.00258
## Cumulative Proportion 0.64074 0.64343 0.64609 0.64872 0.6513 0.65390
## PC55 PC56 PC57 PC58 PC59 PC60
## Standard deviation 1.09894 1.09742 1.09043 1.0856 1.0842 1.07999
## Proportion of Variance 0.00256 0.00256 0.00252 0.0025 0.0025 0.00248
## Cumulative Proportion 0.65646 0.65902 0.66154 0.6640 0.6665 0.66902
## PC61 PC62 PC63 PC64 PC65 PC66
## Standard deviation 1.07538 1.06879 1.06823 1.06471 1.05866 1.05426
## Proportion of Variance 0.00246 0.00243 0.00242 0.00241 0.00238 0.00236
## Cumulative Proportion 0.67147 0.67390 0.67632 0.67873 0.68111 0.68347
## PC67 PC68 PC69 PC70 PC71 PC72
## Standard deviation 1.05036 1.04457 1.04272 1.03745 1.03665 1.03481
## Proportion of Variance 0.00234 0.00232 0.00231 0.00229 0.00228 0.00227
## Cumulative Proportion 0.68581 0.68812 0.69043 0.69272 0.69500 0.69727
## PC73 PC74 PC75 PC76 PC77 PC78
## Standard deviation 1.03066 1.02981 1.02649 1.02356 1.0173 1.01147
## Proportion of Variance 0.00226 0.00225 0.00224 0.00222 0.0022 0.00217
## Cumulative Proportion 0.69953 0.70178 0.70402 0.70624 0.7084 0.71061
## PC79 PC80 PC81 PC82 PC83 PC84
## Standard deviation 1.00939 1.00652 1.00432 1.00093 0.99657 0.99268
## Proportion of Variance 0.00216 0.00215 0.00214 0.00213 0.00211 0.00209
## Cumulative Proportion 0.71277 0.71493 0.71707 0.71919 0.72130 0.72339
## PC85 PC86 PC87 PC88 PC89 PC90
## Standard deviation 0.98692 0.98489 0.98325 0.97984 0.97707 0.97291
## Proportion of Variance 0.00207 0.00206 0.00205 0.00204 0.00203 0.00201
## Cumulative Proportion 0.72546 0.72752 0.72957 0.73161 0.73364 0.73565
## PC91 PC92 PC93 PC94 PC95 PC96
## Standard deviation 0.9712 0.96757 0.96306 0.96026 0.95730 0.94908
## Proportion of Variance 0.0020 0.00199 0.00197 0.00196 0.00195 0.00191
## Cumulative Proportion 0.7377 0.73964 0.74161 0.74357 0.74551 0.74743
## PC97 PC98 PC99 PC100 PC101 PC102
## Standard deviation 0.9452 0.94462 0.93898 0.93849 0.93475 0.93215
## Proportion of Variance 0.0019 0.00189 0.00187 0.00187 0.00186 0.00184
## Cumulative Proportion 0.7493 0.75122 0.75309 0.75496 0.75681 0.75866
## PC103 PC104 PC105 PC106 PC107 PC108
## Standard deviation 0.92806 0.92389 0.9208 0.91923 0.91769 0.91230
## Proportion of Variance 0.00183 0.00181 0.0018 0.00179 0.00179 0.00177
## Cumulative Proportion 0.76049 0.76230 0.7641 0.76589 0.76768 0.76945
## PC109 PC110 PC111 PC112 PC113 PC114
## Standard deviation 0.90861 0.90709 0.90297 0.89911 0.8954 0.88815
## Proportion of Variance 0.00175 0.00175 0.00173 0.00172 0.0017 0.00167
## Cumulative Proportion 0.77120 0.77295 0.77468 0.77640 0.7781 0.77977
## PC115 PC116 PC117 PC118 PC119 PC120
## Standard deviation 0.88580 0.88521 0.88055 0.87628 0.87412 0.87373
## Proportion of Variance 0.00167 0.00166 0.00165 0.00163 0.00162 0.00162
## Cumulative Proportion 0.78144 0.78310 0.78475 0.78638 0.78800 0.78962
## PC121 PC122 PC123 PC124 PC125 PC126
## Standard deviation 0.86964 0.8674 0.86630 0.86225 0.86085 0.85852
## Proportion of Variance 0.00161 0.0016 0.00159 0.00158 0.00157 0.00156
## Cumulative Proportion 0.79123 0.7928 0.79442 0.79600 0.79757 0.79914
## PC127 PC128 PC129 PC130 PC131 PC132
## Standard deviation 0.85560 0.85098 0.84943 0.84492 0.84312 0.8408
## Proportion of Variance 0.00155 0.00154 0.00153 0.00152 0.00151 0.0015
## Cumulative Proportion 0.80069 0.80223 0.80376 0.80527 0.80678 0.8083
## PC133 PC134 PC135 PC136 PC137 PC138
## Standard deviation 0.83536 0.83196 0.83151 0.82934 0.82643 0.82422
## Proportion of Variance 0.00148 0.00147 0.00147 0.00146 0.00145 0.00144
## Cumulative Proportion 0.80977 0.81124 0.81270 0.81416 0.81561 0.81706
## PC139 PC140 PC141 PC142 PC143 PC144
## Standard deviation 0.81733 0.81414 0.8131 0.8125 0.80871 0.80419
## Proportion of Variance 0.00142 0.00141 0.0014 0.0014 0.00139 0.00137
## Cumulative Proportion 0.81848 0.81988 0.8213 0.8227 0.82408 0.82545
## PC145 PC146 PC147 PC148 PC149 PC150
## Standard deviation 0.80353 0.80235 0.79760 0.79576 0.79488 0.78854
## Proportion of Variance 0.00137 0.00137 0.00135 0.00134 0.00134 0.00132
## Cumulative Proportion 0.82682 0.82819 0.82954 0.83088 0.83222 0.83354
## PC151 PC152 PC153 PC154 PC155 PC156
## Standard deviation 0.78677 0.78611 0.7834 0.7810 0.77930 0.77423
## Proportion of Variance 0.00131 0.00131 0.0013 0.0013 0.00129 0.00127
## Cumulative Proportion 0.83486 0.83617 0.8375 0.8388 0.84006 0.84133
## PC157 PC158 PC159 PC160 PC161 PC162
## Standard deviation 0.77246 0.76961 0.76890 0.76577 0.76217 0.76070
## Proportion of Variance 0.00127 0.00126 0.00126 0.00125 0.00123 0.00123
## Cumulative Proportion 0.84260 0.84385 0.84511 0.84635 0.84759 0.84882
## PC163 PC164 PC165 PC166 PC167 PC168
## Standard deviation 0.75843 0.75639 0.75373 0.7515 0.7512 0.74704
## Proportion of Variance 0.00122 0.00121 0.00121 0.0012 0.0012 0.00118
## Cumulative Proportion 0.85004 0.85125 0.85246 0.8537 0.8549 0.85604
## PC169 PC170 PC171 PC172 PC173 PC174
## Standard deviation 0.74416 0.74219 0.73731 0.73608 0.73470 0.73248
## Proportion of Variance 0.00118 0.00117 0.00115 0.00115 0.00115 0.00114
## Cumulative Proportion 0.85722 0.85839 0.85954 0.86069 0.86184 0.86298
## PC175 PC176 PC177 PC178 PC179 PC180
## Standard deviation 0.73050 0.72769 0.72572 0.72396 0.7209 0.7196
## Proportion of