Description Usage Arguments Details Value Author(s) References Examples
Estimation of the conditional covariance matrix using the RiskMetrics 2006 methodology of Zumbach (2007).
1 |
data |
Matrix containing a TxK time series returns. |
tau0 |
optional input parameter. Default 1560 |
tau1 |
optional input parameter. Default 4 |
kmax |
optional input parameter. Default 14 |
rho |
optional input parameter. Default 1.4142 |
More details can be found in Zumbach (2007) and in the MFE Toolbox of Kevin Sheppard (function riskmetrics2006).
The funcion returns an array containing for each t (t = 1, ..., T+1) a KxK matrix with the conditional covariance matrix estimates.
Carlos Trucios
Zumbach, G. (2007) The Riskmetrics 2006 Methodology. Available at SSRN: https://ssrn.com/abstract=1420185 or http://dx.doi.org/10.2139/ssrn.1420185
1 2 |
, , 1
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.76079359 -0.208747593 -0.09470014 -0.22900830 -0.115129088 0.09835845
[2,] -0.20874759 1.028588262 0.17484591 0.03160987 0.007084893 -0.26700505
[3,] -0.09470014 0.174845911 1.08522277 0.06987857 0.040638754 -0.43075516
[4,] -0.22900830 0.031609875 0.06987857 0.73390204 0.172266126 -0.26461783
[5,] -0.11512909 0.007084893 0.04063875 0.17226613 0.705333352 -0.31511751
[6,] 0.09835845 -0.267005048 -0.43075516 -0.26461783 -0.315117514 1.67124098
[7,] 0.18860420 0.011659971 -0.07410369 0.05966181 0.071512863 -0.13530541
[8,] -0.08194530 0.127905806 -0.32811482 -0.14169362 -0.101441113 0.28388249
[9,] -0.06348479 0.064143474 -0.23937420 -0.07572453 -0.131715855 -0.15217441
[10,] -0.02332592 0.126583504 0.00224097 -0.11650109 -0.124523997 -0.16313080
[,7] [,8] [,9] [,10]
[1,] 0.18860420 -0.08194530 -0.06348479 -0.02332592
[2,] 0.01165997 0.12790581 0.06414347 0.12658350
[3,] -0.07410369 -0.32811482 -0.23937420 0.00224097
[4,] 0.05966181 -0.14169362 -0.07572453 -0.11650109
[5,] 0.07151286 -0.10144111 -0.13171585 -0.12452400
[6,] -0.13530541 0.28388249 -0.15217441 -0.16313080
[7,] 1.50086460 -0.01155972 -0.20028002 0.10795714
[8,] -0.01155972 0.87669661 0.04771874 0.20293984
[9,] -0.20028002 0.04771874 1.02815623 0.13918245
[10,] 0.10795714 0.20293984 0.13918245 0.66221543
, , 2
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.76306483 -0.24039784 -0.17499113 -0.24773009 -0.12404373 0.09010741
[2,] -0.24039784 1.01888263 0.25548662 0.06840036 0.01932791 -0.23851101
[3,] -0.17499113 0.25548662 1.15480016 0.13093445 0.06395432 -0.39990686
[4,] -0.24773009 0.06840036 0.13093445 0.71334962 0.16659629 -0.23631384
[5,] -0.12404373 0.01932791 0.06395432 0.16659629 0.66046089 -0.27620988
[6,] 0.09010741 -0.23851101 -0.39990686 -0.23631384 -0.27620988 1.50364570
[7,] 0.25615183 -0.08943242 -0.23468508 -0.01511766 0.02873640 -0.10475410
[8,] -0.03663187 0.07906940 -0.36576799 -0.15930866 -0.09970723 0.25518338
[9,] 0.01768389 -0.01653255 -0.34641344 -0.12317348 -0.14595985 -0.11767630
[10,] 0.02002931 0.07039856 -0.06771671 -0.14166802 -0.12892322 -0.13744877
