Estimates a standard VAR(1)
Arguments
- RiskFactors
A numeric matrix (F x T) representing the time series of risk factors.
- VARtype
String vector with two possible values: 'unconstrained' or 'constrained'.
- Bcon_Mat
Constraints matrix (F+1 x N), which includes an intercept. Entries containing NAs are treated as free parameters.
Default is set to NULL.
Examples
data("CM_Factors")
# Example 1: unconstrained case
VAR(RiskFactors, VARtype= 'unconstrained')
#> $K0Z
#> [,1]
#> GBC -14.04087747
#> CPI_OECD -0.14414165
#> Eco_Act China 0.86689400
#> Inflation China 3.07386085
#> Level China 0.80127640
#> Slope China 0.27826455
#> Curvature China -0.29349098
#> Eco_Act Brazil -1.11904778
#> Inflation Brazil 0.81085652
#> Level Brazil 3.21843467
#> Slope Brazil 2.60592274
#> Curvature Brazil -0.73925571
#> Eco_Act Mexico -1.15972595
#> Inflation Mexico 2.31500616
#> Level Mexico 3.11715090
#> Slope Mexico 0.05242973
#> Curvature Mexico -0.24186592
#> Eco_Act Uruguay -2.04840963
#> Inflation Uruguay 4.60000681
#> Level Uruguay 2.84486371
#> Slope Uruguay -1.70450233
#> Curvature Uruguay -1.29217071
#>
#> $K1Z
#> t(RHS)GBC t(RHS)CPI_OECD t(RHS)Eco_Act China
#> GBC 7.732531e-01 -0.577925285 0.243151365
#> CPI_OECD -3.066644e-04 0.763795083 0.003894332
#> Eco_Act China -2.730115e-02 0.100548524 1.087675621
#> Inflation China 1.375004e-02 0.046211836 0.019467321
#> Level China -5.803648e-03 0.041773193 -0.010262672
#> Slope China 2.172207e-03 0.012061647 0.020998730
#> Curvature China -1.782289e-03 -0.033190039 -0.001536159
#> Eco_Act Brazil 8.062126e-04 -0.215498805 0.042281948
#> Inflation Brazil -3.526406e-05 -0.094705088 0.020390429
#> Level Brazil 5.000038e-02 -0.010919813 -0.056145895
#> Slope Brazil 9.176308e-03 0.060267990 -0.020124097
#> Curvature Brazil 1.166346e-02 -0.047217259 -0.011661058
#> Eco_Act Mexico -2.917180e-03 -0.131864827 0.092267934
#> Inflation Mexico 8.840399e-03 0.111158833 -0.041926132
#> Level Mexico -5.067262e-03 0.029998458 0.010796462
#> Slope Mexico -5.687642e-03 -0.047620264 0.020677539
#> Curvature Mexico 4.142173e-03 -0.128356934 -0.025328259
#> Eco_Act Uruguay -1.566919e-02 0.009100996 0.096581737
#> Inflation Uruguay -8.404294e-03 -0.043494453 -0.011677457
#> Level Uruguay 5.863303e-02 0.560109923 0.036102981
#> Slope Uruguay 8.648463e-03 -0.309051713 -0.016486125
#> Curvature Uruguay -4.780100e-03 -0.105107041 -0.025665850
#> t(RHS)Inflation China t(RHS)Level China t(RHS)Slope China
#> GBC 0.319973288 0.618670138 -0.770247853
#> CPI_OECD 0.074620085 0.048087607 -0.015433875
#> Eco_Act China -0.127822519 -0.073196020 -0.056021808
#> Inflation China 0.863732408 -0.007940719 0.009220007
#> Level China 0.085100165 0.871851335 0.299631313
#> Slope China 0.006988056 0.041801272 0.645396592
#> Curvature China -0.014915318 0.025495413 0.060662753
#> Eco_Act Brazil -0.016419157 -0.053310022 0.023560417
#> Inflation Brazil 0.042989084 0.070175308 0.090832137
#> Level Brazil 0.041761913 0.012837668 0.557624501
#> Slope Brazil 0.024355774 -0.074949226 0.250224033
#> Curvature Brazil 0.012370476 0.018584419 -0.014411143
#> Eco_Act Mexico -0.063375440 0.038143885 0.018083702
#> Inflation Mexico -0.001332311 -0.075420026 0.029952576
#> Level Mexico 0.021330079 0.005358586 0.392811081
#> Slope Mexico -0.031988100 0.075546515 0.161387924
#> Curvature Mexico 0.052828500 -0.024242151 -0.142837225
#> Eco_Act Uruguay -0.004141554 0.134177400 -0.024638688
#> Inflation Uruguay 0.088548791 -0.038027751 -0.397051213
#> Level Uruguay -0.175128003 0.010720216 -0.617331356
#> Slope Uruguay 0.029300758 0.035223539 0.137076883
#> Curvature Uruguay 0.036997211 0.026306135 0.056291710
#> t(RHS)Curvature China t(RHS)Eco_Act Brazil
#> GBC -0.167713711 0.241715170
#> CPI_OECD -0.042245908 0.048270169
#> Eco_Act China -0.610015630 -0.018024802
#> Inflation China -0.112678028 0.060854289
#> Level China -0.009341804 -0.015196913
#> Slope China -0.078962982 -0.007530011
#> Curvature China 0.447297722 0.025908872
#> Eco_Act Brazil -0.031308267 0.996086411
#> Inflation Brazil -0.304064004 -0.018826791
#> Level Brazil 0.279259845 -0.050782331
#> Slope Brazil 0.248544794 -0.050384746
#> Curvature Brazil -0.023852778 0.009485801
