Expected hessian for S-vine copula models
svinecop_hessian(u, model, cores = 1)the data; should have approximately uniform margins..
model inheriting from class svinecop_dist.
number of cores to use; if larger than one, computations are
done in parallel on cores batches .
Returns the observed Hessian matrix. Rows/columns correspond to to model parameters in the order: copula parameters of first tree, copula parameters of second tree, etc. Duplicated parameters in the copula model are omitted.
# load data set
data(returns)
# convert to uniform margins
u <- pseudo_obs(returns[1:100, 1:3])
# fit parametric S-vine copula model with Markov order 1
fit <- svinecop(u, p = 1, family_set = "parametric")
svinecop_loglik(u, fit)
#> [1] 87.19237
svinecop_scores(u, fit)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.89796619 -0.0455069794 3.56297929 -0.053331168 -0.309469402
#> [2,] -1.49893877 0.0459174078 -0.07135452 -0.009058333 0.232360235
#> [3,] -1.87659023 0.0849433852 -1.95676219 0.060004787 -0.905300979
#> [4,] -1.62335130 0.0415111356 -2.44881114 0.074151115 2.154558976
#> [5,] 0.61986562 -0.0227630599 4.85469830 -0.039538035 1.209412557
#> [6,] -1.72866801 0.0495296797 2.06103635 -0.120566303 -1.108936615
#> [7,] -1.09665531 0.0058068143 -1.32026382 0.009859961 0.722070441
#> [8,] 1.38235479 -0.1915837966 4.48864874 -0.210464538 0.800109212
#> [9,] -1.29286144 0.0186438182 -2.46457875 0.068636257 -1.584175996
#> [10,] 0.36053078 -0.0155213157 -1.66877626 0.036919904 -0.816085385
#> [11,] -1.18940952 0.0406884362 1.88648641 -0.065872655 -0.563067327
#> [12,] -0.87198790 0.0252322390 3.50308982 -0.079935464 -1.700259796
#> [13,] -1.29564510 0.0238737576 -2.28794086 0.058072943 -2.258645444
#> [14,] 3.50216865 -0.0717505727 -1.91221703 0.046274551 -0.022144550
#> [15,] 0.13012107 -0.0100598608 -1.65161206 0.037414009 0.186971829
#> [16,] 3.03950037 -0.0804492785 2.62180203 -0.067628774 0.312850852
#> [17,] -0.44951331 0.0082729849 1.45383842 -0.042687598 0.658853754
#> [18,] -0.31942553 0.0021796393 2.46988853 -0.110627615 0.739028525
#> [19,] -2.08258421 0.0745408860 3.50308982 -0.079935464 -0.134551168
#> [20,] 4.29003226 -0.0181678204 -0.99099354 0.009578960 0.006993861
#> [21,] -1.45390056 0.0407002307 -2.22861635 0.053961614 0.648205545
#> [22,] -1.65249609 0.0555190013 -2.03801747 0.047983471 0.524623031
#> [23,] -0.57080914 -0.0128407031 -1.03613553 0.003276593 -0.443957063
#> [24,] -0.96313770 0.0305323637 2.14435263 -0.044757889 -0.379302102
#> [25,] -1.21307663 0.0093445844 -2.72995749 0.093060661 -1.527014171
#> [26,] 5.01334743 0.0394738666 -2.44476697 0.066642077 1.465971485
#> [27,] 0.22935586 -0.0196254202 -1.69942567 0.032402876 0.910689926
#> [28,] -0.35560968 -0.0115355879 0.06523625 -0.026149137 0.783963175
#> [29,] -0.57571042 0.0150118908 4.26863278 -0.041388696 -1.040630677
#> [30,] -1.42162840 0.0303297884 -1.33085085 0.013015501 0.702022204
#> [31,] -1.43624096 0.0513735528 -1.71732599 0.039870800 -0.166403719
#> [32,] 4.64379496 0.0083664923 2.55907257 -0.086899893 0.289598043
#> [33,] -0.03987825 -0.0101440761 -2.10438048 0.049616946 -0.129148946
#> [34,] -1.23012570 0.0373326049 1.62767188 -0.085690937 0.727748495
#> [35,] -1.05586201 0.0267832407 -1.83800453 0.041910436 0.477228414
#> [36,] -0.85287584 0.0192967575 -1.36101672 0.025913027 -0.186042134