[,7] [,8] [,9] [,10]
[1,] 0.25615183 -0.03663187 0.01768389 0.02002931
[2,] -0.08943242 0.07906940 -0.01653255 0.07039856
[3,] -0.23468508 -0.36576799 -0.34641344 -0.06771671
[4,] -0.01511766 -0.15930866 -0.12317348 -0.14166802
[5,] 0.02873640 -0.09970723 -0.14595985 -0.12892322
[6,] -0.10475410 0.25518338 -0.11767630 -0.13744877
[7,] 1.55769854 0.06171089 -0.04997678 0.16700101
[8,] 0.06171089 0.85631306 0.09868192 0.21803120
[9,] -0.04997678 0.09868192 1.04920296 0.18176888
[10,] 0.16700101 0.21803120 0.18176888 0.65446805
, , 3
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.727948564 -0.25020643 -0.16231127 -0.258526885 -0.16628954 0.19935869
[2,] -0.250206428 1.03932584 0.25381989 0.139436907 0.13021044 -0.48609809
[3,] -0.162311272 0.25381989 1.05832549 0.136607373 0.09183983 -0.45234952
[4,] -0.258526885 0.13943691 0.13660737 0.740540064 0.25884866 -0.46678991
[5,] -0.166289536 0.13021044 0.09183983 0.258848665 0.77205242 -0.60738344
[6,] 0.199358686 -0.48609809 -0.45234952 -0.466789908 -0.60738344 2.21800290
[7,] 0.218307702 -0.07628972 -0.20185711 -0.006006835 0.01935847 -0.07930651
[8,] -0.006802559 0.00991495 -0.35129749 -0.207572334 -0.17606329 0.43797152
[9,] -0.008523119 0.03843683 -0.29007590 -0.063714876 -0.07627718 -0.23129065
[10,] 0.011694489 0.07736917 -0.05412891 -0.119570842 -0.10216906 -0.16156127
[,7] [,8] [,9] [,10]
[1,] 0.218307702 -0.006802559 -0.008523119 0.01169449
[2,] -0.076289718 0.009914950 0.038436826 0.07736917
[3,] -0.201857114 -0.351297486 -0.290075898 -0.05412891
[4,] -0.006006835 -0.207572334 -0.063714876 -0.11957084
[5,] 0.019358465 -0.176063292 -0.076277180 -0.10216906
[6,] -0.079306510 0.437971518 -0.231290651 -0.16156127
[7,] 1.428665004 0.055786842 -0.062187323 0.14552481
[8,] 0.055786842 0.861111128 0.053464364 0.19181975
[9,] -0.062187323 0.053464364 0.979186840 0.16863047
[10,] 0.145524813 0.191819753 0.168630470 0.61998562
, , 4
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.68845884 -0.22559506 -0.189694925 -0.25886307 -0.15736628 0.20413989
[2,] -0.22559506 0.97026138 0.264479639 0.13915202 0.11240720 -0.44784471
[3,] -0.18969492 0.26447964 1.252225196 0.27504294 0.12250858 -0.60388724
[4,] -0.25886307 0.13915202 0.275042936 0.77524863 0.25293958 -0.51726366
[5,] -0.15736628 0.11240720 0.122508578 0.25293958 0.71815111 -0.55836952
[6,] 0.20413989 -0.44784471 -0.603887239 -0.51726366 -0.55836952 2.11592331
[7,] 0.15529337 -0.03599531 -0.009517104 0.09866738 0.04549907 -0.18992001
[8,] -0.00383985 0.01331902 -0.361182165 -0.20978634 -0.15796694 0.41348958
[9,] 0.01744205 0.01843690 -0.419277648 -0.14434646 -0.09830083 -0.08624961
[10,] -0.00560108 0.08364827 0.042054431 -0.06191637 -0.08098367 -0.20665729
[,7] [,8] [,9] [,10]
[1,] 0.155293371 -0.00383985 0.01744205 -0.00560108
[2,] -0.035995315 0.01331902 0.01843690 0.08364827
[3,] -0.009517104 -0.36118216 -0.41927765 0.04205443
[4,] 0.098667383 -0.20978634 -0.14434646 -0.06191637
[5,] 0.045499068 -0.15796694 -0.09830083 -0.08098367
