Load the dataset
library(readxl)
data = read_excel("data.xls")## New names:
## • `` -> `...1`head(data)## # A tibble: 6 × 36
## ...1 `Mkt-RF` SMB HML RF Mom Food Beer Smoke Games Books Hshld
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 192701 -0.1 -0.09 4.72 0.25 0.36 -0.7 0.57 -0.33 2.46 9.67 4.07
## 2 192702 4.32 0.31 3.4 0.26 -1.67 4.29 12.8 1.58 1.43 1.41 4.59
## 3 192703 0.33 -1.77 -2.42 0.3 2.97 1.98 -13.6 5.55 0.57 -0.28 -0.08
## 4 192704 0.42 0.3 1.03 0.25 4.53 2.6 2.85 4.09 -3.34 -0.96 1.44
## 5 192705 5.36 0.67 3.41 0.3 3.41 6.14 11.6 11.9 -0.5 3.13 10.6
## 6 192706 -2.27 0.81 -2.15 0.26 0.61 -2.17 10.0 -2.24 -7.05 12.5 -3.01
## # … with 24 more variables: Clths <dbl>, Hlth <dbl>, Chems <dbl>, Txtls <dbl>,
## # Cnstr <dbl>, Steel <dbl>, FabPr <dbl>, ElcEq <dbl>, Autos <dbl>,
## # Carry <dbl>, Mines <dbl>, Coal <dbl>, Oil <dbl>, Util <dbl>, Telcm <dbl>,
## # Servs <dbl>, BusEq <dbl>, Paper <dbl>, Trans <dbl>, Whlsl <dbl>,
## # Rtail <dbl>, Meals <dbl>, Fin <dbl>, Other <dbl>
## # ℹ Use `colnames()` to see all variable namesThe correlation matrix
cor(data[,2:ncol(data)])## Mkt-RF SMB HML RF Mom Food
## Mkt-RF 1.00000000 0.32686335 0.21614469 -0.068722941 -0.33834328 0.83592422
## SMB 0.32686335 1.00000000 0.09411303 -0.059640367 -0.16402317 0.20169790
## HML 0.21614469 0.09411303 1.00000000 0.012114673 -0.40063482 0.21513165
## RF -0.06872294 -0.05964037 0.01211467 1.000000000 0.03912996 0.03222174
## Mom -0.33834328 -0.16402317 -0.40063482 0.039129956 1.00000000 -0.28028936
## Food 0.83592422 0.20169790 0.21513165 0.032221736 -0.28028936 1.00000000
## Beer 0.70767336 0.35103932 0.21498192 -0.011276559 -0.20007656 0.70515359
## Smoke 0.58426803 0.10315355 0.17180885 0.063036113 -0.21916506 0.67055456
## Games 0.83021128 0.41208941 0.25038691 -0.024963142 -0.35699216 0.71904851
## Books 0.83009246 0.40814455 0.25060795 0.009172456 -0.30639893 0.75665581
## Hshld 0.81623422 0.26188343 0.10737331 -0.024208938 -0.19968339 0.78807393
## Clths 0.78063036 0.46013387 0.24671913 -0.020186056 -0.36048249 0.71474998
## Hlth 0.80402194 0.20889603 0.06439342 0.007783335 -0.22577808 0.78446018
## Chems 0.88388934 0.20801221 0.19239222 -0.033856378 -0.30120313 0.74908657
## Txtls 0.82343838 0.49535590 0.34747553 -0.035738490 -0.37113663 0.71960498
## Cnstr 0.91360806 0.40146434 0.24721250 -0.031264016 -0.32322121 0.79630393
## Steel 0.86790893 0.36312043 0.34372291 -0.048751452 -0.39445945 0.65551951
## FabPr 0.92504629 0.40678778 0.26026374 -0.056681978 -0.37235187 0.73821276
## ElcEq 0.90410279 0.25744191 0.20240735 -0.014687595 -0.32462293 0.76099112
## Autos 0.84329650 0.28597087 0.30282599 -0.059863564 -0.38930805 0.68184561
## Carry 0.83236962 0.36262058 0.33740739 -0.033649591 -0.34381384 0.70765228
## Mines 0.70615952 0.34388908 0.24574079 -0.052209760 -0.27121362 0.55415894
## Coal 0.49054241 0.26731145 0.17224087 -0.029589322 -0.13708750 0.37655415
## Oil 0.77259660 0.13773041 0.30233994 -0.023955542 -0.24988261 0.62040936
## Util 0.76176723 0.17514888 0.35472913 0.026695797 -0.33166523 0.71401094
## Telcm 0.75523451 0.16055436 0.09907925 0.034355426 -0.29387445 0.65182288
## Servs 0.49560643 0.28507952 -0.08493496 -0.011450729 -0.09246626 0.40255135
## BusEq 0.84264384 0.32980898 -0.06627832 -0.051595897 -0.22839384 0.62984969
## Paper 0.86909852 0.27565261 0.19733576 -0.024349325 -0.30017387 0.75987854
## Trans 0.85868843 0.34809912 0.43045631 -0.017854810 -0.42315325 0.71895937
## Whlsl 0.79601244 0.45982639 0.20915417 -0.012878976 -0.26037921 0.70285436
## Rtail 0.85874721 0.30293110 0.11499749 -0.009124598 -0.30938833 0.81251360
## Meals 0.75385946 0.36863655 0.16355650 -0.022961691 -0.25081267 0.71643584
## Fin 0.91588379 0.28258562 0.32456573 -0.011648078 -0.42042061 0.82209512
## Other 0.84200773 0.42390835 0.16509945 -0.035673679 -0.29032146 0.72938075
## Beer Smoke Games Books Hshld Clths
## Mkt-RF 0.70767336 0.58426803 0.83021128 0.830092455 0.81623422 0.78063036
## SMB 0.35103932 0.10315355 0.41208941 0.408144550 0.26188343 0.46013387
## HML 0.21498192 0.17180885 0.25038691 0.250607946 0.10737331 0.24671913
## RF -0.01127656 0.06303611 -0.02496314 0.009172456 -0.02420894 -0.02018606
## Mom -0.20007656 -0.21916506 -0.35699216 -0.306398926 -0.19968339 -0.36048249
## Food 0.70515359 0.67055456 0.71904851 0.756655806 0.78807393 0.71474998
## Beer 1.00000000 0.44860609 0.67727781 0.622057959 0.66095269 0.61218133
## Smoke 0.44860609 1.00000000 0.50630367 0.502044734 0.54347455 0.49364824
## Games 0.67727781 0.50630367 1.00000000 0.738285969 0.69132415 0.72333778
## Books 0.62205796 0.50204473 0.73828597 1.000000000 0.72553908 0.73102983
## Hshld 0.66095269 0.54347455 0.69132415 0.725539082 1.00000000 0.66909220
## Clths 0.61218133 0.49364824 0.72333778 0.731029831 0.66909220 1.00000000
## Hlth 0.64427440 0.57247715 0.69206289 0.677021491 0.73765200 0.63121498
## Chems 0.63994690 0.51716728 0.71683403 0.714475356 0.75068426 0.70171970
## Txtls 0.68398589 0.47700828 0.76403454 0.773225768 0.70512316 0.78875213
## Cnstr 0.71893835 0.56327951 0.80001122 0.808510685 0.77538241 0.78943077
## Steel 0.56891137 0.46935383 0.72574219 0.720150159 0.65536351 0.68616988
## FabPr 0.65342983 0.50795374 0.78301996 0.791080185 0.74535429 0.75083999
## ElcEq 0.63418948 0.52145445 0.76837169 0.755586953 0.75059313 0.69442244
## Autos 0.59136323 0.48925775 0.71943085 0.739471768 0.71388828 0.70580281
## Carry 0.63089756 0.49221848 