Variance 0.00113 0.00112 0.00112 0.00111 0.0011 0.0011
## Cumulative Proportion 0.86411 0.86523 0.86635 0.86746 0.8686 0.8697
## PC181 PC182 PC183 PC184 PC185 PC186
## Standard deviation 0.71476 0.71254 0.71174 0.70889 0.70713 0.70384
## Proportion of Variance 0.00108 0.00108 0.00108 0.00107 0.00106 0.00105
## Cumulative Proportion 0.87075 0.87183 0.87290 0.87397 0.87503 0.87609
## PC187 PC188 PC189 PC190 PC191 PC192
## Standard deviation 0.69852 0.69792 0.69408 0.69111 0.68906 0.6872
## Proportion of Variance 0.00104 0.00103 0.00102 0.00101 0.00101 0.0010
## Cumulative Proportion 0.87712 0.87816 0.87918 0.88019 0.88120 0.8822
## PC193 PC194 PC195 PC196 PC197 PC198
## Standard deviation 0.6858 0.68398 0.68154 0.67713 0.67587 0.67271
## Proportion of Variance 0.0010 0.00099 0.00099 0.00097 0.00097 0.00096
## Cumulative Proportion 0.8832 0.88419 0.88518 0.88615 0.88712 0.88809
## PC199 PC200 PC201 PC202 PC203 PC204
## Standard deviation 0.67105 0.66594 0.66521 0.66219 0.66114 0.66012
## Proportion of Variance 0.00096 0.00094 0.00094 0.00093 0.00093 0.00093
## Cumulative Proportion 0.88904 0.88998 0.89092 0.89185 0.89278 0.89371
## PC205 PC206 PC207 PC208 PC209 PC210
## Standard deviation 0.65671 0.65443 0.65384 0.65340 0.6497 0.64834
## Proportion of Variance 0.00092 0.00091 0.00091 0.00091 0.0009 0.00089
## Cumulative Proportion 0.89462 0.89553 0.89644 0.89735 0.8982 0.89913
## PC211 PC212 PC213 PC214 PC215 PC216
## Standard deviation 0.64749 0.64234 0.63943 0.63736 0.63543 0.63312
## Proportion of Variance 0.00089 0.00088 0.00087 0.00086 0.00086 0.00085
## Cumulative Proportion 0.90002 0.90090 0.90177 0.90263 0.90349 0.90434
## PC217 PC218 PC219 PC220 PC221 PC222
## Standard deviation 0.63026 0.62824 0.62601 0.62434 0.62216 0.61631
## Proportion of Variance 0.00084 0.00084 0.00083 0.00083 0.00082 0.00081
## Cumulative Proportion 0.90518 0.90602 0.90685 0.90768 0.90850 0.90931
## PC223 PC224 PC225 PC226 PC227 PC228
## Standard deviation 0.61595 0.6144 0.61153 0.61057 0.60828 0.60805
## Proportion of Variance 0.00081 0.0008 0.00079 0.00079 0.00079 0.00078
## Cumulative Proportion 0.91011 0.9109 0.91171 0.91250 0.91329 0.91407
## PC229 PC230 PC231 PC232 PC233 PC234
## Standard deviation 0.60709 0.60445 0.60179 0.59858 0.59671 0.59519
## Proportion of Variance 0.00078 0.00078 0.00077 0.00076 0.00076 0.00075
## Cumulative Proportion 0.91485 0.91563 0.91640 0.91716 0.91792 0.91867
## PC235 PC236 PC237 PC238 PC239 PC240
## Standard deviation 0.59458 0.59370 0.59114 0.58868 0.58634 0.58426
## Proportion of Variance 0.00075 0.00075 0.00074 0.00074 0.00073 0.00072
## Cumulative Proportion 0.91942 0.92017 0.92091 0.92164 0.92237 0.92310
## PC241 PC242 PC243 PC244 PC245 PC246
## Standard deviation 0.58353 0.58199 0.57759 0.57655 0.5758 0.5735
## Proportion of Variance 0.00072 0.00072 0.00071 0.00071 0.0007 0.0007
## Cumulative Proportion 0.92382 0.92454 0.92525 0.92595 0.9267 0.9274
## PC247 PC248 PC249 PC250 PC251 PC252
## Standard deviation 0.57075 0.56863 0.56739 0.56609 0.56364 0.55943
## Proportion of Variance 0.00069 0.00069 0.00068 0.00068 0.00067 0.00066
## Cumulative Proportion 0.92805 0.92874 0.92942 0.93010 0.93077 0.93144
## PC253 PC254 PC255 PC256 PC257 PC258
## Standard deviation 0.55854 0.55681 0.55520 0.55200 0.55000 0.54788
## Proportion of Variance 0.00066 0.00066 0.00065 0.00065 0.00064 0.00064
## Cumulative Proportion 0.93210 0.93276 0.93341 0.93406 0.93470 0.93534
## PC259 PC260 PC261 PC262 PC263 PC264
## Standard deviation 0.54761 0.54605 0.54476 0.54391 0.54138 0.53911
## Proportion of Variance 0.00064 0.00063 0.00063 0.00063 0.00062 0.00062
## Cumulative Proportion 0.93598 0.93661 0.93724 0.93787 0.93849 0.93911
## PC265 PC266 PC267 PC268 PC269 PC270
## Standard deviation 0.53637 0.53434 0.5326 0.52807 0.52710 0.52491
## Proportion of Variance 0.00061 0.00061 0.0006 0.00059 0.00059 0.00058
## Cumulative Proportion 0.93972 0.94032 0.9409 0.94152 0.94211 0.94269
## PC271 PC272 PC273 PC274 PC275 PC276
## Standard deviation 0.52436 0.52030 0.51710 0.51656 0.51398 0.51362
## Proportion of Variance 0.00058 0.00057 0.00057 0.00057 0.00056 0.00056
## Cumulative Proportion 0.94328 0.94385 0.94442 0.94499 0.94555 0.94611
## PC277 PC278 PC279 PC280 PC281 PC282
## Standard deviation 0.51283 0.51181 0.50905 0.50796 0.50526 0.50400
## Proportion of Variance 0.00056 0.00056 0.00055 0.00055 0.00054 0.00054
## Cumulative Proportion 0.94667 0.94722 0.94777 0.94832 0.94886 0.94940
## PC283 PC284 PC285 PC286 PC287 PC288
## Standard deviation 0.50108 0.49971 0.49788 0.49672 0.49387 0.49214
## Proportion of Variance 0.00053 0.00053 0.00053 0.00052 0.00052 0.00051
## Cumulative Proportion 0.94993 0.95046 0.95099 0.95151 0.95203 0.95255
## PC289 PC290 PC291 PC292 PC293 PC294
## Standard deviation 0.49071 0.49007 0.48795 0.4862 0.4846 0.4834
## Proportion of Variance 0.00051 0.00051 0.00051 0.0005 0.0005 0.0005
## Cumulative Proportion 0.95306 0.95357 0.95407 0.9546 0.9551 0.9556
## PC295 PC296 PC297 PC298 PC299 PC300
## Standard deviation 0.48109 0.47896 0.47513 0.47505 0.47283 0.47164
## Proportion of Variance 0.00049 0.00049 0.00048 0.00048 0.00047 0.00047
## Cumulative Proportion 0.95606 0.95655 0.95703 0.95751 0.95798 0.95845
## PC301 PC302 PC303 PC304 