#> Eco_Act Mexico -0.115250296 0.033506071
#> Inflation Mexico 0.181053406 0.021745705
#> Level Mexico -0.161931734 0.010366640
#> Slope Mexico -0.118715607 0.082126536
#> Curvature Mexico 0.147283623 -0.007911088
#> Eco_Act Uruguay 0.803768713 0.186519246
#> Inflation Uruguay -0.243500248 -0.050508323
#> Level Uruguay -0.341274544 -0.005589889
#> Slope Uruguay -0.148603051 0.038914671
#> Curvature Uruguay 0.087648127 0.020177496
#> t(RHS)Inflation Brazil t(RHS)Level Brazil t(RHS)Slope Brazil
#> GBC -0.3886625757 0.1578145617 -5.056676e-02
#> CPI_OECD -0.0046487070 0.0208818194 3.055594e-03
#> Eco_Act China -0.0488615325 0.0163891996 -5.445040e-02
#> Inflation China -0.0110625552 -0.0221061605 8.296542e-03
#> Level China -0.0985150641 0.0007404906 -2.090090e-02
#> Slope China 0.0037747092 0.0047712654 3.907100e-02
#> Curvature China -0.0001380348 0.0027038716 -2.742055e-02
#> Eco_Act Brazil 0.0429289426 0.0199262192 -1.794334e-02
#> Inflation Brazil 0.8633962385 -0.0007278727 2.628026e-02
#> Level Brazil 0.3825174199 0.8034845199 -1.967584e-01
#> Slope Brazil 0.1721728789 -0.1105642796 7.544521e-01
#> Curvature Brazil 0.0290545081 -0.0031220220 1.350104e-02
#> Eco_Act Mexico 0.0663444323 0.0060493074 -2.765733e-02
#> Inflation Mexico 0.0085927202 -0.0120580120 -3.200845e-03
#> Level Mexico 0.0097707187 -0.0179058075 -4.594422e-02
#> Slope Mexico 0.0067920827 0.0231314434 2.758394e-02
#> Curvature Mexico 0.0331488098 -0.0011616060 1.875757e-02
#> Eco_Act Uruguay 0.1864979912 0.0210378401 6.262269e-06
#> Inflation Uruguay 0.0663388591 -0.0323769389 1.324891e-01
#> Level Uruguay -0.1083315803 0.0991376647 -1.167084e-02
#> Slope Uruguay 0.1393686327 -0.0015718403 3.126599e-02
#> Curvature Uruguay 0.0251677008 -0.0099479074 -4.736893e-02
#> t(RHS)Curvature Brazil t(RHS)Eco_Act Mexico
#> GBC -1.07690865 -0.045649779
#> CPI_OECD -0.10756931 -0.006567888
#> Eco_Act China -0.02320703 -0.194388474
#> Inflation China 0.12276381 -0.050553267
#> Level China 0.07164622 0.017605094
#> Slope China 0.06217441 -0.013511695
#> Curvature China 0.01664670 0.001752231
#> Eco_Act Brazil -0.62159804 -0.025875261
#> Inflation Brazil 0.29051319 -0.006836006
#> Level Brazil 0.23302726 0.247986101
#> Slope Brazil -0.41021415 0.104800265
#> Curvature Brazil 0.75911938 0.025980770
#> Eco_Act Mexico -0.54304321 0.904195656
#> Inflation Mexico -0.26353605 -0.022309209
#> Level Mexico -0.26288529 -0.101064597
#> Slope Mexico 0.01682228 -0.034751744
#> Curvature Mexico 0.04816780 0.042600934
#> Eco_Act Uruguay 0.53977144 -0.104769115
#> Inflation Uruguay -0.06800426 -0.003506336
#> Level Uruguay 1.02867393 -0.097448384
#> Slope Uruguay -0.18640909 0.017314940
#> Curvature Uruguay -0.17547742 0.060043969
#> t(RHS)Inflation Mexico t(RHS)Level Mexico t(RHS)Slope Mexico
#> GBC 0.149500154 0.311235949 -0.2800161669
#> CPI_OECD -0.013306485 0.032075534 -0.1138250769
#> Eco_Act China 0.017454748 -0.022687705 0.0054504287
#> Inflation China -0.235649833 -0.030589462 0.0004905644
#> Level China 0.087367701 -0.061243960 -0.0067899033
#> Slope China -0.026531503 0.018071408 0.0016187946
#> Curvature China -0.006941692 -0.002833581 -0.0313638010
#> Eco_Act Brazil -0.016208309 0.062264301 -0.1201985399
#> Inflation Brazil -0.071943329 -0.028743732 -0.0022589312
#> Level Brazil -0.080187490 -0.106931325 -0.1980815962
#> Slope Brazil -0.036095933 -0.057674708 -0.1404520148
#> Curvature Brazil -0.007359333 0.019012549 0.0073967507
#> Eco_Act Mexico -0.011058879 0.029301686 -0.1645590335
#> Inflation Mexico 0.846170686 -0.065850100 0.0025065058
#> Level Mexico 0.063229249 0.834467575 -0.0753435194
#> Slope Mexico 0.018855271 -0.029698614 0.7017424290
#> Curvature Mexico 0.037741351 0.022262891 0.0678969549
#> Eco_Act Uruguay 0.259686378 0.022018068 -0.1522705919
#> Inflation Uruguay -0.255754703 -0.029648756 0.0562506260
#> Level Uruguay -0.046455546 0.058742112 -0.3148172810
#> Slope Uruguay 0.146726712 0.003847542 0.0299637207
#> Curvature Uruguay 0.020988167 0.025596599 0.0306606744
#> t(RHS)Curvature Mexico t(RHS)Eco_Act Uruguay
#> GBC 1.334562687 0.019536846
#> CPI_OECD 0.008370847 0.013539198
#> Eco_Act China -0.089073260 -0.057451515
#> Inflation China 0.063390626 -0.012568015