0.72249837 0.733203961 0.69321280 0.72168732
## Mines 0.50553332 0.40754124 0.60964106 0.577836917 0.53453312 0.55527197
## Coal 0.35783091 0.27882853 0.39243169 0.396142320 0.32823174 0.41387746
## Oil 0.52113189 0.43718027 0.58190813 0.592946776 0.56683028 0.56149693
## Util 0.58096492 0.51469514 0.63547799 0.649959013 0.62651432 0.57172567
## Telcm 0.51066270 0.45198415 0.61831516 0.608323432 0.59413654 0.54907260
## Servs 0.34656492 0.28774669 0.41290867 0.476255772 0.40127690 0.40821360
## BusEq 0.54277040 0.44146716 0.71710350 0.656845948 0.68310421 0.63303483
## Paper 0.63356402 0.54496988 0.70782357 0.750610881 0.77145914 0.72395399
## Trans 0.62030644 0.49431195 0.75231004 0.774771677 0.66938389 0.74276102
## Whlsl 0.68861154 0.50216225 0.75352395 0.735664127 0.69736132 0.70968270
## Rtail 0.65618599 0.54032069 0.75914043 0.781260178 0.76110676 0.78965639
## Meals 0.62451097 0.48869412 0.72822413 0.708684243 0.67288691 0.69505125
## Fin 0.69049582 0.56698326 0.80552454 0.784830181 0.75096123 0.74952051
## Other 0.63716078 0.53924123 0.77447803 0.741933071 0.73528570 0.72864376
## Hlth Chems Txtls Cnstr Steel FabPr
## Mkt-RF 0.804021938 0.88388934 0.82343838 0.91360806 0.86790893 0.92504629
## SMB 0.208896031 0.20801221 0.49535590 0.40146434 0.36312043 0.40678778
## HML 0.064393417 0.19239222 0.34747553 0.24721250 0.34372291 0.26026374
## RF 0.007783335 -0.03385638 -0.03573849 -0.03126402 -0.04875145 -0.05668198
## Mom -0.225778083 -0.30120313 -0.37113663 -0.32322121 -0.39445945 -0.37235187
## Food 0.784460185 0.74908657 0.71960498 0.79630393 0.65551951 0.73821276
## Beer 0.644274398 0.63994690 0.68398589 0.71893835 0.56891137 0.65342983
## Smoke 0.572477147 0.51716728 0.47700828 0.56327951 0.46935383 0.50795374
## Games 0.692062890 0.71683403 0.76403454 0.80001122 0.72574219 0.78301996
## Books 0.677021491 0.71447536 0.77322577 0.80851069 0.72015016 0.79108018
## Hshld 0.737652000 0.75068426 0.70512316 0.77538241 0.65536351 0.74535429
## Clths 0.631214975 0.70171970 0.78875213 0.78943077 0.68616988 0.75083999
## Hlth 1.000000000 0.70919601 0.63533221 0.71781439 0.61202004 0.69652013
## Chems 0.709196014 1.00000000 0.75582386 0.83964412 0.80256743 0.85302373
## Txtls 0.635332207 0.75582386 1.00000000 0.83639607 0.75771681 0.81597100
## Cnstr 0.717814393 0.83964412 0.83639607 1.00000000 0.80875379 0.88359640
## Steel 0.612020042 0.80256743 0.75771681 0.80875379 1.00000000 0.88297280
## FabPr 0.696520129 0.85302373 0.81597100 0.88359640 0.88297280 1.00000000
## ElcEq 0.731364754 0.82742785 0.74483945 0.84699278 0.80173303 0.85877959
## Autos 0.626261614 0.79642764 0.78253984 0.80252373 0.78377750 0.81744003
## Carry 0.649629475 0.74927509 0.74921477 0.80785818 0.77759712 