#> [37,] 3.37827921 -0.1612497689 6.81003107 0.025353427 0.323507639
#> [38,] 5.46930923 0.0983410702 5.50614928 -0.053799900 0.212060613
#> [39,] -1.13822911 0.0353300754 -1.47776654 0.030615278 0.253569296
#> [40,] 4.05507516 -0.0100897372 -0.89958612 0.009056546 0.291966175
#> [41,] -1.46462339 0.0358813222 -0.49478921 -0.005400327 0.065799134
#> [42,] -1.77874686 0.0570753616 0.48750958 -0.033084397 0.308202935
#> [43,] 0.10448852 -0.0074229847 -1.47353010 0.031902509 0.212060613
#> [44,] -1.48692402 0.0534616430 4.24248293 -0.094376827 -0.331033840
#> [45,] -1.31126818 0.0457691076 3.81498142 -0.054275305 -1.851216971
#> [46,] 0.92620802 -0.1012741274 -1.19518814 0.003015070 0.847477770
#> [47,] -1.10506991 0.0029783192 -1.02920491 -0.006114619 1.209412557
#> [48,] -0.59801574 0.0058656630 8.24729205 0.236742238 2.314868671
#> [49,] -1.34967584 0.0373071638 4.20200691 -0.040024950 -2.404552076
#> [50,] 3.54599410 -0.3051015130 -1.49907544 0.022940382 0.425031971
#> [51,] -1.67896277 0.0498043401 -1.71032209 0.029223691 0.754631127
#> [52,] -1.70334349 0.0567278477 3.18825341 -0.048144694 0.382338286
#> [53,] -0.24856492 0.0038122996 1.22770054 -0.032801916 0.018709301
#> [54,] -2.17429369 0.0857537961 2.15926109 -0.114039690 -0.156558601
#> [55,] -1.16900422 0.0120247989 3.51774497 -0.097551560 0.306867211
#> [56,] -0.89976768 0.0131457088 0.61392255 -0.048736971 0.228545126
#> [57,] -1.61056880 0.0533649051 -1.99280131 0.046428387 0.490512310
#> [58,] -1.58706975 0.0430387222 -2.32309217 0.058292159 -0.597707966
#> [59,] 1.27403246 -0.0445105727 1.28264639 -0.040332509 -0.008677463
#> [60,] -0.13616874 -0.0243865014 -1.96735067 0.045992092 0.190653183
#> [61,] 0.05974575 -0.0343245364 -2.29834703 0.057000271 0.508738554
#> [62,] -1.46998512 0.0380465325 -0.81408089 -0.001124650 0.555068515
#> [63,] -1.04228288 0.0348602970 -1.64089030 0.037688643 0.191476239
#> [64,] -1.12192509 0.0374927433 -1.64308313 0.037633981 0.249538306
#> [65,] -1.12044007 0.0376589502 -1.64180683 0.037665880 0.198703867
#> [66,] -1.11923336 0.0377914386 -1.64089030 0.037688643 0.212699228
#> [67,] -1.05525930 0.0313543249 1.27988163 -0.070183513 0.066853255
#> [68,] -1.38834214 0.0435285952 -1.93446729 0.044418197 0.455057476
#> [69,] 3.09645105 -0.1223259822 -0.89467760 0.015278935 0.276620308
#> [70,] -1.21708282 0.0385882967 -1.98403817 0.046935460 0.126756214
#> [71,] -1.79355140 0.0590916458 -2.20465582 0.053131967 -0.287777227
#> [72,] -0.78231592 0.0241568708 -1.56886191 0.034663113 0.355435259
#> [73,] -0.79973904 -0.0102375062 -1.80050675 0.034399239 0.316824957
#> [74,] -2.40544937 0.1220041287 -2.36963755 0.071850974 -2.718863600
#> [75,] -1.81770002 0.0566887262 -1.37983335 0.019779692 0.649654304
#> [76,] -0.45700786 -0.0093712915 -0.78476784 -0.013926425 0.657473413
#> [77,] -0.93505544 0.0184997138 -1.46955897 0.027629595 -1.383113814
#> [78,] -2.19523951 0.0839589470 1.23985769 -0.073299913 -0.348827375
#> [79,] 1.37593703 -0.1338875229 -1.99652695 0.045391658 -0.290903192
#> [80,] -1.84898430 0.0579767594 -0.88881885 -0.016132203 0.590403907
#> [81,] -1.13041620 0.0004653472 -0.42271752 -0.045529426 1.756609085
#> [82,] -0.37131485 -0.0407187655 -1.77951968 0.033113582 -2.512416224
#> [83,] 1.63261650 -0.0770567315 -0.12907565 -0.049455420 1.357056269