PC305 PC306
## Standard deviation 0.47091 0.46637 0.46572 0.46372 0.46355 0.46068
## Proportion of Variance 0.00047 0.00046 0.00046 0.00046 0.00046 0.00045
## Cumulative Proportion 0.95892 0.95939 0.95985 0.96030 0.96076 0.96121
## PC307 PC308 PC309 PC310 PC311 PC312
## Standard deviation 0.45795 0.45743 0.45591 0.45288 0.45074 0.44933
## Proportion of Variance 0.00045 0.00044 0.00044 0.00044 0.00043 0.00043
## Cumulative Proportion 0.96165 0.96210 0.96254 0.96298 0.96341 0.96384
## PC313 PC314 PC315 PC316 PC317 PC318
## Standard deviation 0.44889 0.44730 0.44515 0.44207 0.44092 0.43991
## Proportion of Variance 0.00043 0.00042 0.00042 0.00041 0.00041 0.00041
## Cumulative Proportion 0.96426 0.96469 0.96511 0.96552 0.96594 0.96635
## PC319 PC320 PC321 PC322 PC323 PC324
## Standard deviation 0.43795 0.4349 0.4340 0.4331 0.43045 0.42932
## Proportion of Variance 0.00041 0.0004 0.0004 0.0004 0.00039 0.00039
## Cumulative Proportion 0.96676 0.9672 0.9676 0.9679 0.96835 0.96874
## PC325 PC326 PC327 PC328 PC329 PC330
## Standard deviation 0.42847 0.42618 0.42390 0.42138 0.41777 0.41750
## Proportion of Variance 0.00039 0.00039 0.00038 0.00038 0.00037 0.00037
## Cumulative Proportion 0.96913 0.96951 0.96990 0.97027 0.97064 0.97101
## PC331 PC332 PC333 PC334 PC335 PC336
## Standard deviation 0.41642 0.41549 0.41387 0.41342 0.41199 0.40995
## Proportion of Variance 0.00037 0.00037 0.00036 0.00036 0.00036 0.00036
## Cumulative Proportion 0.97138 0.97175 0.97211 0.97248 0.97284 0.97319
## PC337 PC338 PC339 PC340 PC341 PC342
## Standard deviation 0.40823 0.40765 0.40528 0.40274 0.40177 0.39976
## Proportion of Variance 0.00035 0.00035 0.00035 0.00034 0.00034 0.00034
## Cumulative Proportion 0.97355 0.97390 0.97425 0.97459 0.97493 0.97527
## PC343 PC344 PC345 PC346 PC347 PC348
## Standard deviation 0.39954 0.39830 0.39593 0.39403 0.39220 0.39145
## Proportion of Variance 0.00034 0.00034 0.00033 0.00033 0.00033 0.00033
## Cumulative Proportion 0.97561 0.97595 0.97628 0.97661 0.97694 0.97726
## PC349 PC350 PC351 PC352 PC353 PC354
## Standard deviation 0.39073 0.38906 0.38832 0.38334 0.38267 0.38146
## Proportion of Variance 0.00032 0.00032 0.00032 0.00031 0.00031 0.00031
## Cumulative Proportion 0.97759 0.97791 0.97823 0.97854 0.97885 0.97916
## PC355 PC356 PC357 PC358 PC359 PC360 PC361
## Standard deviation 0.37997 0.3790 0.3777 0.3769 0.3748 0.3732 0.37131
## Proportion of Variance 0.00031 0.0003 0.0003 0.0003 0.0003 0.0003 0.00029
## Cumulative Proportion 0.97947 0.9798 0.9801 0.9804 0.9807 0.9810 0.98126
## PC362 PC363 PC364 PC365 PC366 PC367
## Standard deviation 0.36839 0.36616 0.36535 0.36449 0.36220 0.35994
## Proportion of Variance 0.00029 0.00028 0.00028 0.00028 0.00028 0.00028
## Cumulative Proportion 0.98155 0.98184 0.98212 0.98240 0.98268 0.98296
## PC368 PC369 PC370 PC371 PC372 PC373
## Standard deviation 0.35800 0.35574 0.35384 0.35078 0.34927 0.34881
## Proportion of Variance 0.00027 0.00027 0.00027 0.00026 0.00026 0.00026
## Cumulative Proportion 0.98323 0.98350 0.98376 0.98402 0.98428 0.98454
## PC374 PC375 PC376 PC377 PC378 PC379
## Standard deviation 0.34598 0.34531 0.34303 0.34238 0.34164 0.33982
## Proportion of Variance 0.00025 0.00025 0.00025 0.00025 0.00025 0.00025
## Cumulative Proportion 0.98480 0.98505 0.98530 0.98555 0.98580 0.98604
## PC380 PC381 PC382 PC383 PC384 PC385
## Standard deviation 0.33804 0.33591 0.33574 0.33397 0.33291 0.33270
## Proportion of Variance 0.00024 0.00024 0.00024 0.00024 0.00024 0.00024
## Cumulative Proportion 0.98628 0.98652 0.98676 0.98700 0.98723 0.98747
## PC386 PC387 PC388 PC389 PC390 PC391
## Standard deviation 0.32987 0.32575 0.32541 0.32343 0.32235 0.32045
## Proportion of Variance 0.00023 0.00023 0.00022 0.00022 0.00022 0.00022
## Cumulative Proportion 0.98770 0.98793 0.98815 0.98837 0.98859 0.98881
## PC392 PC393 PC394 PC395 PC396 PC397
## Standard deviation 0.31985 0.31853 0.31626 0.31493 0.31394 0.31164
## Proportion of Variance 0.00022 0.00022 0.00021 0.00021 0.00021 0.00021
## Cumulative Proportion 0.98903 0.98924 0.98946 0.98967 0.98988 0.99008
## PC398 PC399 PC400 PC401 PC402 PC403 PC404
## Standard deviation 0.3091 0.3086 0.3074 0.3064 0.3060 0.3034 0.29902
## Proportion of Variance 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.00019
## Cumulative Proportion 0.9903 0.9905 0.9907 0.9909 0.9911 0.9913 0.99147
## PC405 PC406 PC407 PC408 PC409 PC410
## Standard deviation 0.29808 0.29743 0.29626 0.29558 0.29161 0.29098
## Proportion of Variance 0.00019 0.00019 0.00019 0.00019 0.00018 0.00018
## Cumulative Proportion 0.99166 0.99185 0.99203 0.99222 0.99240 0.99258
## PC411 PC412 PC413 PC414 PC415 PC416
## Standard deviation 0.28853 0.28789 0.28648 0.28603 0.28535 0.28195
## Proportion of Variance 0.00018 0.00018 0.00017 0.00017 0.00017 0.00017
## Cumulative Proportion 0.99276 0.99293 0.99311 0.99328 0.99345 0.99362
## PC417 PC418 PC419 PC420 PC421 PC422
## Standard deviation 0.28032 0.27909 0.27533 0.27499 0.27283 0.27187
## Proportion of Variance 0.00017 0.00017 0.00016 0.00016 0.00016 0.00016
## Cumulative Proportion 0.99379 0.99395 0.99411 0.99428 0.99443 0.99459
## PC423 PC424 PC425 PC426 PC427 PC428
## Standard deviation 0.27081 0.26896 0.26711 0.26549 0.26497 0.26316
