Critical Values: Constant Model
"Freq = 1," "p = 1,..,5"
Trace Lambda
1 11.96591 14.3084 19.15244 11.96591 14.3084 19.15244
2 25.33234 28.18929 34.17934 19.42429 21.81952 26.89734
3 42.40214 46.02544 52.73163 25.99134 28.35264 34.30575
4 63.57798 67.68133 75.99406 32.29822 34.91794 41.03214
5 89.19402 93.91098 103.47587 38.51377 41.17167 46.46918
"Freq = 2," "p = 1,..,5"
Trace Lambda
1 8.47652 10.51359 15.78948 8.47652 10.51359 15.78948
2 19.73502 22.6004 28.52882 16.55501 19.05594 24.48584
3 35.74732 38.91366 45.51562 23.88019 26.30747 31.44069
4 56.6758 60.67533 69.05906 30.8011 33.44158 38.89055
5 82.08287 86.50896 96.38501 37.55359 40.27457 45.93851
"Freq = 3," "p = 1,..,5"
Trace Lambda
1 7.39836 9.4069 14.35656 7.39836 9.4069 14.35656
2 17.99192 20.71316 26.12183 15.0723 17.35662 22.5481
3 32.90922 35.77095 42.92628 22.08337 24.69282 29.99618
4 52.48284 56.38972 64.27689 29.33437 32.11669 37.83719
5 76.70433 81.37919 90.2707 36.22397 38.74516 45.1397
"Freq = 4," "p = 1,..,5"
Trace Lambda
1 7.05204 8.85902 13.35081 7.05204 8.85902 13.35081
2 17.1943 19.7394 25.06085 14.19221 16.54828 21.3657
3 31.45236 34.62302 41.07153 21.32647 23.96644 28.6611
4 50.0063 53.82681 61.7989 28.27393 30.86204 36.18487
5 73.81947 78.36771 87.3374 35.21214 37.83603 43.96069
"Freq = 5," "p = 1,..,5"
Trace Lambda
1 6.84752 8.62743 12.70534 6.84752 8.62743 12.70534
2 16.85144 19.13382 24.05343 13.84803 16.0725 20.56514
3 30.56817 33.68254 39.81796 20.5407 22.72801 27.82667
4 48.91592 52.29388 60.05373 27.21844 30.08076 35.71887
5 72.02403 76.0114 84.72916 34.04224 36.78717 42.63075
Freq = maxq "p = 1,..,5"
Trace Lambda
1 12.77571 15.07919 19.87438 12.77571 15.07919 19.87438
2 26.10865 28.85249 34.72286 20.63956 22.98041 28.09212
3 43.32021 46.78274 53.19109 27.42833 29.74012 35.53437
4 64.83038 68.89566 76.91632 34.05011 36.71878 42.16141
5 90.67428 95.51971 104.39743 40.20088 42.85702 49.16653
********************************************************
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More Detailed Results
**********************
Model with a constant (freq = 1,..,5)
********* p = 1
j = 1
90% 95% 99%
Trace(1) 11.96591 14.30840 19.15244
Lambda(1) 11.96591 14.30840 19.15244
j = 2
90% 95% 99%
Trace(1) 8.47652 10.51359 15.78948
Lambda(1) 8.47652 10.51359 15.78948
j = 3
90% 95% 99%
Trace(1) 7.39836 9.40690 14.35656
Lambda(1) 7.39836 9.40690 14.35656
j = 4
90% 95% 99%
Trace(1) 7.05204 8.85902 13.35081
Lambda(1) 7.05204 8.85902 13.35081
j = 5
90% 95% 99%
Trace(1) 6.84752 8.62743 12.70534
Lambda(1) 6.84752 8.62743 12.70534
********* p = 2
j = 1
90% 95% 99%
Trace(1) 25.33234 28.18929 34.17934
Trace(2) 7.89702 9.29868 11.92837