#> [84,] 0.93504965 -0.0335061583 -1.92432937 0.046541003 -0.103306439
#> [85,] 0.92034552 -0.0323251066 -1.92106210 0.046380381 0.205883966
#> [86,] -0.04896449 -0.0927214771 -0.98581054 -0.013360699 -1.063011702
#> [87,] 3.11602760 -0.2150969074 -2.08661532 0.049140587 0.534080754
#> [88,] 6.96475211 0.6550970397 -2.92924200 0.112490895 -1.891070226
#> [89,] 2.84096449 -0.1904053518 -1.58876176 0.032424868 -1.369974010
#> [90,] 3.54599410 -0.3051015130 6.24027309 -0.201216444 0.383313887
#> [91,] 2.72183932 -0.1902712167 -1.82925906 0.038188058 -0.626457640
#> [92,] 3.21362018 -0.0497226870 1.79454983 -0.056960312 0.179552524
#> [93,] 1.50390385 -0.1495418485 5.82349776 -0.228372757 -1.505034680
#> [94,] 0.01205395 -0.0230565054 -1.91528672 0.045267403 -0.212128294
#> [95,] 2.94043679 -0.0595246510 5.63915855 -0.109570858 -1.369974010
#> [96,] -1.57181614 0.0399897246 -3.00055444 0.123827025 2.409437745
#> [97,] 0.74651691 -0.0257376269 -1.00999514 0.017540380 -0.777534730
#> [98,] -0.58027157 0.0158771941 -0.85709850 0.012238608 0.216819889
#> [99,] -1.53154631 0.0526894224 -0.60411142 0.006813654 0.241647205
#> [,6] [,7] [,8]
#> [1,] -0.165636494 -0.58957844 0.016269953
#> [2,] 0.112915124 0.69224937 0.541753352
#> [3,] -0.048223887 -1.01556066 -0.072329211
#> [4,] -0.048242041 1.11141963 -0.362026496
#> [5,] -0.217132829 -0.67623514 -0.143237351
#> [6,] 0.025416445 2.30936280 0.090291218
#> [7,] -0.052359490 2.21733501 -0.288106921
#> [8,] -0.136834669 3.91702977 -0.361950399
#> [9,] -0.036871054 1.37226598 -0.189521591
#> [10,] 0.127677121 0.08323565 0.113257794
#> [11,] 0.158856940 -0.34634164 1.133044207
#> [12,] -0.129543652 -0.65771560 -0.453521199
#> [13,] 0.011584904 -0.13300024 -0.430912843
#> [14,] 0.087624348 -0.19542281 1.253033883
#> [15,] 0.109208736 -0.18170356 2.367858159
#> [16,] 0.502851781 -0.10255813 -1.451151365
#> [17,] 0.278236969 0.68868093 -1.235968100
#> [18,] 0.268685583 0.65449488 -0.987815639
#> [19,] 0.163360843 -0.71400391 0.983091839
#> [20,] 0.375421885 0.05241809 0.468313987
#> [21,] -0.041166564 -0.20209251 0.215416811
#> [22,] -0.062274681 -0.11355323 -0.318355686
#> [23,] -0.061888832 -0.32616783 -0.410430938
#> [24,] -0.065105666 0.98953927 -0.372067961
#> [25,] 0.012521470 0.70839383 -0.361975488
#> [26,] 0.165390683 0.13728851 -0.280901914
#> [27,] 0.148036931 -0.06231383 -0.939888587
#> [28,] -0.196381176 -0.20817827 1.022466387
#> [29,] -0.096950215 -0.56906946 0.017855859
#> [30,] -0.047413316 -0.70445641 -0.366426193
#> [31,] -0.057169516 -0.12227408 -0.358893657
#> [32,] -0.221936806 0.92690759 0.292184513
#> [33,] 0.056524335 0.97515732 2.087585481
#> [34,] 0.127963261 -0.02709280 -0.682934044
#> [35,] -0.081542717 0.11858978 0.359047126
#> [36,] -0.111524552 -0.26388785 0.436311575
#> [37,] -0.251302527 3.75531010 -0.702987640
#> [38,] -0.307921529 -10.23527689 1.760043794
#> [39,] -0.057574659 1.30241816 1.506392458
#> [40,] -0.061388729 0.14805671 0.940072925
#> [41,] 0.126680041 -0.59026273 -1.305992535
#> [42,] 0.033406278 0.99296015 -0.479485374
#> [43,] -0.064473246 -0.13835640 -0.544325314
#> [44,] 0.090511652 0.12826005 0.354997157
#> [45,] 0.003159728 -0.75076087 -0.196243848
#> [46,] -0.052538824 -0.72402711 -0.330856116
#> [47,] -0.222592095 -0.39369824 1.018983823