## Proportion of Variance 0.00016 0.00015 0.00015 0.00015 0.00015 0.00015
## Cumulative Proportion 0.99475 0.99490 0.99505 0.99520 0.99535 0.99550
## PC429 PC430 PC431 PC432 PC433 PC434
## Standard deviation 0.26174 0.25937 0.25735 0.25631 0.25377 0.25262
## Proportion of Variance 0.00015 0.00014 0.00014 0.00014 0.00014 0.00014
## Cumulative Proportion 0.99564 0.99579 0.99593 0.99607 0.99620 0.99634
## PC435 PC436 PC437 PC438 PC439 PC440
## Standard deviation 0.24953 0.24862 0.24747 0.24452 0.24341 0.24124
## Proportion of Variance 0.00013 0.00013 0.00013 0.00013 0.00013 0.00012
## Cumulative Proportion 0.99647 0.99660 0.99673 0.99686 0.99698 0.99711
## PC441 PC442 PC443 PC444 PC445 PC446
## Standard deviation 0.23855 0.23738 0.23493 0.23292 0.23127 0.23049
## Proportion of Variance 0.00012 0.00012 0.00012 0.00012 0.00011 0.00011
## Cumulative Proportion 0.99723 0.99735 0.99746 0.99758 0.99769 0.99781
## PC447 PC448 PC449 PC450 PC451 PC452
## Standard deviation 0.22840 0.22804 0.22597 0.22265 0.2205 0.2190
## Proportion of Variance 0.00011 0.00011 0.00011 0.00011 0.0001 0.0001
## Cumulative Proportion 0.99792 0.99803 0.99814 0.99824 0.9983 0.9984
## PC453 PC454 PC455 PC456 PC457 PC458
## Standard deviation 0.2148 0.2146 0.2129 0.21084 0.20901 0.20628
## Proportion of Variance 0.0001 0.0001 0.0001 0.00009 0.00009 0.00009
## Cumulative Proportion 0.9985 0.9986 0.9987 0.99883 0.99893 0.99902
## PC459 PC460 PC461 PC462 PC463 PC464
## Standard deviation 0.20535 0.20202 0.20150 0.19910 0.19694 0.19363
## Proportion of Variance 0.00009 0.00009 0.00009 0.00008 0.00008 0.00008
## Cumulative Proportion 0.99911 0.99919 0.99928 0.99936 0.99944 0.99952
## PC465 PC466 PC467 PC468 PC469 PC470
## Standard deviation 0.19207 0.18565 0.18365 0.17935 0.17877 0.17375
## Proportion of Variance 0.00008 0.00007 0.00007 0.00007 0.00007 0.00006
## Cumulative Proportion 0.99960 0.99968 0.99975 0.99982 0.99988 0.99995
## PC471
## Standard deviation 0.15689
## Proportion of Variance 0.00005
## Cumulative Proportion 1.00000How many principal components must be retained in order to capture at least 80% of the total variance in data?
As seen in the table where the plot was based, can be seen that 2 componets, must be taken, in order to reach 80% of the cumuled variance. (0.8042544) had been reached when those two components had been taken
What is the magnitude of the estimated reconstruction error if we only retain top two of the PCA components?
If we take just the first two PCA components, we would have a cumulative variance of 0.8042544, as seen in a previous table, so we are loosing the 19.57456% of the total variance
- Analysis of principal components and weights
- Compute and plot the time series of the 1st principal component and observe temporal patterns. Identify the date with the lowest value for this component and conduct a quick research on the Internet to see if you can identify event(s) that might explain the observed behavior.
#summary(zoo.pca)[2]
p1 <-- prcomp(log.return.data)$rotation[,"PC1"]
p1t <- zoo(p1, date )
plot (p1t)
According with the previous plot, for PC1, some events are seen.
3 drops and 2 increases can be seen. 2 of the dros apear to be bigger that the other, and bigger than the 2 increases too. So, in overall, can be say that the marked suffered more drops than increases, and that at least 2 drops were bigger than any other event.
Can say that the "drops" were 3 times greater than "increases".
Next, some events that could explain what happened on those dates:End of 2011 https://en.wikipedia.org/wiki/August_2011_stock_markets_fall http://money.cnn.com/2011/07/08/markets/markets_newyork/index.htm
Mid 2012 https://www.usatoday.com/story/money/markets/2012/12/31/stocks-post-doubledigit-gains-in-2012/1800223/ http://theweek.com/articles/469099/why-2012-good-year-stock-market
Beging of 2013** () http://roccacharts.blogspot.com.co/2013/02/aapl-apple-comienzo-o-fin-de-la-caida.html http://money.cnn.com/2013/02/21/investing/stocks-markets/index.html http://www.businessinsider.com/two-charts-show-why-apple-stock-dropped-2013-4
Mid End of 2013 http://www.marketwatch.com/story/us-stocks-edge-lower-as-shutdown-drags-on-2013-10-08 http://money.cnn.com/2013/08/16/investing/stocks-markets/index.html
Beging of 2014 https://www.thestreet.com/story/12195485/1/stocks-begin-2014-with-inflating-bubbles.html
End of 2014** https://dealbook.nytimes.com/2014/12/31/bull-market-for-stocks-lasts-through-2014/ http://money.cnn.com/2014/10/09/investing/stocks-markets-wall-street-selloff/index.html http://www.cnbc.com/2013/12/30/why-the-market-could-see-a-17-drop-in-2014.html
Mid 2015 http://www.businessinsider.com/bank-of-america-on-mid-2015-stock-market-2015-6
The Plot below, corresponding to the second principal component, shows events, the same dates than the principal component one, but with other magnitudes. aditionally, two events apear to be contrary to the PC1, Showing 4 increase events and 3 drop events.
In this case. the "drop" magnitude is yet greater than "increases", but the relation is much lower than in the PC1´s plot. Can say that "increases"" are a little more than a half than "drops". - Extract the weights from PCA model for 1st and 2nd principal components.