0.83187807
## Mines 0.518686426 0.66679550 0.61966087 0.68256376 0.73347342 0.70605096
## Coal 0.359489347 0.43330629 0.41915471 0.47823968 0.47158144 0.51037682
## Oil 0.573067913 0.69197357 0.60244740 0.69189849 0.67883324 0.71470054
## Util 0.627146500 0.66173577 0.63932872 0.70158740 0.59095043 0.66026727
## Telcm 0.604774688 0.64800811 0.57488549 0.64563796 0.59035074 0.63924704
## Servs 0.400630047 0.38155559 0.37211412 0.45825128 0.37546106 0.45250165
## BusEq 0.683919538 0.71974680 0.64357917 0.74832231 0.73253607 0.79374677
## Paper 0.726007530 0.86269476 0.74942249 0.82358926 0.78640851 0.83730814
## Trans 0.657308494 0.77101574 0.78805186 0.82376083 0.80326514 0.84514090
## Whlsl 0.666021970 0.69414760 0.76003742 0.80326240 0.68426741 0.75424745
## Rtail 0.722086801 0.75750414 0.77649328 0.81636327 0.69134771 0.77414696
## Meals 0.646285438 0.65947623 0.69365272 0.75266269 0.60404557 0.70431941
## Fin 0.759323086 0.80297968 0.77965065 0.86287401 0.76334768 0.83269741
## Other 0.691306114 0.76354945 0.76893007 0.82217976 0.73252812 0.79097877
## ElcEq Autos Carry Mines Coal Oil
## Mkt-RF 0.90410279 0.84329650 0.83236962 0.70615952 0.49054241 0.77259660
## SMB 0.25744191 0.28597087 0.36262058 0.34388908 0.26731145 0.13773041
## HML 0.20240735 0.30282599 0.33740739 0.24574079 0.17224087 0.30233994
## RF -0.01468759 -0.05986356 -0.03364959 -0.05220976 -0.02958932 -0.02395554
## Mom -0.32462293 -0.38930805 -0.34381384 -0.27121362 -0.13708750 -0.24988261
## Food 0.76099112 0.68184561 0.70765228 0.55415894 0.37655415 0.62040936
## Beer 0.63418948 0.59136323 0.63089756 0.50553332 0.35783091 0.52113189
## Smoke 0.52145445 0.48925775 0.49221848 0.40754124 0.27882853 0.43718027
## Games 0.76837169 0.71943085 0.72249837 0.60964106 0.39243169 0.58190813
## Books 0.75558695 0.73947177 0.73320396 0.57783692 0.39614232 0.59294678
## Hshld 0.75059313 0.71388828 0.69321280 0.53453312 0.32823174 0.56683028
## Clths 0.69442244 0.70580281 0.72168732 0.55527197 0.41387746 0.56149693
## Hlth 0.73136475 0.62626161 0.64962947 0.51868643 0.35948935 0.57306791
## Chems 0.82742785 0.79642764 0.74927509 0.66679550 0.43330629 0.69197357
## Txtls 0.74483945 0.78253984 0.74921477 0.61966087 0.41915471 0.60244740
## Cnstr 0.84699278 0.80252373 0.80785818 0.68256376 0.47823968 0.69189849
## Steel 0.80173303 0.78377750 0.77759712 0.73347342 0.47158144 0.67883324
## FabPr 0.85877959 0.81744003 0.83187807 0.70605096 0.51037682 0.71470054
## ElcEq 1.00000000 0.78809099 0.78650216 0.63458029 0.40850746 0.64178857
## Autos 0.78809099 1.00000000 0.73158011 0.59251094 0.34687468 0.60515523
## Carry 0.78650216 0.73158011 1.00000000 0.61808637 0.47145668 0.65231037
## Mines 0.63458029 0.59251094 