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Model with a trend
***********************************
90% 95% 99%
*** Freq = 1, p = 1,..,5
1 Trace(1) 15.92629 18.09039 23.13090
2 Trace(1) 32.60420 35.55617 42.05774
3 Trace(1) 52.73863 56.49866 64.29932
4 Trace(1) 76.92394 81.12916 89.62183
5 Trace(1) 104.98884 109.17405 118.98810
1 Lambda(1) 15.92629 18.09039 23.13090
2 Lambda(1) 22.97027 25.46954 30.92691
3 Lambda(1) 29.50385 32.22024 37.47534
4 Lambda(1) 35.86276 38.25462 43.75503
5 Lambda(1) 41.85272 44.55845 50.41063
*** Freq = 2, p = 1,..,5
1 Trace(1) 13.42129 15.86571 20.85068
2 Trace(1) 28.08645 31.17837 38.31604
3 Trace(1) 46.94701 50.74269 58.20886
4 Trace(1) 69.96733 74.78432 83.11733
5 Trace(1) 97.46749 102.38793 112.22756
1 Lambda(1) 13.42129 15.86571 20.85068
2 Lambda(1) 21.38229 24.05796 28.93712
3 Lambda(1) 27.94128 30.45904 36.13643
4 Lambda(1) 34.77303 37.58944 43.42374
5 Lambda(1) 41.26979 43.98831 49.73163
*** Freq = 3, p = 1,..,5
1 Trace(1) 11.82088 14.21382 18.67103
2 Trace(1) 25.22305 28.55989 34.51127
3 Trace(1) 43.02937 46.79052 54.49390
4 Trace(1) 65.30130 69.25963 78.00512
5 Trace(1) 91.89456 96.24529 106.04841
1 Lambda(1) 11.82088 14.21382 18.67103
2 Lambda(1) 19.64398 22.17946 27.77477
3 Lambda(1) 26.69494 29.61400 34.98442
4 Lambda(1) 33.62306 36.66324 42.41659
5 Lambda(1) 39.97296 42.69462 48.66725
*** Freq = 4, p = 1,..,5
1 Trace(1) 11.16867 13.22626 18.10014
2 Trace(1) 23.76402 26.89691 32.96706
3 Trace(1) 40.46416 44.13739 51.56758
4 Trace(1) 61.94397 66.35955 74.40877
5 Trace(1) 87.85069 92.48682 102.52780
1 Lambda(1) 11.16867 13.22626 18.10014
2 Lambda(1) 18.56379 20.99576 26.02601
3 Lambda(1) 25.33768 28.10436 33.75171
4 Lambda(1) 32.38881 35.01388 40.75330
5 Lambda(1) 38.97883 41.95523 47.97076
*** Freq = 5, p = 1,..,5
1 Trace(1) 10.55050 12.58547 17.18919
2 Trace(1) 23.05486 25.83584 31.94371
3 Trace(1) 39.59401 43.00055 49.94990
4 Trace(1) 60.34547 64.33425 72.32450
5 Trace(1) 85.37926 89.88038 99.27682
1 Lambda(1) 10.55050 12.58547 17.18919
2 Lambda(1) 17.91457 20.27764 25.70681
3 Lambda(1) 24.59048 27.17991 33.33271
4 Lambda(1) 31.48946 34.32537 40.40508
5 Lambda(1) 38.20402 41.09012 46.39900
*** Freq = maxq, p = 1,..,5
1 Trace(1) 17.30189 19.52010 24.27098
2 Trace(1) 33.86703 37.08639 43.06904
3 Trace(1) 54.09262 57.70728 65.05912
4 Trace(1) 78.62984 82.40116 91.30152
5 Trace(1) 106.50309 110.99023 120.87198
1 Lambda(1) 17.30189 19.52010 24.27098
2 Lambda(1) 24.68907 27.10130 32.45098
3 Lambda(1) 31.28083 33.97494 39.39224
4 Lambda(1) 37.67745 40.39670 45.91960
5 Lambda(1) 43.91339 46.65765 52.83049
************************************************************
More detailed results below:
Trend Model
Frequency = 1
p=1
90% 95% 99%
Trace(1) 15.92629 18.09039 23.13090
Lambda(1) 15.92629 18.09039 23.13090
p=2
90% 95% 99%
Trace(1) 31.56404 34.63529 40.62200
Trace(2) 11.02695 12.38333 15.19439
Lambda(1) 22.52953 25.11238 30.47641
Lambda(2) 11.02695 12.38333 15.19439
p=3
90% 95% 99%
Trace(1) 52.73863 56.49866 64.29932
Trace(2) 25.91838 28.01836 31.69511
Trace(3) 9.83134 10.88235 12.91850
Lambda(1) 29.50385 32.22024 37.47534