prcomp(log.return.data)$rotation[,"PC1"]## MMM ACE ABT ANF ADBE
## 2.534324e-04 4.242656e-04 -7.105428e-05 2.849963e-04 5.726191e-04
## AMD AES AET AFL A
## -4.833868e-05 3.913908e-04 4.584344e-04 6.233554e-04 9.667904e-04
## APD ARG AKS AKAM AA
## 1.901613e-04 1.462052e-04 1.152964e-03 1.725941e-04 4.689306e-04
## ATI AGN ALL ALTR MO
## 6.974859e-04 -8.322261e-04 2.847716e-04 3.456671e-04 -2.360787e-04
## AMZN AEE AEP AXP AIG
## -5.682580e-06 6.038653e-04 -1.880672e-04 3.603231e-04 8.377200e-04
## AMT AMP ABC AMGN APH
## 1.433001e-04 5.865390e-04 -7.481451e-05 -4.974105e-04 9.918407e-05
## APC ADI AON APA AIV
## 2.943229e-04 6.501483e-05 1.488933e-04 7.827020e-04 -3.271332e-04
## APOL AAPL AMAT ADM AIZ
## -1.339512e-03 -3.818817e-04 5.378829e-04 1.648637e-04 1.071177e-03
## T ADSK ADP AN AZO
## -5.461744e-05 -1.243825e-04 1.187974e-04 2.479417e-04 2.030521e-04
## AVB AVY AVP BHI BLL
## -2.297085e-04 9.278339e-05 1.638516e-03 5.888284e-04 1.889678e-04
## BAC BK BCR BAX BBT
## 7.009029e-04 6.554195e-04 -6.857052e-05 1.949944e-04 3.935908e-04
## BDX BBBY BMS BRK.B BBY
## 7.429941e-05 4.634342e-04 1.604621e-04 2.801572e-04 -8.225634e-04
## BIG BIIB BLK HRB BMC
## 2.050458e-04 -3.483059e-04 5.348949e-04 -9.818444e-06 1.623359e-01
## BA BXP BSX BMY BRCM
## 5.759309e-04 -1.971968e-04 5.478695e-04 -1.356917e-04 1.045098e-03
## BF.B CHRW CA CVC COG
## 3.047916e-04 5.294136e-04 4.005104e-04 -1.805652e-04 -7.417198e-05
## CAM CPB COF CAH CFN
## 5.771409e-04 3.079808e-05 5.268858e-04 1.204587e-04 4.917886e-04
## KMX CCL CAT CBG CBS
## 6.174567e-04 1.142341e-03 1.901130e-04 7.975651e-04 2.082988e-04
## CELG CNP CTL CERN CF
## -1.357923e-04 1.446233e-04 2.991568e-04 1.513650e-05 1.047728e-04
## SCHW CHK CVX CB CI
## 3.851534e-04 3.029669e-04 -1.357302e-05 1.784234e-04 9.876890e-05
## CINF CTAS CSCO C CTXS
## 2.582890e-04 2.351938e-04 -4.044133e-05 1.388008e-03 4.227732e-04
## CLF CLX CME CMS COH
## 3.427323e-04 1.288094e-04 2.602006e-04 2.279915e-04 4.869795e-04
## KO CCE CTSH CL CMCSA
## -1.615097e-04 6.025661e-05 1.282844e-04 -2.163191e-04 3.121703e-05
## CMA CSC CPWR CAG COP
## 1.490352e-03 5.194014e-04 5.401609e-04 8.976231e-05 2.898812e-04
## CNX ED STZ GLW COST
## 2.954764e-04 5.852028e-05 4.812036e-04 2.785013e-04 2.765143e-04
## CVH COV CSX CMI CVS
## -5.022219e-05 2.133259e-04 1.408285e-04 8.637167e-04 3.107190e-04
## DHI DHR DRI DVA DF
## 8.664309e-04 5.858561e-04 2.765843e-04 1.007229e-04 3.670610e-04
## DE DNR XRAY DVN DV
## 6.211863e-04 3.191028e-04 2.894856e-04 3.096952e-04 -2.707384e-04
## DO DTV DFS DISCA D
## 2.759605e-04 3.136356e-04 2.274549e-04 9.785847e-05 -2.569244e-05
## RRD DOV DOW DPS DTE
## 1.395683e-04 4.458182e-04 6.351476e-04 5.364060e-04 2.278037e-04
## DD DUK DNB ETFC EMN
## 4.511213e-04 -3.642897e-05 -3.691167e-04 6.540628e-04 6.188778e-04
## ETN EBAY ECL EIX EW
## 3.461492e-04 -5.290155e-05 1.014422e-04 1.116891e-04 -5.808879e-05
## EMC EMR ETR EOG EQT
## 1.161674e-04 4.785725e-04 1.671290e-04 6.387372e-04 4.235219e-05
## EFX EQR EL EXC EXPE
## 3.495479e-04 -1.980086e-04 4.262165e-04 6.320307e-05 -9.589035e-05
## EXPD ESRX XOM FFIV FDO
## 1.208647e-03 2.440893e-04 5.839174e-05 4.788436e-04 4.349413e-04
## FAST FII FDX FIS FITB
## -1.203500e-04 8.960881e-05 6.277911e-04 5.373554e-04 4.341595e-04
## FHN FSLR FE FISV FLIR
## 4.559296e-04 -3.443853e-05 -8.087565e-05 4.344965e-05 -1.729604e-04
## FLS FLR FMC FTI F
## 5.621459e-04 3.516598e-04 2.649172e-04 4.606680e-04 3.149692e-04
## BEN FCX FTR GME GCI
## 4.848871e-04 8.003792e-04 9.371747e-04 -9.800220e-04 5.494996e-04
## GPS GD GE GIS GPC
## -4.996875e-04 3.949467e-04 6.993984e-04 -6.863891e-05 6.005897e-04
## GNW GILD GS GT GWW
## 8.561931e-04 1.793392e-04 5.835058e-04 7.716771e-04 6.517108e-05
## HAL HOG HAR HRS HIG
## 6.081025e-04 1.632499e-04 8.569431e-04 4.904373e-04 8.713667e-04
## HAS HCP HCN HP HES
## 3.485264e-04 -8.443225e-05 -1.810017e-04 3.052713e-04 8.207880e-04
## HPQ HD HON HRL HSP
## 7.870356e-04 2.152926e-05 6.684008e-04 -5.298433e-06 5.728254e-04
## HST HCBK HUM HBAN ITW
## 7.071257e-04 5.396041e-04 -2.854360e-04 8.928484e-04 2.782859e-04
## TEG INTC ICE IBM IFF
## -1.733966e-05 2.267524e-04 2.387202e-05 1.294587e-04 2.790186e-04
## IGT IP IPG INTU ISRG
## -5.126461e-04 3.353832e-05 5.119520e-04 -6.489059e-05 -1.029112e-03
## IVZ IRM JBL JEC JNS
## 6.365604e-04 3.191438e-04 5.152038e-04 2.278970e-04 4.680613e-04
## JDSU JNJ JCI JOY JPM
## 1.042088e-03 3.321361e-05 -7.535505e-05 3.343512e-04 7.689847e-04
## JNPR K KEY KMB KIM
## 3.657649e-04 -2.584309e-05 4.328920e-04 2.872455e-04 4.420938e-05
## KLAC KSS KR LLL LH
## 5.415050e-04 5.468106e-04 2.447387e-04 3.822035e-04 2.703726e-05
## LM LEG LEN LUK LXK
## 5.643040e-04 3.981523e-04 9.242679e-04 8.665601e-04 8.994855e-04
## LIFE LLY LNC LLTC LMT
## -6.838541e-02 2.188366e-04 8.066168e-04 2.950819e-04 5.307708e-04
## L LO LOW LSI MTB
## 3.771221e-04 -1.399158e-05 1.037929e-04 -3.622322e-01 4.112679e-04
## M MRO MAR MMC MAS
## 3.126668e-04 5.968281e-04 7.325125e-04 2.542295e-04 1.397782e-03
## ANR MA MAT