0.61808637 1.00000000 0.43604331 0.63854319
## Coal 0.40850746 0.34687468 0.47145668 0.43604331 1.00000000 0.47870029
## Oil 0.64178857 0.60515523 0.65231037 0.63854319 0.47870029 1.00000000
## Util 0.69884012 0.62539443 0.62953296 0.51935790 0.36407984 0.61763836
## Telcm 0.65360585 0.60425280 0.56062890 0.46451602 0.30450574 0.49800529
## Servs 0.40602523 0.35650971 0.39029962 0.32315951 0.28693125 0.34667304
## BusEq 0.77226091 0.68379532 0.65911050 0.55389980 0.38080146 0.55533579
## Paper 0.80195098 0.77237691 0.74304097 0.63801945 0.44229476 0.65732247
## Trans 0.79171297 0.74009187 0.82288985 0.63928719 0.50531229 0.63486291
## Whlsl 0.70697163 0.68523259 0.70189728 0.59027111 0.41161130 0.57606482
## Rtail 0.78576165 0.76702880 0.70470690 0.55526089 0.35018206 0.56267358
## Meals 0.69028807 0.63187893 0.68026912 0.53835528 0.38914931 0.52316771
## Fin 0.84251401 0.77569539 0.78157868 0.63762108 0.42523558 0.68657337
## Other 0.76553162 0.73073483 0.74291302 0.62855032 0.39877625 0.62430910
## Util Telcm Servs BusEq Paper Trans
## Mkt-RF 0.7617672 0.75523451 0.49560643 0.84264384 0.86909852 0.85868843
## SMB 0.1751489 0.16055436 0.28507952 0.32980898 0.27565261 0.34809912
## HML 0.3547291 0.09907925 -0.08493496 -0.06627832 0.19733576 0.43045631
## RF 0.0266958 0.03435543 -0.01145073 -0.05159590 -0.02434933 -0.01785481
## Mom -0.3316652 -0.29387445 -0.09246626 -0.22839384 -0.30017387 -0.42315325
## Food 0.7140109 0.65182288 0.40255135 0.62984969 0.75987854 0.71895937
## Beer 0.5809649 0.51066270 0.34656492 0.54277040 0.63356402 0.62030644
## Smoke 0.5146951 0.45198415 0.28774669 0.44146716 0.54496988 0.49431195
## Games 0.6354780 0.61831516 0.41290867 0.71710350 0.70782357 0.75231004
## Books 0.6499590 0.60832343 0.47625577 0.65684595 0.75061088 0.77477168
## Hshld 0.6265143 0.59413654 0.40127690 0.68310421 0.77145914 0.66938389
## Clths 0.5717257 0.54907260 0.40821360 0.63303483 0.72395399 0.74276102
## Hlth 0.6271465 0.60477469 0.40063005 0.68391954 0.72600753 0.65730849
## Chems 0.6617358 0.64800811 0.38155559 0.71974680 0.86269476 0.77101574
## Txtls 0.6393287 0.57488549 0.37211412 0.64357917 0.74942249 0.78805186
## Cnstr 0.7015874 0.64563796 0.45825128 0.74832231 0.82358926 0.82376083
## Steel 0.5909504 0.59035074 0.37546106 0.73253607 0.78640851 0.80326514
## FabPr 0.6602673 0.63924704 0.45250165 0.79374677 0.83730814 0.84514090
## ElcEq 0.6988401 0.65360585 0.40602523 0.77226091 0.80195098 0.79171297
## Autos 0.6253944 0.60425280 0.35650971 0.68379532 0.77237691 0.74009187
## Carry 0.6295330 0.56062890 0.39029962 0.65911050 0.74304097 0.82288985
## Mines 0.5193579 0.46451602 0.32315951 0.55389980 0.63801945 0.63928719
## Coal 0.3640798 0.30450574 0.28693125 