#> Level China -0.056768881 -0.049641498
#> Slope China -0.022278847 0.027434370
#> Curvature China -0.027159183 -0.008002078
#> Eco_Act Brazil 0.107560897 -0.052681635
#> Inflation Brazil -0.127208411 -0.018942244
#> Level Brazil 0.385622913 -0.134009624
#> Slope Brazil 0.420400321 -0.054767792
#> Curvature Brazil -0.061174859 -0.006408793
#> Eco_Act Mexico -0.035206066 0.006850973
#> Inflation Mexico -0.091489898 -0.001465787
#> Level Mexico 0.090686659 0.016593729
#> Slope Mexico 0.038537437 -0.026666176
#> Curvature Mexico 0.289723748 0.015657734
#> Eco_Act Uruguay -0.212132739 0.864609111
#> Inflation Uruguay -0.160244245 0.043566941
#> Level Uruguay 0.006035328 -0.006688668
#> Slope Uruguay -0.246710850 0.041870482
#> Curvature Uruguay 0.039792586 -0.039627496
#> t(RHS)Inflation Uruguay t(RHS)Level Uruguay
#> GBC 0.370766328 -0.1839402284
#> CPI_OECD -0.019085190 -0.0492522588
#> Eco_Act China -0.018032384 -0.0153360309
#> Inflation China -0.051482576 -0.0080839218
#> Level China 0.033249260 0.0247699272
#> Slope China -0.018220640 -0.0133052969
#> Curvature China 0.010465664 0.0002473502
#> Eco_Act Brazil 0.016998118 -0.0624265546
#> Inflation Brazil 0.009994626 0.0165130242
#> Level Brazil -0.138192428 0.3201378738
#> Slope Brazil -0.098218702 0.1852199736
#> Curvature Brazil 0.002761791 -0.0121442512
#> Eco_Act Mexico 0.011991568 -0.0791110459
#> Inflation Mexico -0.082296486 0.0466126486
#> Level Mexico -0.156192625 0.0675205726
#> Slope Mexico -0.017708288 -0.0156102741
#> Curvature Mexico -0.026864455 0.0126484355
#> Eco_Act Uruguay -0.033857633 -0.0688415981
#> Inflation Uruguay 0.655836432 0.0706050988
#> Level Uruguay -0.010595942 0.7352026974
#> Slope Uruguay 0.005009970 -0.0122384246
#> Curvature Uruguay 0.007348643 0.0288949567
#> t(RHS)Slope Uruguay t(RHS)Curvature Uruguay
#> GBC 0.3241538010 -0.093708147
#> CPI_OECD 0.0043000065 0.110897942
#> Eco_Act China 0.0503486063 0.166906529
#> Inflation China 0.0126091443 0.222594064
#> Level China -0.0004802449 -0.027879595
#> Slope China 0.0571842072 0.131432791
#> Curvature China -0.0061345812 -0.001027603
#> Eco_Act Brazil -0.0229982309 -0.186067729
#> Inflation Brazil 0.0422623175 0.142065065
#> Level Brazil 0.3993170476 -0.409080143
#> Slope Brazil 0.2218009630 -0.297937873
#> Curvature Brazil -0.0006679187 -0.094650621
#> Eco_Act Mexico 0.0619266345 0.040481312
#> Inflation Mexico 0.0210444548 -0.113652861
#> Level Mexico -0.0231644724 0.596886188
#> Slope Mexico -0.0020384154 -0.007946134
#> Curvature Mexico -0.0635881717 -0.131947082
#> Eco_Act Uruguay -0.0645895930 0.067626233
#> Inflation Uruguay -0.0275510994 0.045419712
#> Level Uruguay 0.1646359082 0.356924246
#> Slope Uruguay 0.6929424718 -0.080276491
#> Curvature Uruguay 0.0144724795 0.623633656
#>
#> $SSZ
#> GBC CPI_OECD Eco_Act China Inflation China
#> GBC 3.6483063359 0.0338173539 -5.416458e-02 -0.0215672166
#> CPI_OECD 0.0338173539 0.0494186969 -1.317264e-03 0.0102016554
#> Eco_Act China -0.0541645768 -0.0013172641 6.124235e-02 -0.0181598769
#> Inflation China -0.0215672166 0.0102016554 -1.815988e-02 0.2764043306
#> Level China 0.0028850911 0.0228884121 -2.830622e-02 0.0298293766
#> Slope China 0.0260303047 0.0066827271 -1.083072e-02 0.0038273990
#> Curvature China 0.0113798269 0.0027326386 -9.050590e-03 0.0087416397
#> Eco_Act Brazil 0.0075792936 0.0020232189 1.072339e-02 -0.0029751744
#> Inflation Brazil 0.0409741732 0.0097680681 -5.679896e-03 0.0077021929
#> Level Brazil 0.0335244776 0.0307622931 1.123037e-02 0.0585620678
#> Slope Brazil -0.0422127194 0.0163973782 -2.732068e-03 0.0245704222
#> Curvature Brazil 0.0216033023 0.0003739243 1.847849e-03 0.0062752306
#> Eco_Act Mexico -0.1114609900 0.0117985563 2.419970e-02 -0.0005303322
#> Inflation Mexico 0.0005958416 0.0053677598 -2.330976e-03 -0.0035166618
#> Level Mexico 0.1894641671 -0.0107864084 -2.847018e-02 -0.0264227943
#> Slope Mexico -0.0410280478 -0.0151386987 -8.137782e-03 -0.0095936910
#> Curvature Mexico -0.0008247167 -0.0049171913 -2.223864e-03 0.0144272862
#> Eco_Act Uruguay -0.0218067080 -0.0013675428 3.543652e-03 -0.0196859870
#> Inflation Uruguay 0.0126816019 0.0071060876 -1.290998e-02 0.0355263522
#> Level Uruguay -0.1344983069 0.0097672988 3.534048e-03 -0.0050875443