Lambda(2) 17.55398 18.93271 22.20644
Lambda(3) 9.83134 10.88235 12.91850
p=4
90% 95% 99%
Trace(1) 76.92394 81.12916 89.62183
Trace(2) 44.18509 46.98792 52.19313
Trace(3) 22.87426 24.61567 28.18312
Trace(4) 8.97074 9.84767 11.80192
Lambda(1) 35.86276 38.25462 43.75503
Lambda(2) 23.02184 24.84072 28.05994
Lambda(3) 15.18269 16.44621 18.73297
Lambda(4) 8.97074 9.84767 11.80192
p=5
90% 95% 99%
Trace(1) 104.98884 109.17405 118.98810
Trace(2) 66.44334 69.46923 76.60724
Trace(3) 39.95158 42.12837 46.83197
Trace(4) 21.05350 22.62595 25.49730
Trace(5) 8.34059 9.13420 10.85839
Lambda(1) 41.85272 44.55845 50.41063
Lambda(2) 28.65656 30.38027 33.90009
Lambda(3) 20.26775 21.51586 24.52164
Lambda(4) 14.01799 15.05099 16.88097
Lambda(5) 8.34059 9.13420 10.85839
Frequency = 2
p=1
90% 95% 99%
Trace(1) 13.42129 15.86571 20.85068
Lambda(1) 13.42129 15.86571 20.85068
p=2
90% 95% 99%
Trace(1) 31.76872 34.79213 41.13525
Trace(2) 11.13868 12.50808 15.33522
Lambda(1) 22.62921 25.22413 30.52674
Lambda(2) 11.13868 12.50808 15.33522
p=3
90% 95% 99%
Trace(1) 46.94701 50.74269 58.20886
Trace(2) 21.45235 23.54742 28.25902
Trace(3) 7.08174 8.35455 10.65054
Lambda(1) 27.94128 30.45904 36.13643
Lambda(2) 15.94664 17.58224 20.67224
Lambda(3) 7.08174 8.35455 10.65054
p=4
90% 95% 99%
Trace(1) 69.96733 74.78432 83.11733
Trace(2) 38.58614 41.27860 46.88793
Trace(3) 18.39520 20.16386 23.80244
Trace(4) 6.15972 7.17678 9.12233
Lambda(1) 34.77303 37.58944 43.42374
Lambda(2) 22.13481 23.78869 27.07310
Lambda(3) 13.69834 15.10195 17.52372
Lambda(4) 6.15972 7.17678 9.12233
p=5
90% 95% 99%
Trace(1) 97.46749 102.38793 112.22756
Trace(2) 59.95317 63.41058 69.79793
Trace(3) 34.26794 36.62745 41.15526
Trace(4) 16.45677 18.13053 21.42525
Trace(5) 5.60658 6.37785 8.46797
Lambda(1) 41.26979 43.98831 49.73163
Lambda(2) 27.95728 29.73019 33.22479
Lambda(3) 19.24695 20.80018 23.58045
Lambda(4) 12.49423 13.55195 15.52812
Lambda(5) 5.60658 6.37785 8.46797
Frequency =3
p=1
90% 95% 99%
Trace(1) 11.82088 14.21382 18.67103
Lambda(1) 11.82088 14.21382 18.67103
p=2
90% 95% 99%
Trace(1) 32.21268 35.26290 41.82017
Trace(2) 11.37141 12.65386 15.56417
Lambda(1) 22.81384 25.41894 30.76878
Lambda(2) 11.37141 12.65386 15.56417
p=3
90% 95% 99%
Trace(1) 43.02937 46.79052 54.49390
Trace(2) 18.67556 20.91946 25.18256
Trace(3) 6.04134 7.18819 9.36015
Lambda(1) 26.69494 29.61400 34.98442
Lambda(2) 14.12934 15.74269 19.12130
Lambda(3) 6.04134 7.18819 9.36015
p=4
90% 95% 99%
Trace(1) 65.30130 69.25963 78.00512
Trace(2) 34.67846 37.28527 41.96357
Trace(3) 16.08911 17.78978 20.71617
Trace(4) 5.35350 6.12717 7.94718
Lambda(1) 33.62306 36.66324 42.41659
Lambda(2) 20.39095 22.31695 25.92490
Lambda(3) 11.98338 13.06268 15.45590
Lambda(4) 5.35350 6.12717 7.94718
p=5
90% 95% 99%
Trace(1) 91.89456 96.24529 106.04841
Trace(2) 55.12932 58.12447 64.58196
Trace(3) 30.77601 32.95708 37.31323
Trace(4) 14.75146 16.01814 18.85479
Trace(5) 5.03902 5.80522 7.19313
Lambda(1) 39.97296 42.69462 48.66725
Lambda(2) 26.73186 28.56903 31.96196
Lambda(3) 17.70648 19.16183 21.63719
Lambda(4) 10.88262 11.83215 13.94820
Lambda(5) 5.03902 5.80522 7.19313