Lambda(1) 19.42429 21.81952 26.89734
Lambda(2) 7.89702 9.29868 11.92837
j = 2
90% 95% 99%
Trace(1) 19.73502 22.60040 28.52882
Trace(2) 4.97313 6.19880 8.39221
Lambda(1) 16.55501 19.05594 24.48584
Lambda(2) 4.97313 6.19880 8.39221
j = 3
90% 95% 99%
Trace(1) 17.99192 20.71316 26.12183
Trace(2) 4.41453 5.52720 7.86186
Lambda(1) 15.07230 17.35662 22.54810
Lambda(2) 4.41453 5.52720 7.86186
j = 4
90% 95% 99%
Trace(1) 17.19430 19.73940 25.06085
Trace(2) 4.30858 5.32809 7.68586
Lambda(1) 14.19221 16.54828 21.36570
Lambda(2) 4.30858 5.32809 7.68586
j = 5
90% 95% 99%
Trace(1) 16.85144 19.13382 24.05343
Trace(2) 4.30176 5.24694 7.46333
Lambda(1) 13.84803 16.07250 20.56514
Lambda(2) 4.30176 5.24694 7.46333
********* p = 3
j = 1
90% 95% 99%
Trace(1) 42.40214 46.02544 52.73163
Trace(2) 18.96166 20.94914 24.99704
Trace(3) 6.28931 7.40923 9.31540
Lambda(1) 25.99134 28.35264 34.30575
Lambda(2) 14.33902 15.75862 18.66279
Lambda(3) 6.28931 7.40923 9.31540
j = 2
90% 95% 99%
Trace(1) 35.74732 38.91366 45.51562
Trace(2) 14.47733 15.96647 19.46014
Trace(3) 3.95975 4.82926 6.72718
Lambda(1) 23.88019 26.30747 31.44069
Lambda(2) 11.69256 13.06404 16.60917
Lambda(3) 3.95975 4.82926 6.72718
j = 3
90% 95% 99%
Trace(1) 32.90922 35.77095 42.92628
Trace(2) 13.02909 14.56254 18.11652
Trace(3) 3.56033 4.44878 6.28796
Lambda(1) 22.08337 24.69282 29.99618
Lambda(2) 10.44246 12.08189 14.67532
Lambda(3) 3.56033 4.44878 6.28796
j = 4
90% 95% 99%
Trace(1) 31.45236 34.62302 41.07153
Trace(2) 12.40724 14.00364 17.25796
Trace(3) 3.52883 4.32814 5.88210
Lambda(1) 21.32647 23.96644 28.66110
Lambda(2) 9.91208 11.28648 14.28303
Lambda(3) 3.52883 4.32814 5.88210
j = 5
90% 95% 99%
Trace(1) 30.56817 33.68254 39.81796
Trace(2) 12.04971 13.68674 16.90924
Trace(3) 3.45948 4.29019 5.80936
Lambda(1) 20.54070 22.72801 27.82667
Lambda(2) 9.62523 10.93939 13.74196
Lambda(3) 3.45948 4.29019 5.80936
********* p = 4
j = 1
90% 95% 99%
Trace(1) 63.57798 67.68133 75.99406
Trace(2) 34.22949 37.02255 42.55213
Trace(3) 16.08344 17.89801 21.40622
Trace(4) 5.40069 6.33783 8.28080
Lambda(1) 32.29822 34.91794 41.03214
Lambda(2) 19.97983 21.79634 25.03900
Lambda(3) 12.31304 13.52742 15.75077
Lambda(4) 5.40069 6.33783 8.28080
j = 2
90% 95% 99%
Trace(1) 56.67580 60.67533 69.05906
Trace(2) 28.86949 31.31471 35.90081
Trace(3) 12.32858 13.73554 16.32256
Trace(4) 3.50884 4.30542 5.81373
Lambda(1) 30.80110 33.44158 38.89055
Lambda(2) 18.37676 20.16309 23.04586
Lambda(3) 9.94751 11.07823 13.53806
Lambda(4) 3.50884 4.30542 5.81373
j = 3
90% 95% 99%
Trace(1) 52.48284 56.38972 64.27689
Trace(2) 26.03200 28.28410 32.49568
Trace(3) 11.06815 12.61330 15.14738
Trace(4) 3.21873 3.96840 5.41957