#> Slope Uruguay -0.0012988997 -0.0022608054 -1.204687e-03 0.0106394862
#> Curvature Uruguay 0.0131377026 -0.0006354582 2.946577e-05 0.0021842823
#> Level China Slope China Curvature China Eco_Act Brazil
#> GBC 0.0028850911 0.0260303047 0.0113798269 0.007579294
#> CPI_OECD 0.0228884121 0.0066827271 0.0027326386 0.002023219
#> Eco_Act China -0.0283062159 -0.0108307207 -0.0090505900 0.010723392
#> Inflation China 0.0298293766 0.0038273990 0.0087416397 -0.002975174
#> Level China 0.1821429985 0.0133044543 0.0018542715 -0.012223337
#> Slope China 0.0133044543 0.0518076400 0.0042542942 -0.001719478
#> Curvature China 0.0018542715 0.0042542942 0.0175551686 -0.003203987
#> Eco_Act Brazil -0.0122233366 -0.0017194785 -0.0032039867 0.047134989
#> Inflation Brazil 0.0016528110 0.0053620546 0.0023076032 -0.004545105
#> Level Brazil 0.0305832565 0.0102018664 -0.0093635429 -0.001257038
#> Slope Brazil 0.0023799006 0.0041943222 -0.0091459794 0.016516210
#> Curvature Brazil -0.0008322802 0.0014525247 0.0022283265 -0.006445112
#> Eco_Act Mexico -0.0004730396 0.0017540483 -0.0034227169 0.035689917
#> Inflation Mexico 0.0116000298 0.0017036667 0.0017034668 -0.003233685
#> Level Mexico -0.0205329470 0.0134913941 0.0007469754 -0.014030888
#> Slope Mexico -0.0168978128 -0.0036249831 0.0013742524 -0.013201011
#> Curvature Mexico -0.0085800496 -0.0035914833 -0.0004978508 0.001974621
#> Eco_Act Uruguay 0.0246549364 0.0064732824 0.0057573308 0.008399707
#> Inflation Uruguay 0.0319075817 -0.0060487445 -0.0046653946 0.009751942
#> Level Uruguay 0.0032195735 -0.0250400800 0.0002447287 -0.014262387
#> Slope Uruguay 0.0030582827 0.0026219479 -0.0031452583 0.001203101
#> Curvature Uruguay -0.0078161083 0.0004353141 0.0011923529 -0.001489523
#> Inflation Brazil Level Brazil Slope Brazil Curvature Brazil
#> GBC 0.0409741732 0.0335244776 -0.0422127194 0.0216033023
#> CPI_OECD 0.0097680681 0.0307622931 0.0163973782 0.0003739243
#> Eco_Act China -0.0056798965 0.0112303687 -0.0027320685 0.0018478489
#> Inflation China 0.0077021929 0.0585620678 0.0245704222 0.0062752306
#> Level China 0.0016528110 0.0305832565 0.0023799006 -0.0008322802
#> Slope China 0.0053620546 0.0102018664 0.0041943222 0.0014525247
#> Curvature China 0.0023076032 -0.0093635429 -0.0091459794 0.0022283265
#> Eco_Act Brazil -0.0045451050 -0.0012570380 0.0165162101 -0.0064451118
#> Inflation Brazil 0.0954082551 0.0407845191 0.0047223500 0.0127475140
#> Level Brazil 0.0407845191 0.9228250399 0.4315689704 0.0381023090
#> Slope Brazil 0.0047223500 0.4315689704 0.3301045640 -0.0105497976
#> Curvature Brazil 0.0127475140 0.0381023090 -0.0105497976 0.0207381828
#> Eco_Act Mexico 0.0056517659 0.0026233980 0.0245979929 -0.0046079333
#> Inflation Mexico -0.0020216177 -0.0552173314 -0.0081398767 -0.0034435771
#> Level Mexico -0.0133176229 0.0266939727 0.0025297990 -0.0033640920
#> Slope Mexico 0.0016979730 0.0110866581 0.0004002269 -0.0019858786
#> Curvature Mexico -0.0055781019 -0.0370264131 -0.0137140276 0.0001730775
#> Eco_Act Uruguay 0.0031113534 0.0141137581 -0.0169509139 0.0082770772
#> Inflation Uruguay 0.0286345486 0.0596996226 0.0388076979 -0.0001419588
#> Level Uruguay 0.0294975277 0.0174873206 -0.0379197250 0.0131291076
#> Slope Uruguay 0.0037696436 0.0002372014 0.0060236916 -0.0005373854
#> Curvature Uruguay -0.0004332629 0.0300600743 0.0175788421 -0.0008301444
#> Eco_Act Mexico Inflation Mexico Level Mexico Slope Mexico
#> GBC -0.1114609900 0.0005958416 0.1894641671 -0.0410280478
#> CPI_OECD 0.0117985563 0.0053677598 -0.0107864084 -0.0151386987
#> Eco_Act China 0.0241996986 -0.0023309764 -0.0284701843 -0.0081377819
#> Inflation China -0.0005303322 -0.0035166618 -0.0264227943 -0.0095936910
#> Level China -0.0004730396 0.0116000298 -0.0205329470 -0.0168978128
#> Slope China 0.0017540483 0.0017036667 0.0134913941 -0.0036249831
#> Curvature China -0.0034227169 0.0017034668 0.0007469754 0.0013742524
#> Eco_Act Brazil 0.0356899171 -0.0032336854 -0.0140308879 -0.0132010106
#> Inflation Brazil 0.0056517659 -0.0020216177 -0.0133176229 0.0016979730
#> Level Brazil 0.0026233980 -0.0552173314 0.0266939727 0.0110866581
#> Slope Brazil 0.0245979929 -0.0081398767 0.0025297990 0.0004002269