0.38080146 0.44229476 0.50531229
## Oil 0.6176384 0.49800529 0.34667304 0.55533579 0.65732247 0.63486291
## Util 1.0000000 0.63631053 0.32469038 0.52585572 0.64296319 0.65726216
## Telcm 0.6363105 1.00000000 0.42870722 0.63915905 0.61536660 0.61830660
## Servs 0.3246904 0.42870722 1.00000000 0.52157310 0.43096418 0.39967868
## BusEq 0.5258557 0.63915905 0.52157310 1.00000000 0.72582894 0.65899003
## Paper 0.6429632 0.61536660 0.43096418 0.72582894 1.00000000 0.76712480
## Trans 0.6572622 0.61830660 0.39967868 0.65899003 0.76712480 1.00000000
## Whlsl 0.6278460 0.57950676 0.41871465 0.64433497 0.70549411 0.72283327
## Rtail 0.6363110 0.66511205 0.44583038 0.72098556 0.75969836 0.73400294
## Meals 0.5837423 0.55961942 0.44412356 0.62155014 0.67514935 0.70259093
## Fin 0.8000227 0.70724056 0.42274992 0.71052793 0.80032340 0.82138360
## Other 0.6338862 0.60766321 0.43150920 0.70533040 0.76394115 0.74445103
## Whlsl Rtail Meals Fin Other
## Mkt-RF 0.79601244 0.858747215 0.75385946 0.91588379 0.84200773
## SMB 0.45982639 0.302931101 0.36863655 0.28258562 0.42390835
## HML 0.20915417 0.114997486 0.16355650 0.32456573 0.16509945
## RF -0.01287898 -0.009124598 -0.02296169 -0.01164808 -0.03567368
## Mom -0.26037921 -0.309388329 -0.25081267 -0.42042061 -0.29032146
## Food 0.70285436 0.812513596 0.71643584 0.82209512 0.72938075
## Beer 0.68861154 0.656185992 0.62451097 0.69049582 0.63716078
## Smoke 0.50216225 0.540320692 0.48869412 0.56698326 0.53924123
## Games 0.75352395 0.759140429 0.72822413 0.80552454 0.77447803
## Books 0.73566413 0.781260178 0.70868424 0.78483018 0.74193307
## Hshld 0.69736132 0.761106757 0.67288691 0.75096123 0.73528570
## Clths 0.70968270 0.789656395 0.69505125 0.74952051 0.72864376
## Hlth 0.66602197 0.722086801 0.64628544 0.75932309 0.69130611
## Chems 0.69414760 0.757504136 0.65947623 0.80297968 0.76354945
## Txtls 0.76003742 0.776493282 0.69365272 0.77965065 0.76893007
## Cnstr 0.80326240 0.816363272 0.75266269 0.86287401 0.82217976
## Steel 0.68426741 0.691347712 0.60404557 0.76334768 0.73252812
## FabPr 0.75424745 0.774146960 0.70431941 0.83269741 0.79097877
## ElcEq 0.70697163 0.785761646 0.69028807 0.84251401 0.76553162
## Autos 0.68523259 0.767028800 0.63187893 0.77569539 0.73073483
## Carry 0.70189728 0.704706903 0.68026912 0.78157868 0.74291302
## Mines 0.59027111 0.555260891 0.53835528 0.63762108 0.62855032
## Coal 0.41161130 0.350182062 0.38914931 0.42523558 0.39877625
## Oil 0.57606482 0.562673584 0.52316771 0.68657337 0.62430910
## Util 0.62784598 0.636311031 0.58374228 0.80002269 0.63388615
## Telcm 0.57950676 0.665112051 0.55961942 0.70724056 0.60766321
## Servs 0.41871465 0.445830384 0.44412356 0.42274992 0.43150920
## BusEq 0.64433497 