[6,] -0.189920006 0.41348958 -0.08624961 -0.20665729
[7,] 1.411728335 0.02080812 -0.16169350 0.17938570
[8,] 0.020808124 0.81810285 0.07294124 0.16468756
[9,] -0.161693500 0.07294124 0.99220601 0.10141129
[10,] 0.179385701 0.16468756 0.10141129 0.61569795
, , 5
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.712918221 -0.16436167 -0.22421524 -0.23475310 -0.12895930 0.2105105
[2,] -0.164361674 0.92054763 0.20186504 0.11381420 0.09739672 -0.3690361
[3,] -0.224215245 0.20186504 1.18830526 0.23650436 0.09097727 -0.5668917
[4,] -0.234753102 0.11381420 0.23650436 0.71382341 0.22136152 -0.4507061
[5,] -0.128959297 0.09739672 0.09097727 0.22136152 0.66685198 -0.4786589
[6,] 0.210510461 -0.36903609 -0.56689172 -0.45070612 -0.47865893 1.9116629
[7,] 0.290386930 0.05105410 -0.15316016 0.08566674 0.07070652 -0.0822227
[8,] 0.018529356 0.03539592 -0.34926443 -0.18811655 -0.13063156 0.3768995
[9,] -0.097331659 -0.02798362 -0.27017953 -0.11557626 -0.11063992 -0.1364043
[10,] -0.006727509 0.07439376 0.03714729 -0.06263133 -0.07771599 -0.1840960
[,7] [,8] [,9] [,10]
[1,] 0.29038693 0.01852936 -0.09733166 -0.006727509
[2,] 0.05105410 0.03539592 -0.02798362 0.074393758
[3,] -0.15316016 -0.34926443 -0.27017953 0.037147294
[4,] 0.08566674 -0.18811655 -0.11557626 -0.062631332
[5,] 0.07070652 -0.13063156 -0.11063992 -0.077715989
[6,] -0.08222270 0.37689948 -0.13640428 -0.184095965
[7,] 1.67626598 0.08141338 -0.40754084 0.152225788
[8,] 0.08141338 0.78413446 0.02012999 0.154504252
[9,] -0.40754084 0.02012999 1.08472891 0.098425632
[10,] 0.15222579 0.15450425 0.09842563 0.583408334
, , 6
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.85499322 -0.184872415 -0.08748312 -0.35632732 -0.09064424 0.18987515
[2,] -0.18487241 0.869350908 0.15696324 0.12534860 0.07352927 -0.32346141
[3,] -0.08748312 0.156963236 1.13798897 0.11973813 0.09126858 -0.49718931
[4,] -0.35632732 0.125348598 0.11973813 0.77354467 0.17499419 -0.40103902
[5,] -0.09064424 0.073529266 0.09126858 0.17499419 0.62428764 -0.41771823
[6,] 0.18987515 -0.323461407 -0.49718931 -0.40103902 -0.41771823 1.72025607
[7,] 0.37559040 0.020916693 -0.06074266 -0.01445641 0.08072050 -0.07072557
[8,] -0.07070629 0.057117166 -0.36014942 -0.10550703 -0.12455644 0.32730419
[9,] -0.14239844 -0.003788923 -0.27278379 -0.05540020 -0.10872070 -0.12289034
[10,] -0.05856244 0.078581287 0.00126460 -0.02194070 -0.08177357 -0.16676253
[,7] [,8] [,9] [,10]
[1,] 0.37559040 -0.07070629 -0.142398441 -0.05856244
[2,] 0.02091669 0.05711717 -0.003788923 0.07858129
[3,] -0.06074266 -0.36014942 -0.272783790 0.00126460
[4,] -0.01445641 -0.10550703 -0.055400198 -0.02194070
[5,] 0.08072050 -0.12455644 -0.108720702 -0.08177357
[6,] -0.07072557 0.32730419 -0.122890335 -0.16676253
[7,] 1.61667888 0.01432706 -0.401499470 0.09908344
[8,] 0.01432706 0.77811885 0.042681104 0.16940494
[9,] -0.40149947 0.04268110 1.007241164 0.10757735
[10,] 0.09908344 0.16940494 0.107577349 0.56981901
, , 7