#> Curvature Brazil -0.0046079333 -0.0034435771 -0.0033640920 -0.0019858786
#> Eco_Act Mexico 0.0794681552 0.0025730379 -0.0304038787 -0.0155504017
#> Inflation Mexico 0.0025730379 0.0773835115 -0.0117398189 -0.0009160856
#> Level Mexico -0.0304038787 -0.0117398189 0.3995667749 0.1034848389
#> Slope Mexico -0.0155504017 -0.0009160856 0.1034848389 0.1547721833
#> Curvature Mexico -0.0036696263 -0.0009405656 -0.0001430818 0.0013658420
#> Eco_Act Uruguay 0.0202949658 0.0145002454 -0.0386083902 -0.0210540897
#> Inflation Uruguay 0.0087501506 0.0024109434 -0.0165937211 -0.0106733038
#> Level Uruguay -0.0336121301 0.0077508103 -0.0276655387 -0.0471944453
#> Slope Uruguay 0.0098443956 -0.0058405678 -0.0164278686 0.0025655429
#> Curvature Uruguay 0.0031112769 -0.0044500633 0.0173252674 0.0080290537
#> Curvature Mexico Eco_Act Uruguay Inflation Uruguay
#> GBC -0.0008247167 -0.021806708 0.0126816019
#> CPI_OECD -0.0049171913 -0.001367543 0.0071060876
#> Eco_Act China -0.0022238645 0.003543652 -0.0129099772
#> Inflation China 0.0144272862 -0.019685987 0.0355263522
#> Level China -0.0085800496 0.024654936 0.0319075817
#> Slope China -0.0035914833 0.006473282 -0.0060487445
#> Curvature China -0.0004978508 0.005757331 -0.0046653946
#> Eco_Act Brazil 0.0019746212 0.008399707 0.0097519424
#> Inflation Brazil -0.0055781019 0.003111353 0.0286345486
#> Level Brazil -0.0370264131 0.014113758 0.0596996226
#> Slope Brazil -0.0137140276 -0.016950914 0.0388076979
#> Curvature Brazil 0.0001730775 0.008277077 -0.0001419588
#> Eco_Act Mexico -0.0036696263 0.020294966 0.0087501506
#> Inflation Mexico -0.0009405656 0.014500245 0.0024109434
#> Level Mexico -0.0001430818 -0.038608390 -0.0165937211
#> Slope Mexico 0.0013658420 -0.021054090 -0.0106733038
#> Curvature Mexico 0.0756084566 -0.016413685 0.0011826445
#> Eco_Act Uruguay -0.0164136852 0.199245503 0.0055049127
#> Inflation Uruguay 0.0011826445 0.005504913 0.1644424451
#> Level Uruguay 0.0124571846 0.012677341 0.0519775754
#> Slope Uruguay -0.0063901482 -0.029750345 -0.0210330986
#> Curvature Uruguay -0.0052314192 0.004923432 0.0017077508
#> Level Uruguay Slope Uruguay Curvature Uruguay
#> GBC -0.1344983069 -0.0012988997 1.313770e-02
#> CPI_OECD 0.0097672988 -0.0022608054 -6.354582e-04
#> Eco_Act China 0.0035340484 -0.0012046872 2.946577e-05
#> Inflation China -0.0050875443 0.0106394862 2.184282e-03
#> Level China 0.0032195735 0.0030582827 -7.816108e-03
#> Slope China -0.0250400800 0.0026219479 4.353141e-04
#> Curvature China 0.0002447287 -0.0031452583 1.192353e-03
#> Eco_Act Brazil -0.0142623865 0.0012031010 -1.489523e-03
#> Inflation Brazil 0.0294975277 0.0037696436 -4.332629e-04
#> Level Brazil 0.0174873206 0.0002372014 3.006007e-02
#> Slope Brazil -0.0379197250 0.0060236916 1.757884e-02
#> Curvature Brazil 0.0131291076 -0.0005373854 -8.301444e-04
#> Eco_Act Mexico -0.0336121301 0.0098443956 3.111277e-03
#> Inflation Mexico 0.0077508103 -0.0058405678 -4.450063e-03
#> Level Mexico -0.0276655387 -0.0164278686 1.732527e-02
#> Slope Mexico -0.0471944453 0.0025655429 8.029054e-03
#> Curvature Mexico 0.0124571846 -0.0063901482 -5.231419e-03
#> Eco_Act Uruguay 0.0126773412 -0.0297503452 4.923432e-03
#> Inflation Uruguay 0.0519775754 -0.0210330986 1.707751e-03
#> Level Uruguay 0.8156704607 -0.0910032459 -4.549058e-02
#> Slope Uruguay -0.0910032459 0.1847923174 -1.479170e-03
#> Curvature Uruguay -0.0454905842 -0.0014791700 2.989588e-02
#>
# Example 2: constrained case
K <- nrow(RiskFactors)
Bcon_Mat <- matrix(0, nrow = K, ncol = K+1)
Bcon_Mat[ , 1:3] <- NaN
VAR(RiskFactors, VARtype= 'constrained', Bcon_Mat)
#> $K0Z
#> [,1]
#> GBC 0.5331693
#> CPI_OECD 0.1595189
#> Eco_Act China 14.9945053
#> Inflation China 0.4792326
#> Level China 5.2356974
#> Slope China 2.5788292
#> Curvature China -0.3372277
#> Eco_Act Brazil 2.6839043
#> Inflation Brazil 6.1743284
#> Level Brazil 27.9040161
#> Slope Brazil 3.6383000
#> Curvature Brazil -1.2655527
#> Eco_Act Mexico 2.5897811
#> Inflation Mexico 3.7008451
#> Level Mexico 13.5489927
#> Slope Mexico 4.6676391
#> Curvature Mexico -0.2468844
#> Eco_Act Uruguay 2.8563699
#> Inflation Uruguay 7.8536436
#> Level Uruguay 6.8289454
#> Slope Uruguay 2.8977482
#> Curvature Uruguay -1.5785849