Lambda(1) 29.33437 32.11669 37.83719
Lambda(2) 16.48961 18.08997 21.59147
Lambda(3) 8.84319 10.01850 12.18163
Lambda(4) 3.21873 3.96840 5.41957
j = 4
90% 95% 99%
Trace(1) 50.00630 53.82681 61.79890
Trace(2) 24.85037 26.95208 31.47405
Trace(3) 10.49420 12.10349 14.64934
Trace(4) 3.10010 3.91230 5.40182
Lambda(1) 28.27393 30.86204 36.18487
Lambda(2) 15.77372 17.28738 20.52342
Lambda(3) 8.39038 9.40549 11.57693
Lambda(4) 3.10010 3.91230 5.40182
j = 5
90% 95% 99%
Trace(1) 48.91592 52.29388 60.05373
Trace(2) 24.20390 26.18796 30.54559
Trace(3) 10.41480 11.76416 14.09707
Trace(4) 3.08522 3.84325 5.26179
Lambda(1) 27.21844 30.08076 35.71887
Lambda(2) 15.28160 16.72424 19.91154
Lambda(3) 8.20123 9.17347 11.20775
Lambda(4) 3.08522 3.84325 5.26179
********* p = 5
j = 1
90% 95% 99%
Trace(1) 89.19402 93.91098 103.47587
Trace(2) 54.07660 57.39069 63.47652
Trace(3) 30.67938 32.76653 37.00973
Trace(4) 14.65796 16.22976 19.36038
Trace(5) 4.89992 5.85689 7.52670
Lambda(1) 38.51377 41.17167 46.46918
Lambda(2) 25.57399 27.28758 30.79950
Lambda(3) 17.54819 18.79134 21.36937
Lambda(4) 11.18224 12.14258 14.22616
Lambda(5) 4.89992 5.85689 7.52670
j = 2
90% 95% 99%
Trace(1) 82.08287 86.50896 96.38501
Trace(2) 48.04066 51.17546 57.05505
Trace(3) 25.81922 28.05658 31.98275
Trace(4) 11.47892 12.75390 15.46984
Trace(5) 3.39303 4.06750 5.55145
Lambda(1) 37.55359 40.27457 45.93851
Lambda(2) 24.14084 25.91284 29.56156
Lambda(3) 15.93062 17.31233 20.15372
Lambda(4) 9.17769 10.22576 12.06996
Lambda(5) 3.39303 4.06750 5.55145
j = 3
90% 95% 99%
Trace(1) 76.70433 81.37919 90.27070
Trace(2) 43.93785 46.84494 52.48392
Trace(3) 23.12170 25.16100 28.86354
Trace(4) 10.19413 11.44545 13.95099
Trace(5) 3.08445 3.73608 5.07631
Lambda(1) 36.22397 38.74516 45.13970
Lambda(2) 22.95494 24.89768 28.54985
Lambda(3) 14.33296 15.46239 17.91001
Lambda(4) 8.14844 8.99867 10.85386
Lambda(5) 3.08445 3.73608 5.07631
j = 4
90% 95% 99%
Trace(1) 73.81947 78.36771 87.33740
Trace(2) 41.80520 44.85101 50.82031
Trace(3) 22.09254 23.91400 28.11003
Trace(4) 9.77741 10.85360 13.52222
Trace(5) 2.98290 3.67870 4.97313
Lambda(1) 35.21214 37.83603 43.96069
Lambda(2) 21.83638 23.57035 27.53302
Lambda(3) 13.65091 14.75693 17.32471
Lambda(4) 7.77173 8.59398 10.43574
Lambda(5) 2.98290 3.67870 4.97313
j = 5
90% 95% 99%
Trace(1) 72.02403 76.01140 84.72916
Trace(2) 40.91723 43.78951 48.84831
Trace(3) 21.59599 23.42291 27.13541
Trace(4) 9.65371 10.79928 12.95742
Trace(5) 2.92457 3.58838 4.87616
Lambda(1) 34.04224 36.78717 42.63075
Lambda(2) 21.18641 22.90571 26.22821
Lambda(3) 13.16240 14.46864 16.82729
Lambda(4) 7.68743 8.48240 9.98522
Lambda(5) 2.92457 3.58838 4.87616