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.78819838 -0.17189491 -0.08604624 -0.30653407 -0.08332437 0.1826545
[2,] -0.17189491 0.88298685 0.21002511 0.04292537 0.04771545 -0.4320804
[3,] -0.08604624 0.21002511 1.10860593 0.03720103 0.06492318 -0.5987351
[4,] -0.30653407 0.04292537 0.03720103 0.77084365 0.16741370 -0.2122564
[5,] -0.08332437 0.04771545 0.06492318 0.16741370 0.58571935 -0.3422168
[6,] 0.18265454 -0.43208038 -0.59873505 -0.21225635 -0.34221682 1.8901256
[7,] 0.30976856 0.11330295 0.04178243 -0.08804310 0.05523264 -0.2722904
[8,] -0.06082103 0.02657828 -0.35702006 -0.06830134 -0.10265236 0.3604848
[9,] -0.14499865 0.15051694 -0.09286545 -0.18403766 -0.12464105 -0.4343970
[10,] -0.05644515 0.12169123 0.05316756 -0.07547715 -0.08629270 -0.2628321
[,7] [,8] [,9] [,10]
[1,] 0.30976856 -0.06082103 -0.14499865 -0.05644515
[2,] 0.11330295 0.02657828 0.15051694 0.12169123
[3,] 0.04178243 -0.35702006 -0.09286545 0.05316756
[4,] -0.08804310 -0.06830134 -0.18403766 -0.07547715
[5,] 0.05523264 -0.10265236 -0.12464105 -0.08629270
[6,] -0.27229040 0.36048481 -0.43439703 -0.26283208
[7,] 1.60667943 -0.03107639 -0.15904254 0.15972072
[8,] -0.03107639 0.75168757 -0.03107297 0.13487200
[9,] -0.15904254 -0.03107297 1.24457951 0.21099848
[10,] 0.15972072 0.13487200 0.21099848 0.58106760
, , 8
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.82370873 -0.30373932 -0.13761083 -0.20131437 -0.04517002 0.1354043
[2,] -0.30373932 1.07283447 0.28662233 -0.08066659 -0.01633983 -0.3415160
[3,] -0.13761083 0.28662233 1.05291657 -0.01548576 0.03286949 -0.5173482
[4,] -0.20131437 -0.08066659 -0.01548576 0.76479014 0.17572762 -0.2079626
[5,] -0.04517002 -0.01633983 0.03286949 0.17572762 0.56206527 -0.3121995
[6,] 0.13540432 -0.34151596 -0.51734819 -0.20796256 -0.31219950 1.7097701
[7,] 0.37101515 -0.06804205 -0.03443166 0.01404997 0.08666702 -0.2646302
[8,] -0.16575956 0.20864107 -0.24969236 -0.14965265 -0.12870343 0.3448118
[9,] -0.14321921 0.16075502 -0.08059743 -0.16891703 -0.11812962 -0.3722177
[10,] -0.11860999 0.22192937 0.09140197 -0.12710627 -0.10620619 -0.2152575
[,7] [,8] [,9] [,10]
[1,] 0.37101515 -0.165759557 -0.143219209 -0.11860999
[2,] -0.06804205 0.208641068 0.160755017 0.22192937
[3,] -0.03443166 -0.249692356 -0.080597432 0.09140197
[4,] 0.01404997 -0.149652650 -0.168917033 -0.12710627
[5,] 0.08666702 -0.128703426 -0.118129618 -0.10620619
[6,] -0.26463018 0.344811777 -0.372217717 -0.21525754
[7,] 1.58852538 -0.148178152 -0.169493237 0.06335178
[8,] -0.14817815 0.840890407 -0.007678484 0.21150138
[9,] -0.16949324 -0.007678484 1.131029313 0.19960108
[10,] 0.06335178 0.211501379 0.199601078 0.60417449
, , 9
[,1] [,2] [,3] [,4] [,5]
[1,] 0.78778804 -0.268177381 -0.127393602 -0.210795391 -0.124491083
[2,] -0.26817738 0.989409584 0.253268073 -0.067386363 -0.008428207
[3,] -0.12739360 0.253268073 0.966640191 -0.005994566 0.048709387
[4,] -0.21079539 -0.067386363 -0.005994566 0.732762995 0.237260574
[5,] -0.12449108 -0.008428207 0.048709387 0.237260574 0.757510206