#>
#> $K1Z
#> GBC CPI_OECD Eco_Act China Inflation China
#> GBC 0.975170488 -0.274567367 0 0
#> CPI_OECD 0.007553187 0.918584099 0 0
#> Eco_Act China 0.507493794 -2.216520432 0 0
#> Inflation China 0.050392051 1.020750275 0 0
#> Level China -0.101596361 0.804232317 0 0
#> Slope China 0.033717039 0.077729090 0 0
#> Curvature China -0.002480743 -0.016312573 0 0
#> Eco_Act Brazil 0.285310505 -0.310161690 0 0
#> Inflation Brazil -0.071434006 -0.225501624 0 0
#> Level Brazil 0.295781057 0.101113899 0 0
#> Slope Brazil 0.030118784 -0.111431617 0 0
#> Curvature Brazil 0.005458128 0.006833234 0 0
#> Eco_Act Mexico 0.040574140 -0.280315161 0 0
#> Inflation Mexico 0.017601344 0.196377533 0 0
#> Level Mexico 0.267543047 0.656006019 0 0
#> Slope Mexico 0.045017126 -0.254056638 0 0
#> Curvature Mexico 0.007317416 -0.031111910 0 0
#> Eco_Act Uruguay 0.169042373 0.392680150 0 0
#> Inflation Uruguay -0.063536004 -0.041166215 0 0
#> Level Uruguay 0.342294867 0.686479509 0 0
#> Slope Uruguay 0.028165165 -0.550877690 0 0
#> Curvature Uruguay -0.008652923 0.077572251 0 0
#> Level China Slope China Curvature China Eco_Act Brazil
#> GBC 0 0 0 0
#> CPI_OECD 0 0 0 0
#> Eco_Act China 0 0 0 0
#> Inflation China 0 0 0 0
#> Level China 0 0 0 0
#> Slope China 0 0 0 0
#> Curvature China 0 0 0 0
#> Eco_Act Brazil 0 0 0 0
#> Inflation Brazil 0 0 0 0
#> Level Brazil 0 0 0 0
#> Slope Brazil 0 0 0 0
#> Curvature Brazil 0 0 0 0
#> Eco_Act Mexico 0 0 0 0
#> Inflation Mexico 0 0 0 0
#> Level Mexico 0 0 0 0
#> Slope Mexico 0 0 0 0
#> Curvature Mexico 0 0 0 0
#> Eco_Act Uruguay 0 0 0 0
#> Inflation Uruguay 0 0 0 0
#> Level Uruguay 0 0 0 0
#> Slope Uruguay 0 0 0 0
#> Curvature Uruguay 0 0 0 0
#> Inflation Brazil Level Brazil Slope Brazil Curvature Brazil
#> GBC 0 0 0 0
#> CPI_OECD 0 0 0 0
#> Eco_Act China 0 0 0 0
#> Inflation China 0 0 0 0
#> Level China 0 0 0 0
#> Slope China 0 0 0 0
#> Curvature China 0 0 0 0
#> Eco_Act Brazil 0 0 0 0
#> Inflation Brazil 0 0 0 0
#> Level Brazil 0 0 0 0
#> Slope Brazil 0 0 0 0
#> Curvature Brazil 0 0 0 0
#> Eco_Act Mexico 0 0 0 0
#> Inflation Mexico 0 0 0 0
#> Level Mexico 0 0 0 0
#> Slope Mexico 0 0 0 0
#> Curvature Mexico 0 0 0 0
#> Eco_Act Uruguay 0 0 0 0
#> Inflation Uruguay 0 0 0 0
#> Level Uruguay 0 0 0 0
#> Slope Uruguay 0 0 0 0
#> Curvature Uruguay 0 0 0 0
#> Eco_Act Mexico Inflation Mexico Level Mexico Slope Mexico
#> GBC 0 0 0 0
#> CPI_OECD 0 0 0 0
#> Eco_Act China 0 0 0 0
#> Inflation China 0 0 0 0
#> Level China 0 0 0 0
#> Slope China 0 0 0 0
#> Curvature China 0 0 0 0
#> Eco_Act Brazil 0 0 0 0
#> Inflation Brazil 0 0 0 0
#> Level Brazil 0 0 0 0
#> Slope Brazil 0 0 0 0
#> Curvature Brazil 0 0 0 0
#> Eco_Act Mexico 0 0 0 0
#> Inflation Mexico 0 0 0 0
#> Level Mexico 0 0 0 0
#> Slope Mexico 0 0 0 0
#> Curvature Mexico 0 0 0 0
#> Eco_Act Uruguay 0 0 0 0
#> Inflation Uruguay 0 0 0 0
#> Level Uruguay 0 0 0 0
#> Slope Uruguay 0 0 0 0
#> Curvature Uruguay 0 0 0 0
#> Curvature Mexico Eco_Act Uruguay Inflation Uruguay
#> GBC 0 0 0
#> CPI_OECD 0 0 0
#> Eco_Act China 0 0 0
#> Inflation China 0 0 0
#> Level China 0 0 0
#> Slope China 0 0 0
#> Curvature China 0 0 0
#> Eco_Act Brazil 0 0 0
#> Inflation Brazil 0 0 0
#> Level Brazil 0 0 0
#> Slope Brazil 0 0 0
#> Curvature Brazil 0 0 0
#> Eco_Act Mexico 0 0 0
#> Inflation Mexico 0 0 0
#> Level Mexico 0 0 0
#> Slope Mexico 0 0 0
#> Curvature Mexico 0 0 0
#> Eco_Act Uruguay 0 0 0
#> Inflation Uruguay 0 0 0
#> Level Uruguay 0 0 0
#> Slope Uruguay 0 0 0
#> Curvature Uruguay 0 0 0
#> Level Uruguay Slope Uruguay Curvature Uruguay
#> GBC 0 0 0
#> CPI_OECD 0 0 0
#> Eco_Act China 0 0 0
#> Inflation China 0 0 0
#> Level China 0 0 0
#> Slope China 0 0 0
#> Curvature China 0 0 0
#> Eco_Act Brazil 0 0 0
#> Inflation Brazil 0 0 0
#> Level Brazil 0 0 0
#> Slope Brazil 0 0 0
#> Curvature Brazil 0 0 0
#> Eco_Act Mexico 0 0 0
#> Inflation Mexico 0 0 0
#> Level Mexico 0 0 0
#> Slope Mexico 0 0 0
#> Curvature Mexico 0 0 0
#> Eco_Act Uruguay 0 0 0
#> Inflation Uruguay 0 0 0
#> Level Uruguay 0 0 0
#> Slope Uruguay 0 0 0
#> Curvature Uruguay 0 0 0
#>
#> $SSZ
#> GBC CPI_OECD Eco_Act China Inflation China
#> GBC 4.953079733 0.1050024906 1.85455421 0.0482164203
#> CPI_OECD 0.105002491 0.0759776971 0.08292347 0.1390486697