MKC MCD
## 7.645512e-04 6.195544e-05 4.482492e-04 -9.067261e-05 -2.899881e-06
## MCK MJN MWV MDT MRK
## 3.821569e-04 -2.063936e-05 -5.528586e-04 4.087448e-04 1.811289e-05
## MET MCHP MU MSFT TAP
## 6.774920e-04 2.617979e-04 2.569161e-04 2.338751e-05 1.679785e-04
## MON MWW MCO MS MOS
## 8.262517e-05 1.138598e-03 -3.323342e-04 1.131601e-03 9.697552e-05
## MSI MUR MYL NBR NDAQ
## 3.299168e-04 3.156953e-04 -2.687713e-04 5.520914e-04 1.668972e-04
## NOV NTAP NFLX NWL NFX
## 3.040679e-04 2.294618e-04 -1.210307e-03 5.681230e-04 7.389664e-04
## NEM NEE GAS NKE NI
## 5.497974e-04 6.203608e-05 1.396842e-04 3.873973e-05 1.812197e-04
## NE NBL JWN NSC NTRS
## 7.344806e-04 2.688900e-04 1.606000e-04 1.664055e-05 5.553686e-04
## NOC NU CMG NRG NUE
## 3.464999e-04 -8.060485e-05 5.305021e-05 7.392803e-04 5.956970e-04
## NVDA ORLY OXY OMC OKE
## 4.745464e-04 -1.469616e-04 5.670207e-04 3.523485e-04 2.672166e-05
## ORCL OI PCAR IR PLL
## 1.384632e-04 5.267291e-04 3.372452e-04 5.289276e-04 4.514679e-04
## PH PDCO PAYX BTU JCP
## 6.655111e-04 7.792427e-04 9.961078e-05 6.311034e-04 3.279949e-04
## PBCT POM PEP PKI PFE
## 2.884807e-04 -8.772861e-05 1.644952e-04 7.969510e-04 -3.292777e-04
## PCG PM PNW PXD PBI
## 1.747971e-04 -8.217181e-05 2.288306e-04 2.209336e-04 2.227779e-04
## PCL PNC RL PPG PPL
## 1.338242e-04 5.506001e-04 2.963280e-04 2.665912e-04 4.126669e-05
## PX PCP PCLN PFG PG
## 2.367000e-04 2.294239e-04 -1.110228e-04 5.967621e-04 2.207787e-06
## PGR PLD PRU PEG PSA
## 2.865017e-04 2.213957e-04 5.348873e-04 7.013661e-05 -7.649952e-05
## PHM QEP PWR QCOM DGX
## 1.301629e-03 4.254149e-04 5.796318e-04 -1.321818e-04 2.891386e-04
## RSH RRC RTN RHT RF
## 1.010883e-03 4.324359e-04 3.634016e-04 6.357033e-04 9.047762e-04
## RSG RAI RHI ROK COL
## 9.882288e-05 -1.595315e-04 2.137068e-04 6.327958e-04 3.820866e-04
## ROP ROST RDC R SWY
## 3.229179e-04 1.279903e-04 5.638156e-04 1.071464e-03 2.807512e-04
## CRM SNDK SCG SLB SNI
## 2.656848e-04 -3.664020e-04 1.385089e-04 5.010225e-04 3.655808e-05
## SEE SHLD SRE SHW SIAL
## 6.356978e-05 9.422288e-04 2.187726e-04 -2.885802e-04 2.011169e-04
## SPG SLM SJM SNA SO
## -2.510472e-04 5.779145e-04 2.211857e-04 5.414249e-04 -1.296433e-04
## LUV SWN SE S STJ
## 5.841912e-04 1.093869e-04 2.943860e-04 7.262986e-04 3.339923e-04
## SWK SPLS SBUX HOT STT
## 4.643908e-04 -1.517736e-05 7.442419e-06 5.550948e-04 6.810282e-04
## SRCL SYK STI SVU SYMC
## 3.480863e-05 3.113414e-04 2.370521e-04 1.588505e-03 2.419580e-04
## SYY TROW TGT TEL TE
## 2.039014e-04 6.108138e-04 4.484784e-04 4.208151e-04 2.249846e-04
## THC TDC TER TSO TXN
## 2.616260e-04 -1.775019e-04 6.290688e-04 -3.018830e-04 1.877158e-04
## TXT HSY TRV TMO TIF
## 4.613845e-04 -4.330898e-05 2.666602e-04 3.470052e-04 1.313013e-04
## TWX TWC TIE TJX TMK
## 4.899614e-04 2.627623e-04 9.152295e-01 7.444240e-06 2.918255e-03
## TSS TSN TYC USB UNP
## -2.254876e-04 1.002386e-04 2.692626e-04 5.637878e-04 2.383150e-04
## UNH UPS X UTX UNM
## 2.457504e-05 2.355397e-04 7.784340e-04 2.348077e-04 3.084274e-04
## URBN VFC VLO VAR VTR
## 6.550752e-05 -5.142984e-04 5.886625e-05 3.134079e-04 -2.440609e-04
## VRSN VZ VIAB V VNO
## -4.041238e-04 3.340993e-04 3.324852e-04 1.179457e-04 -1.256593e-04
## VMC WMT WAG DIS WM
## -2.722100e-05 4.366925e-04 1.546493e-04 2.457738e-04 2.441896e-04
## WAT WLP WFC WDC WU
## 4.378060e-05 6.461576e-04 5.348426e-04 1.536538e-04 6.190430e-04
## WY WHR WFM WMB WIN
## 3.900421e-04 8.823346e-04 -2.816601e-04 4.352886e-04 5.691894e-04
## WEC WYN WYNN XEL XRX
## -1.793161e-05 5.784501e-04 -3.797323e-04 -4.328238e-06 6.358336e-04
## XLNX XL YHOO YUM ZMH
## 1.463972e-04 4.743176e-04 -1.087533e-04 3.755188e-05 5.227760e-04
## ZION
## 8.494489e-04prcomp(log.return.data)$rotation[,"PC2"]## MMM ACE ABT ANF ADBE
## 4.994089e-04 9.121001e-04 7.565907e-05 -1.853760e-04 1.876898e-04
## AMD AES AET AFL A
## -5.637528e-04 -1.294423e-04 3.244355e-04 1.430304e-03 -4.172662e-04
## APD ARG AKS AKAM AA
## 2.868371e-04 -1.988899e-05 -1.876764e-03 4.010166e-04 -1.204128e-03
## ATI AGN ALL ALTR MO
## 9.515009e-04 2.037110e-03 6.920145e-04 -2.045232e-04 5.802674e-04
## AMZN AEE AEP AXP AIG
## -7.349528e-04 8.256540e-04 5.810936e-05 7.658600e-04 5.471844e-04
## AMT AMP ABC AMGN APH
## 1.015344e-03 5.833571e-05 3.455009e-04 7.809938e-04 -1.975566e-05
## APC ADI AON APA AIV
## -7.430365e-04 8.001353e-04 1.633419e-04 -6.721624e-04 1.310647e-03
## APOL AAPL AMAT ADM AIZ
## 1.525445e-03 -4.307999e-04 6.388617e-04 -1.258778e-04 -2.374278e-04
## T ADSK ADP AN AZO
## 1.026062e-03 -1.095118e-04 1.117368e-03 6.845288e-04 -7.701284e-05
## AVB AVY AVP BHI BLL
## 8.687496e-04 1.264430e-03 -1.956491e-03 -6.117378e-04 4.202781e-04
## BAC BK BCR BAX BBT
## 9.155963e-04 2.848073e-04 1.181830e-03 -7.338909e-05 3.606447e-04
## BDX BBBY BMS BRK.B BBY
## 6.661814e-04 5.970730e-05 1.672362e-04 7.219306e-04 9.517075e-04
## BIG BIIB BLK HRB BMC
## -4.796890e-04 5.560308e-04 -2.495117e-04 -5.849871e-04 8.607344e-01
## BA BXP BSX BMY BRCM
## 3.477746e-04 3.554540e-04 2.715840e-04 3.012525e-04 7.635772e-04