[6,] 0.09291439 -0.298204668 -0.456681036 -0.162374125 -0.207611767
[7,] 0.24268674 -0.046123835 -0.009891400 0.099545189 0.301412006
[8,] -0.12642923 0.184829068 -0.235500079 -0.155458211 -0.169612395
[9,] -0.06889043 0.139287119 -0.094915563 -0.204092707 -0.275657426
[10,] -0.07716981 0.191110641 0.071324733 -0.141958746 -0.168807724
[,6] [,7] [,8] [,9] [,10]
[1,] 0.09291439 0.24268674 -0.1264292 -0.06889043 -0.07716981
[2,] -0.29820467 -0.04612384 0.1848291 0.13928712 0.19111064
[3,] -0.45668104 -0.00989140 -0.2355001 -0.09491556 0.07132473
[4,] -0.16237413 0.09954519 -0.1554582 -0.20409271 -0.14195875
[5,] -0.20761177 0.30141201 -0.1696124 -0.27565743 -0.16880772
[6,] 1.57417657 -0.16389384 0.2883145 -0.37678515 -0.21388616
[7,] -0.16389384 1.67933740 -0.1835164 -0.32729753 -0.01028481
[8,] 0.28831445 -0.18351636 0.8029646 0.03685280 0.21227510
[9,] -0.37678515 -0.32729753 0.0368528 1.15680035 0.23125032
[10,] -0.21388616 -0.01028481 0.2122751 0.23125032 0.59214379
, , 10
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.74102882 -0.25444196 -0.09043988 -0.20985418 -0.07151165 0.09837892
[2,] -0.25444196 0.95018866 0.18809406 -0.02766804 -0.08186355 -0.29332245
[3,] -0.09043988 0.18809406 0.93194853 -0.04118421 0.12219992 -0.37927323
[4,] -0.20985418 -0.02766804 -0.04118421 0.70855570 0.14016327 -0.17655385
[5,] -0.07151165 -0.08186355 0.12219992 0.14016327 0.85493676 -0.12563651
[6,] 0.09837892 -0.29332245 -0.37927323 -0.17655385 -0.12563651 1.46224701
[7,] 0.21736556 -0.04636334 0.00176738 0.08399386 0.28298629 -0.13960951
[8,] -0.11882410 0.17707558 -0.22927124 -0.13060567 -0.17013216 0.24930000
[9,] -0.08047664 0.15632072 -0.12369960 -0.14765483 -0.30622216 -0.35491732
[10,] -0.06923126 0.17244055 0.05588791 -0.12554509 -0.16166401 -0.19493901
[,7] [,8] [,9] [,10]
[1,] 0.217365556 -0.1188241 -0.08047664 -0.069231259
[2,] -0.046363339 0.1770756 0.15632072 0.172440552
[3,] 0.001767380 -0.2292712 -0.12369960 0.055887912
[4,] 0.083993863 -0.1306057 -0.14765483 -0.125545094
[5,] 0.282986286 -0.1701322 -0.30622216 -0.161664014
[6,] -0.139609506 0.2493000 -0.35491732 -0.194939007
[7,] 1.539083329 -0.1611174 -0.30520575 -0.005185108
[8,] -0.161117419 0.7587448 0.04158880 0.196634238
[9,] -0.305205749 0.0415888 1.08091929 0.210513020
[10,] -0.005185108 0.1966342 0.21051302 0.559953865
, , 11
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.75108839 -0.32889588 -0.018039893 -0.17252322 -0.08245827 0.1429490
[2,] -0.32889588 1.06285932 0.062613558 -0.05640467 -0.04860216 -0.3575262
[3,] -0.01803989 0.06261356 0.924270382 -0.01744271 0.09000699 -0.2880465
[4,] -0.17252322 -0.05640467 -0.017442713 0.66193436 0.12343672 -0.1435052
[5,] -0.08245827 -0.04860216 0.090006988 0.12343672 0.78337365 -0.1323987
[6,] 0.14294904 -0.35752615 -0.288046474 -0.14350517 -0.13239875 1.3931353
[7,] 0.18420162 -0.02667362 -0.005594295 0.07883604 0.24749087 -0.1334349
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