#> Eco_Act China 1.854554208 0.0829234663 12.60022138 -0.5276293995
#> Inflation China 0.048216420 0.1390486697 -0.52762940 2.3985984585
#> Level China -0.335304642 -0.0278893549 -3.00192369 0.0693633126
#> Slope China -0.007840209 0.0082631298 0.39839723 -0.1228898733
#> Curvature China 0.002394379 0.0071421757 0.03794157 0.0024317559
#> Eco_Act Brazil 1.250729081 0.2055401515 5.27850600 0.7124522427
#> Inflation Brazil -0.495073672 -0.0104859899 -0.38671255 0.5867179886
#> Level Brazil 0.438745731 -0.1492528356 5.62283697 -1.9886593523
#> Slope Brazil 0.015314156 -0.0120704382 -0.30677153 0.1411948385
#> Curvature Brazil -0.176439434 0.0030863156 -0.23147916 0.2392214345
#> Eco_Act Mexico 0.564282530 0.2395399130 6.37453971 0.6398179189
#> Inflation Mexico 0.065427510 -0.0525890462 -0.82395976 -0.6546989091
#> Level Mexico 0.925404595 -0.0726172724 0.45647992 -2.5849221744
#> Slope Mexico 0.075356042 -0.0136789651 0.96527717 -0.0070971247
#> Curvature Mexico 0.013584223 -0.0039725175 -0.07670157 0.1120555652
#> Eco_Act Uruguay 0.079832770 -0.0014890765 3.07222539 -0.1012842395
#> Inflation Uruguay -0.056980605 0.0008212241 -1.20445459 1.0569235765
#> Level Uruguay 0.461144710 -0.2240341836 0.91285091 -2.2011393044
#> Slope Uruguay -0.013790165 -0.0053591482 0.37718562 -0.0282234679
#> Curvature Uruguay 0.124015224 0.0315424799 -0.09518253 0.0008817952
#> Level China Slope China Curvature China Eco_Act Brazil
#> GBC -0.335304642 -0.007840209 0.002394379 1.25072908
#> CPI_OECD -0.027889355 0.008263130 0.007142176 0.20554015
#> Eco_Act China -3.001923695 0.398397233 0.037941575 5.27850600
#> Inflation China 0.069363313 -0.122889873 0.002431756 0.71245224
#> Level China 1.910434010 0.086364054 -0.003237178 -2.33334731
#> Slope China 0.086364054 0.290954025 0.008590125 -0.18885633
#> Curvature China -0.003237178 0.008590125 0.029286716 0.04768005
#> Eco_Act Brazil -2.333347315 -0.188856330 0.047680052 5.79878377
#> Inflation Brazil 0.641224430 0.432963177 0.013460457 -1.54111546
#> Level Brazil 0.128870260 2.137779308 0.114747081 -3.56117319
#> Slope Brazil 0.162560686 0.080359722 -0.067360494 0.21121691
#> Curvature Brazil 0.084676709 0.029905647 0.003300819 -0.12137079
#> Eco_Act Mexico -1.881923289 0.212009891 0.101696913 5.11793704
#> Inflation Mexico 0.242442254 -0.081036894 -0.026728803 -0.30067946
#> Level Mexico -0.752591064 0.229690573 -0.015670280 -0.73407893
#> Slope Mexico -0.048986798 0.240733552 0.007760569 0.29066775
#> Curvature Mexico -0.059208872 -0.038841138 -0.002216033 0.06582625
#> Eco_Act Uruguay -0.458704370 0.431410991 0.026238930 0.73208058
#> Inflation Uruguay 0.373487668 -0.207273563 -0.035107716 -0.38924896
#> Level Uruguay -0.141085224 0.202943610 -0.021997376 -1.96530725
#> Slope Uruguay 0.268914858 0.400913785 -0.014691766 -0.21791446
#> Curvature Uruguay -0.088162314 -0.007944056 0.017444839 0.31761891
#> Inflation Brazil Level Brazil Slope Brazil Curvature Brazil
#> GBC -0.49507367 0.43874573 0.015314156 -0.176439434
#> CPI_OECD -0.01048599 -0.14925284 -0.012070438 0.003086316
#> Eco_Act China -0.38671255 5.62283697 -0.306771527 -0.231479158
#> Inflation China 0.58671799 -1.98865935 0.141194839 0.239221435
#> Level China 0.64122443 0.12887026 0.162560686 0.084676709
#> Slope China 0.43296318 2.13777931 0.080359722 0.029905647
#> Curvature China 0.01346046 0.11474708 -0.067360494 0.003300819
#> Eco_Act Brazil -1.54111546 -3.56117319 0.211216913 -0.121370787
#> Inflation Brazil 2.94495792 9.11905686 0.051867494 0.233036392
#> Level Brazil 9.11905686 55.65397057 -0.576351106 -0.039541869
#> Slope Brazil 0.05186749 -0.57635111 1.993278885 0.007318773
#> Curvature Brazil 0.23303639 -0.03954187 0.007318773 0.123761408
#> Eco_Act Mexico 0.07068656 2.69487444 0.082697475 0.081968736
#> Inflation Mexico -0.68964621 -1.63420428 0.294992982 -0.131914677
#> Level Mexico -2.19295939 -1.30417555 -0.675166564 -0.487799840
#> Slope Mexico 0.72529434 3.90285632 -0.048357756 0.020751537
#> Curvature Mexico -0.05567733 -0.23430957 -0.037064210 0.018652695
#> Eco_Act Uruguay 0.46347893 3.06248379 -0.255281360 0.197258661
#> Inflation Uruguay 0.75587011 -0.58766458 0.562824784 0.091559579