## BF.B CHRW CA CVC COG
## 5.713840e-04 9.033629e-04 6.389082e-05 -4.467520e-04 -7.140290e-04
## CAM CPB COF CAH CFN
## -1.101399e-03 5.902496e-04 8.757477e-04 1.613713e-03 4.355460e-04
## KMX CCL CAT CBG CBS
## 2.004082e-03 3.746067e-04 4.516379e-04 1.171742e-03 7.203779e-04
## CELG CNP CTL CERN CF
## 2.499355e-04 -5.734997e-04 8.049602e-04 5.684118e-04 3.202557e-04
## SCHW CHK CVX CB CI
## -1.085331e-04 -2.767117e-03 -8.496511e-04 6.157345e-04 6.053669e-04
## CINF CTAS CSCO C CTXS
## 1.907991e-04 9.054468e-04 8.685544e-04 2.551496e-04 1.053205e-03
## CLF CLX CME CMS COH
## -7.061109e-04 -7.563573e-04 5.505492e-04 3.903649e-04 1.832064e-03
## KO CCE CTSH CL CMCSA
## 5.212668e-04 -4.952500e-04 8.750434e-04 -4.839767e-04 6.328517e-04
## CMA CSC CPWR CAG COP
## 2.512958e-04 1.628453e-03 1.464475e-04 -2.056483e-04 -1.040763e-03
## CNX ED STZ GLW COST
## -6.759569e-04 -3.144431e-05 4.018383e-04 3.513779e-05 2.009319e-05
## CVH COV CSX CMI CVS
## -4.405538e-06 1.096626e-03 2.725508e-04 1.331639e-03 -7.969454e-05
## DHI DHR DRI DVA DF
## 1.094115e-04 1.375689e-04 1.029635e-03 2.065702e-04 -1.830858e-04
## DE DNR XRAY DVN DV
## 1.523322e-03 -1.271845e-03 6.628221e-04 8.044312e-06 1.088980e-03
## DO DTV DFS DISCA D
## 2.723378e-04 6.817591e-04 1.810410e-03 -6.473501e-04 2.908818e-06
## RRD DOV DOW DPS DTE
## -1.806191e-04 -2.828398e-04 -3.449187e-04 -9.710470e-06 4.930493e-04
## DD DUK DNB ETFC EMN
## 3.424421e-04 -9.318162e-05 1.215287e-03 3.064468e-04 1.349885e-03
## ETN EBAY ECL EIX EW
## -3.986821e-05 4.793333e-04 -6.308135e-04 5.459267e-04 5.285639e-04
## EMC EMR ETR EOG EQT
## 9.451584e-04 1.202089e-04 5.488036e-04 -1.297868e-03 -5.520982e-04
## EFX EQR EL EXC EXPE
## 3.830883e-04 4.828506e-04 -2.238028e-04 -2.669927e-04 7.464812e-05
## EXPD ESRX XOM FFIV FDO
## 1.572991e-03 8.769377e-05 -1.350066e-04 6.668839e-04 1.198428e-03
## FAST FII FDX FIS FITB
## 1.790914e-04 2.717300e-04 7.694134e-04 9.430135e-04 -3.159547e-05
## FHN FSLR FE FISV FLIR
## 7.474240e-04 -6.435458e-04 -1.572617e-04 1.145315e-03 -4.415454e-04
## FLS FLR FMC FTI F
## 6.638396e-04 1.801691e-04 3.992752e-04 -8.977586e-04 5.126500e-04
## BEN FCX FTR GME GCI
## 9.181936e-04 -1.720362e-04 -5.724679e-04 -4.373195e-04 -1.089928e-04
## GPS GD GE GIS GPC
## 1.090688e-03 -4.075841e-04 9.195268e-04 5.754276e-05 2.317202e-04
## GNW GILD GS GT GWW
## 2.894774e-03 -1.761789e-03 4.242078e-04 3.380319e-04 1.261472e-04
## HAL HOG HAR HRS HIG
## -6.461778e-04 1.236025e-03 9.113230e-04 3.362443e-04 8.679953e-04
## HAS HCP HCN HP HES
## 3.794128e-04 1.041982e-03 2.783344e-04 -2.908529e-04 3.806302e-05
## HPQ HD HON HRL HSP
## -1.463892e-03 6.249965e-04 3.305640e-05 5.977666e-04 4.905132e-04
## HST HCBK HUM HBAN ITW
## 1.583053e-03 9.106673e-04 3.596698e-04 5.763169e-04 6.281151e-04
## TEG INTC ICE IBM IFF
## -1.253601e-03 8.224257e-04 4.326793e-04 6.219692e-04 7.553525e-04
## IGT IP IPG INTU ISRG
## 2.566567e-03 -1.528122e-03 1.567118e-03 7.082690e-04 1.603251e-03
## IVZ IRM JBL JEC JNS
## 1.755550e-05 2.384667e-04 1.162418e-03 3.349622e-04 8.010222e-04
## JDSU JNJ JCI JOY JPM
## 5.422494e-04 4.333422e-05 6.222524e-04 6.109138e-04 9.214787e-04
## JNPR K KEY KMB KIM
## 1.433820e-03 2.360502e-04 1.359491e-03 -8.168672e-04 1.172614e-03
## KLAC KSS KR LLL LH
## 5.468667e-04 -6.182168e-04 5.182829e-04 4.943828e-04 -5.638959e-04
## LM LEG LEN LUK LXK
## 4.501496e-04 2.171362e-04 -4.994333e-04 3.009207e-04 -1.293504e-03
## LIFE LLY LNC LLTC LMT
## -4.704115e-02 -2.612942e-05 1.142118e-03 6.431292e-04 1.425199e-04
## L LO LOW LSI MTB
## 3.763582e-04 1.333295e-03 1.863100e-04 -3.977719e-01 3.456091e-04
## M MRO MAR MMC MAS
## 3.784148e-04 -6.338293e-04 1.860794e-03 7.436837e-04 -1.733605e-03
## ANR MA MAT MKC MCD
## -3.328587e-03 2.755307e-04 -8.393263e-04 6.399191e-04 4.571696e-04
## MCK MJN MWV MDT MRK
## 4.598714e-04 1.728943e-03 1.161270e-03 4.505784e-04 9.015928e-04
## MET MCHP MU MSFT TAP
## 7.926219e-04 1.705738e-04 -1.138886e-04 1.375000e-03 1.081973e-03
## MON MWW MCO MS MOS
## 3.308739e-04 9.780295e-04 6.626453e-04 5.243007e-04 -1.948333e-04
## MSI MUR MYL NBR NDAQ
## 7.424499e-04 -4.092733e-04 2.269038e-04 -9.578654e-04 1.180500e-03
## NOV NTAP NFLX NWL NFX
## -8.238651e-04 6.171110e-04 2.896492e-03 7.423029e-04 -1.081080e-03
## NEM NEE GAS NKE NI
## -4.959459e-04 2.657241e-05 -1.554627e-05 6.293653e-04 -6.778012e-04
## NE NBL JWN NSC NTRS
## -6.681765e-04 1.634225e-04 7.295255e-05 -3.202018e-04 4.395185e-04
## NOC NU CMG NRG NUE
## 7.867680e-04 8.774813e-06 1.100196e-03 -5.248907e-04 1.810124e-04
## NVDA ORLY OXY OMC OKE
## 1.242081e-03 2.246318e-04 -5.294373e-04 5.568116e-04 -8.529922e-04
## ORCL OI PCAR IR PLL
## 1.647449e-04 9.434716e-04 6.923646e-04 -5.947089e-04 6.186959e-04
## PH PDCO PAYX BTU JCP
## 8.400328e-04 1.093224e-03 1.127383e-03 -1.665656e-03 -1.208141e-03
## PBCT POM PEP PKI PFE
## 6.279448e-04 -1.068111e-04 8.107985e-06 4.972008e-04 5.010735e-04
## PCG PM PNW PXD PBI
## 1.301413e-04 -6.257807e-05 -1.454459e-04 4.100596e-04 1.470650e-04
## PCL PNC RL PPG PPL
## 4.212717e-04 