0.720985560 0.62155014 0.71052793 0.70533040
## Paper 0.70549411 0.759698360 0.67514935 0.80032340 0.76394115
## Trans 0.72283327 0.734002938 0.70259093 0.82138360 0.74445103
## Whlsl 1.00000000 0.739322250 0.68089867 0.75908905 0.73670429
## Rtail 0.73932225 1.000000000 0.75147373 0.81331857 0.74895717
## Meals 0.68089867 0.751473727 1.00000000 0.72550680 0.67997143
## Fin 0.75908905 0.813318574 0.72550680 1.00000000 0.79780235
## Other 0.73670429 0.748957171 0.67997143 0.79780235 1.00000000industry = names(data)[7:ncol(data)]
factors=c("Mkt-RF","SMB","HML","Mom")
highly = rep(NA,30)
negatively = rep(NA,30)
for ( i in 1:30){
highly = which.max(cor(data[,c(2,3,4,6)],data[industry[i]]))
negatively = which.min(cor(data[,c(2,3,4,6)],data[industry[i]]))
}
data.frame(industry,Highly = factors[highly],Negatively = factors[negatively])## industry Highly Negatively
## 1 Food Mkt-RF Mom
## 2 Beer Mkt-RF Mom
## 3 Smoke Mkt-RF Mom
## 4 Games Mkt-RF Mom
## 5 Books Mkt-RF Mom
## 6 Hshld Mkt-RF Mom
## 7 Clths Mkt-RF Mom
## 8 Hlth Mkt-RF Mom
## 9 Chems Mkt-RF Mom
## 10 Txtls Mkt-RF Mom
## 11 Cnstr Mkt-RF Mom
## 12 Steel Mkt-RF Mom
## 13 FabPr Mkt-RF Mom
## 14 ElcEq Mkt-RF Mom
## 15 Autos Mkt-RF Mom
## 16 Carry Mkt-RF Mom
## 17 Mines Mkt-RF Mom
## 18 Coal Mkt-RF Mom
## 19 Oil Mkt-RF Mom
## 20 Util Mkt-RF Mom
## 21 Telcm Mkt-RF Mom
## 22 Servs Mkt-RF Mom
## 23 BusEq Mkt-RF Mom
## 24 Paper Mkt-RF Mom
## 25 Trans Mkt-RF Mom
## 26 Whlsl Mkt-RF Mom
## 27 Rtail Mkt-RF Mom
## 28 Meals Mkt-RF Mom
## 29 Fin Mkt-RF Mom
## 30 Other Mkt-RF Momcor(data["RF"],data[,7:36])## Food Beer Smoke Games Books Hshld
## RF 0.03222174 -0.01127656 0.06303611 -0.02496314 0.009172456 -0.02420894
## Clths Hlth Chems Txtls Cnstr Steel
## RF -0.02018606 0.007783335 -0.03385638 -0.03573849 -0.03126402 -0.04875145
## FabPr ElcEq Autos Carry Mines Coal
## RF -0.05668198 -0.01468759 -0.05986356 -0.03364959 -0.05220976 -0.02958932
## Oil Util Telcm Servs BusEq Paper
## RF -0.02395554 0.0266958 0.03435543 -0.01145073 -0.0515959 -0.02434933
## Trans Whlsl Rtail Meals Fin Other
## RF -0.01785481 -0.01287898 -0.009124598 -0.02296169 -0.01164808 -0.03567368RF does not correlate highly with the 30 industry time series.
par(mfrow=c(2,2))
acf(data["Mkt-RF"],lag.max=10,main="Mkt-RF")
acf(data["SMB"],lag.max=10,main="SMB")
acf(data["HML"],lag.max=10,main="HML")
acf(data["Mom"],lag.max=10,main="Mom")
There is no AR(1) model in the four-factor time series. For SMB and Mom, the first order acf is not significant, thus it cannot be AR(1) model. For Mkt-RF, the acf is significant for lag 1 and lag 3. For HML, the acf is significant for lag 1,4 and 9. Thus, they cannot be AR(1) time series since for AR(1) time series, the acf decays to zero.