#> Level Uruguay 0.61301122 12.23597967 -0.031147220 -0.379299998
#> Slope Uruguay 1.23108156 4.95475440 0.539645602 0.044955014
#> Curvature Uruguay -0.05184797 0.34346198 -0.069130585 -0.056032144
#> Eco_Act Mexico Inflation Mexico Level Mexico Slope Mexico
#> GBC 0.56428253 0.06542751 0.92540460 0.075356042
#> CPI_OECD 0.23953991 -0.05258905 -0.07261727 -0.013678965
#> Eco_Act China 6.37453971 -0.82395976 0.45647992 0.965277170
#> Inflation China 0.63981792 -0.65469891 -2.58492217 -0.007097125
#> Level China -1.88192329 0.24244225 -0.75259106 -0.048986798
#> Slope China 0.21200989 -0.08103689 0.22969057 0.240733552
#> Curvature China 0.10169691 -0.02672880 -0.01567028 0.007760569
#> Eco_Act Brazil 5.11793704 -0.30067946 -0.73407893 0.290667752
#> Inflation Brazil 0.07068656 -0.68964621 -2.19295939 0.725294340
#> Level Brazil 2.69487444 -1.63420428 -1.30417555 3.902856317
#> Slope Brazil 0.08269747 0.29499298 -0.67516656 -0.048357756
#> Curvature Brazil 0.08196874 -0.13191468 -0.48779984 0.020751537
#> Eco_Act Mexico 8.83462822 -1.01527395 -3.65584424 0.921513519
#> Inflation Mexico -1.01527395 0.95094227 0.71039969 -0.148217821
#> Level Mexico -3.65584424 0.71039969 10.03071855 -0.433590945
#> Slope Mexico 0.92151352 -0.14821782 -0.43359094 0.812838352
#> Curvature Mexico 0.00946134 -0.01113968 -0.08741479 -0.013445301
#> Eco_Act Uruguay 1.43560251 0.02508504 -0.89948096 0.398565653
#> Inflation Uruguay -0.69430020 -0.33416564 -1.90759294 -0.190451830
#> Level Uruguay -3.46918478 0.58720024 4.90560528 0.029359151
#> Slope Uruguay 0.78438847 0.07204942 -1.10426061 0.631015456
#> Curvature Uruguay 0.42012569 -0.04507954 0.33323955 0.074420465
#> Curvature Mexico Eco_Act Uruguay Inflation Uruguay
#> GBC 0.013584223 0.079832770 -0.0569806052
#> CPI_OECD -0.003972517 -0.001489076 0.0008212241
#> Eco_Act China -0.076701569 3.072225390 -1.2044545867
#> Inflation China 0.112055565 -0.101284240 1.0569235765
#> Level China -0.059208872 -0.458704370 0.3734876682
#> Slope China -0.038841138 0.431410991 -0.2072735631
#> Curvature China -0.002216033 0.026238930 -0.0351077164
#> Eco_Act Brazil 0.065826250 0.732080578 -0.3892489598
#> Inflation Brazil -0.055677334 0.463478925 0.7558701118
#> Level Brazil -0.234309565 3.062483790 -0.5876645807
#> Slope Brazil -0.037064210 -0.255281360 0.5628247836
#> Curvature Brazil 0.018652695 0.197258661 0.0915595792
#> Eco_Act Mexico 0.009461340 1.435602508 -0.6943002008
#> Inflation Mexico -0.011139684 0.025085038 -0.3341656402
#> Level Mexico -0.087414790 -0.899480963 -1.9075929395
#> Slope Mexico -0.013445301 0.398565653 -0.1904518296
#> Curvature Mexico 0.111849894 0.047870740 0.0200726684
#> Eco_Act Uruguay 0.047870740 4.359343321 -0.6263624785
#> Inflation Uruguay 0.020072668 -0.626362478 1.6185438125
#> Level Uruguay -0.039218660 -0.134553366 -0.2741654256
#> Slope Uruguay -0.098295526 0.707335870 -0.0697679319
#> Curvature Uruguay -0.019015218 -0.486670081 -0.0736774261
#> Level Uruguay Slope Uruguay Curvature Uruguay
#> GBC 0.461144710 -0.013790165 0.1240152242
#> CPI_OECD -0.224034184 -0.005359148 0.0315424799
#> Eco_Act China 0.912850913 0.377185625 -0.0951825329
#> Inflation China -2.201139304 -0.028223468 0.0008817952
#> Level China -0.141085224 0.268914858 -0.0881623139
#> Slope China 0.202943610 0.400913785 -0.0079440561
#> Curvature China -0.021997376 -0.014691766 0.0174448392
#> Eco_Act Brazil -1.965307248 -0.217914458 0.3176189101
#> Inflation Brazil 0.613011215 1.231081565 -0.0518479701
#> Level Brazil 12.235979665 4.954754397 0.3434619813
#> Slope Brazil -0.031147220 0.539645602 -0.0691305854
#> Curvature Brazil -0.379299998 0.044955014 -0.0560321441
#> Eco_Act Mexico -3.469184777 0.784388465 0.4201256931
#> Inflation Mexico 0.587200240 0.072049421 -0.0450795401
#> Level Mexico 4.905605276 -1.104260605 0.3332395463
#> Slope Mexico 0.029359151 0.631015456 0.0744204653
#> Curvature Mexico -0.039218660 -0.098295526 -0.0190152183
#> Eco_Act Uruguay -0.134553366 0.707335870 -0.4866700814
#> Inflation Uruguay -0.274165426 -0.069767932 -0.0736774261
#> Level Uruguay 9.378088688 0.003837500 0.0059159930
#> Slope Uruguay 0.003837500 1.590936183 -0.0041356338
#> Curvature Uruguay 0.005915993 -0.004135634 0.2377087317
#>