7.907004e-04 1.772839e-04 5.742643e-04 -4.029033e-04
## PX PCP PCLN PFG PG
## -8.905026e-05 1.071538e-03 1.084433e-03 9.251154e-04 -1.996977e-04
## PGR PLD PRU PEG PSA
## 1.012091e-03 5.488574e-04 8.592297e-04 1.539525e-04 3.372947e-05
## PHM QEP PWR QCOM DGX
## 1.334435e-04 -1.927195e-03 -1.835849e-03 -2.198370e-05 -2.973636e-04
## RSH RRC RTN RHT RF
## -3.958857e-04 -1.404813e-03 1.121241e-03 1.132675e-04 2.057091e-03
## RSG RAI RHI ROK COL
## 7.426386e-04 1.008177e-03 8.996440e-04 5.680032e-04 6.153671e-04
## ROP ROST RDC R SWY
## 8.113956e-04 9.737628e-04 -1.196449e-03 -1.164123e-04 -1.941718e-04
## CRM SNDK SCG SLB SNI
## 6.637868e-04 1.334726e-03 4.347224e-05 -1.078531e-03 6.233985e-04
## SEE SHLD SRE SHW SIAL
## -8.419709e-05 2.412348e-03 -2.713943e-04 -3.812535e-05 -6.302930e-05
## SPG SLM SJM SNA SO
## 2.912570e-04 8.001919e-04 -4.508871e-04 8.441387e-04 1.584969e-05
## LUV SWN SE S STJ
## 2.057005e-03 -1.482339e-03 -9.637667e-04 1.372658e-03 1.024661e-03
## SWK SPLS SBUX HOT STT
## 6.210982e-04 3.513127e-04 6.422518e-04 1.630993e-03 6.725812e-04
## SRCL SYK STI SVU SYMC
## 4.696345e-04 -3.673209e-04 7.790156e-04 -2.228410e-03 9.244253e-04
## SYY TROW TGT TEL TE
## 5.438047e-04 2.575607e-04 5.705541e-04 1.013044e-03 -3.344185e-04
## THC TDC TER TSO TXN
## -4.617426e-04 9.600376e-04 7.790887e-04 -5.214392e-04 1.114228e-04
## TXT HSY TRV TMO TIF
## 1.502176e-03 -6.081409e-04 3.100453e-04 2.932616e-04 4.138642e-04
## TWX TWC TIE TJX TMK
## -4.618701e-04 4.175481e-04 -3.136359e-01 9.260773e-04 -6.053002e-04
## TSS TSN TYC USB UNP
## 4.914771e-04 -4.942492e-05 -7.618297e-04 7.157696e-04 1.346411e-04
## UNH UPS X UTX UNM
## 1.814545e-04 1.053562e-03 -9.644693e-04 9.723152e-04 1.059740e-03
## URBN VFC VLO VAR VTR
## 3.735884e-04 -3.693484e-04 6.455580e-04 9.195541e-04 4.633680e-04
## VRSN VZ VIAB V VNO
## -1.197605e-04 5.024612e-04 2.975724e-04 5.383766e-04 5.757358e-04
## VMC WMT WAG DIS WM
## -1.991789e-03 2.641982e-04 -1.519736e-04 1.124950e-03 5.208963e-05
## WAT WLP WFC WDC WU
## 1.019392e-03 6.201881e-04 3.037750e-04 -8.551960e-05 5.488627e-04
## WY WHR WFM WMB WIN
## 1.580056e-04 -4.736885e-04 -1.526429e-03 -1.572810e-03 8.166013e-04
## WEC WYN WYNN XEL XRX
## 5.443529e-04 1.423680e-03 8.746912e-04 7.316964e-04 4.110637e-04
## XLNX XL YHOO YUM ZMH
## -3.598142e-04 1.695696e-04 -3.305579e-04 1.038662e-03 -1.818347e-04
## ZION
## 6.285299e-04- Create a plot to show weights of the 1st principal component grouped by the industry sector (for example, you may draw a bar plot of mean weight per sector). Observe the distribution of weights (magnitudes, signs). Based on your observation, what kind of information do you think the 1st principal component might have captured?
library(knitr)
library(ggplot2)
p1 <- import.csv('C:/Users/pdiazq/Desktop/TareaAI/p1.csv')
df <- data.frame(p1, qty=p1[, 2], category=p1[ ,3])
ggplot(df, aes(x=category, y=qty)) + geom_bar(stat="identity")+ coord_flip()
The plot below, shows the main industries that contribute to the PCA principal component one.Stocks related with “Materials”" and “Information technologies”, were the most important for the numbers of the marked of stocks. As concluded in the temporal analysis of the Principal Component one, 5 drop events for the market were seen (two of them of bigger magnitude), and two events increasing the market value.
So I can conclude that the main reason for the total marked drop seen in those 4 years was because the materials markets, but information technology contributed negatively to this drop.- Make a similar plot for the 2nd principal component. What kind of information do you think does this component reveal? (Hint: look at the signs and magnitudes.
library(knitr)
p2 <- import.csv('C:/Users/pdiazq/Desktop/TareaAI/p2.csv')
df2 <- data.frame(p2, qty=p2[, 2], category=p2[ ,3])
ggplot(df2, aes(x=category, y=qty)) + geom_bar(stat="identity")+ coord_flip()
The plot below, shows again the main contribution of Materials and Information Technology stocks, but almost inverted (according to the PC(one)). In fact, the temporal plot shows some other aditional information, compared with the aported by Component one. 3 main bigger drops and 4 increases in the market.
Suppose we wanted to construct a new stock index using one principal component to track the overall market tendencies. Which of the two components would you prefer to use for this purpose, the 1st or the 2nd? Why?
Two components could be complementary. Some information is a little similar but some other are a little different.
Component one shows: More pronuncied drop, due to Materials and inhibited in a little proportion by information technology
Component two shows: Not so pronuncied drop, due to information technology and inhibited in a big proportion by materials
So in both cases, can be say that materiasl has a big impact in “drops”, and information technology has a not so notorious impact on “increasing”
The PC1 shows this conclussion and I would choose this component, because has more weight.