#> [48,] -0.047115133 2.24384055 -0.118474934
#> [49,] 0.035716918 -5.51053684 -0.341656485
#> [50,] 0.157397897 -0.80360522 4.719526273
#> [51,] -0.014480913 0.06076266 0.986708850
#> [52,] 0.143010161 -0.19596188 -0.368045078
#> [53,] -0.127614882 -0.71387592 -0.551255300
#> [54,] 0.090930676 2.15311506 0.172590482
#> [55,] 0.001223506 2.29411574 -0.395662174
#> [56,] -0.184353557 -0.61949090 -0.353313481
#> [57,] -0.050074647 -0.40697223 -0.330725869
#> [58,] -0.047201213 -0.38865976 -0.369937948
#> [59,] -0.160489190 0.88779079 -0.233847053
#> [60,] -0.060863294 0.42702324 -1.039877301
#> [61,] 0.014994683 -0.22894236 0.852395442
#> [62,] -0.038618493 0.55975405 -0.167776347
#> [63,] -0.062873736 -0.06141078 -0.375119442
#> [64,] -0.068974917 -0.12464808 -0.472590967
#> [65,] -0.067676672 -0.30866849 -0.081656447
#> [66,] -0.066444683 -0.31276192 -0.098608250
#> [67,] 0.153938376 0.19756853 0.166197345
#> [68,] -0.048073159 -0.22333365 -0.318095830
#> [69,] 0.289049240 -0.22969011 2.274899964
#> [70,] -0.039503849 0.03851031 0.865655962
#> [71,] -0.061395943 -0.32252861 -0.404371026
#> [72,] 0.059517983 -0.31711036 -0.016570356
#> [73,] -0.163372329 -0.23200106 0.945169579
#> [74,] -0.028479557 -0.22632305 1.418574974
#> [75,] 0.036434514 0.50707714 -1.049475090
#> [76,] 0.158595440 -0.13613753 0.732974391
#> [77,] -0.119160027 -0.18630871 -0.677657996
#> [78,] 0.118772815 -0.07998640 0.623762760
#> [79,] 0.058244504 -0.52704564 1.685567563
#> [80,] -0.004330557 -0.35029969 1.971128347
#> [81,] -0.049077860 -0.41524054 -0.361612492
#> [82,] -0.177243511 -0.21033779 -0.022586942
#> [83,] 0.337283752 -0.23188422 2.114530017
#> [84,] 0.049962309 -0.27976326 -1.872449152
#> [85,] 0.037149792 -0.24991733 1.904600724
#> [86,] -0.286648632 -0.17373165 -1.412215655
#> [87,] 0.036115298 -0.18530808 -2.863960675
#> [88,] 0.309127803 -0.21179775 -4.342396202
#> [89,] 0.157094910 -0.29556854 -4.754437535
#> [90,] -0.229564057 0.31704753 2.170759967
#> [91,] -0.130901802 -0.20905745 -1.127294032
#> [92,] -0.197706374 0.69307028 4.165764443
#> [93,] -0.366661580 1.47822892 -2.162846466
#> [94,] -0.046092306 -0.25258728 -1.390067940
#> [95,] 0.541702369 0.84148838 -1.412280830
#> [96,] -0.024722780 -0.19836356 0.045863801
#> [97,] -0.091274037 -0.32178742 0.002632332
#> [98,] 0.141428750 -0.26665916 -1.074521558
#> [99,] 0.039703201 0.07060206 -0.608026300
svinecop_hessian(u, fit)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] -3.896383e+00 0.0628972988 0.00000000 0.0000000000 0.000000
#> [2,] 6.289730e-02 -0.0076251195 0.00000000 0.0000000000 0.000000
#> [3,] 0.000000e+00 0.0000000000 -5.84245758 0.0414896789 0.000000
#> [4,] 0.000000e+00 0.0000000000 0.04148968 -0.0060639013 0.000000
#> [5,] 0.000000e+00 0.0000000000 0.00000000 0.0000000000 -1.006142
#> [6,] 3.568397e-05 0.0002391028 -0.03908895 0.0007626501 0.000000
#> [7,] 0.000000e+00 0.0000000000 -0.26477391 -0.0013786859 0.000000
#> [8,] -4.604411e-01 0.0047708430 0.01984588 0.0007009467 0.000000
#> [,6] [,7] [,8]
#> [1,] 0.000000000 0.000000 0.000000
#> [2,] 0.000000000 0.000000 0.000000
#> [3,] 0.000000000 0.000000 0.000000
#> [4,] 0.000000000 0.000000 0.000000
#> [5,] 0.000000000 0.000000 0.000000
#> [6,] -0.024143498 0.000000 0.000000
#> [7,] 0.000000000 -2.052046 0.000000
#> [8,] -0.003965246 0.000000 -1.846482