Provides posterior mean, standard deviations, as well as 5 and 95 percentiles of the parameters: autoregressive parameters \(\mathbf{A}\), and the covariance matrix \(\Sigma\).
Usage
# S3 method for class 'PosteriorBVAR'
summary(object, ...)Arguments
- object
an object of class PosteriorBVAR obtained using the
estimate()function applied to a Bayesian VAR model specification set by functionspecify_bvar$new()containing draws from the posterior distribution of the parameters.- ...
additional arguments affecting the summary produced.
Value
A list reporting the posterior mean, standard deviations, as well as 5 and 95 percentiles of the parameters: autoregressive parameters \(\mathbf{A}\), and the covariance matrix \(\Sigma\)..
Author
Tomasz Woźniak wozniak.tom@pm.me
Examples
# simple workflow
############################################################
spec = specify_bvar$new(us_macro_chan) # specify the model
burn = estimate(spec, 5) # run the burn-in
#> **************************************************|
#> bvars: Forecasting with Large |
#> Bayesian Vector Autoregressions |
#> **************************************************|
#> Gibbs sampler for the BVAR model |
#> **************************************************|
#> Progress of the MCMC simulation for 5 draws
#> Every draw is saved via MCMC thinning
#> Press Esc to interrupt the computations
#> **************************************************|
post = estimate(burn, 10) # estimate the model
#> **************************************************|
#> bvars: Forecasting with Large |
#> Bayesian Vector Autoregressions |
#> **************************************************|
#> Gibbs sampler for the BVAR model |
#> **************************************************|
#> Progress of the MCMC simulation for 10 draws
#> Every draw is saved via MCMC thinning
#> Press Esc to interrupt the computations
#> **************************************************|
summary(post)
#> $A
#> $A$equation1
#> mean sd 5% quantile 95% quantile
#> lag1_var1 0.35419970 0.11362600 0.21411090 0.511461718
#> lag1_var2 -0.12159478 0.24194279 -0.51924801 0.143508256
#> lag1_var3 -0.26280585 0.20190460 -0.51576998 0.045860331
#> lag1_var4 0.15094428 0.04666814 0.10201603 0.230555111
#> lag1_var5 0.09147052 0.03903512 0.03678679 0.143493954
#> lag1_var6 -0.02116092 0.06857528 -0.10949860 0.086609423
#> lag1_var7 0.03871308 0.05821355 -0.02532238 0.114758237
#> lag1_var8 0.40485853 0.20018661 0.14771340 0.706077119
#> lag1_var9 1.60330024 0.86141076 0.16945795 2.544003932
#> lag1_var10 -0.03425140 0.04086826 -0.09698792 0.009047624
#> lag1_var11 -0.03075890 0.19014029 -0.28533492 0.222693644
#> lag1_var12 0.07047461 0.06387961 -0.01327710 0.146703255
#> lag1_var13 -0.08549023 0.04272740 -0.15139998 -0.035284380
#> lag1_var14 0.16265397 0.26562662 -0.18892480 0.521160602
#> lag1_var15 -0.05194019 0.01373230 -0.07237971 -0.036780772
#> lag1_var16 0.07068746 0.19290076 -0.20050205 0.314753911
#> lag1_var17 0.01732279 0.08625260 -0.08216622 0.136587058
#> lag1_var18 0.06180207 0.06005137 -0.03355544 0.124578444
#> lag1_var19 -0.18905609 0.10222214 -0.35578191 -0.078978223
#> lag1_var20 0.09632399 0.02101309 0.06974737 0.123320691
#> const -16.41417859 6.02398207 -26.07475950 -9.699204935
#>
#> $A$equation2
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.021269021 0.08510005 -0.130122307 0.0989424250
#> lag1_var2 0.560317630 0.06804340 0.490154761 0.6673735664
#> lag1_var3 0.377380186 0.11831327 0.218879691 0.5408001601
#> lag1_var4 0.038593972 0.03720099 -0.015095507 0.0894104028
#> lag1_var5 0.085362829 0.06368998 -0.015706775 0.1585012401
#> lag1_var6 0.027751498 0.06510312 -0.057039053 0.1255220473
#> lag1_var7 0.012400256 0.02660549 -0.020858926 0.0526721393
#> lag1_var8 0.123551151 0.10762149 -0.001438232 0.2849675706
#> lag1_var9 0.381078760 0.45506979 -0.026564808 1.1109664248
#> lag1_var10 0.004065788 0.02617459 -0.030520772 0.0435356674
#> lag1_var11 -0.014271242 0.09133857 -0.139870254 0.0970274811
#> lag1_var12 0.115341253 0.03627183 0.074868042 0.1711421946
#> lag1_var13 0.046280159 0.03129465 0.006356045 0.0900895536
#> lag1_var14 -0.337796900 0.14510488 -0.544247630 -0.1400383317
#> lag1_var15 -0.017240988 0.01133210 -0.029695363 -0.0006217526
#> lag1_var16 -0.055262470 0.09362383 -0.181692757 0.0735775016
#> lag1_var17 0.040770387 0.06250247 -0.040007994 0.1359556126
#> lag1_var18 0.018426194 0.03741846 -0.038261813 0.0585412602
#> lag1_var19 0.025732152 0.03705966 -0.017965968 0.0768961076
#> lag1_var20 -0.002145717 0.01213379 -0.020656947 0.0089650420
#> const -6.350210852 4.27817165 -12.654062615 -0.9152278037
#>
#> $A$equation3
#> mean sd 5% quantile 95% quantile
#> lag1_var1 0.0325087363 0.030943788 0.004869687 0.080322383
#> lag1_var2 -0.1350965796 0.047325744 -0.202344909 -0.074418903
#> lag1_var3 0.8848034715 0.041134838 0.828573237 0.939606378
#> lag1_var4 0.0135420445 0.012696730 -0.001210454 0.032411770
#> lag1_var5 0.0001794308 0.030522471 -0.042662340 0.038706883
#> lag1_var6 0.0194106158 0.036550706 -0.030668009 0.066064224
#> lag1_var7 -0.0014740281 0.019542064 -0.018690332 0.030820059
#> lag1_var8 -0.1400585601 0.041059930 -0.197518687 -0.081963611
#> lag1_var9 -0.0095506867 0.330229438 -0.466988094 0.404452122
#> lag1_var10 0.0254910871 0.012653582 0.005452468 0.040946506
#> lag1_var11 0.1740161755 0.070769769 0.096764040 0.286625957
#> lag1_var12 0.0166331302 0.023560660 -0.011633673 0.050825244
#> lag1_var13 0.0293275439 0.006080890 0.020990759 0.036836610
#> lag1_var14 0.1161539299 0.053480730 0.052719089 0.201888036
#> lag1_var15 -0.0039861089 0.004824445 -0.011806520 0.001284782
#> lag1_var16 -0.0125171955 0.050567805 -0.074718640 0.065478047
#> lag1_var17 0.0504299243 0.017918891 0.029730671 0.078014686
#> lag1_var18 -0.0032988336 0.008825758 -0.016608268 0.006800818
#> lag1_var19 -0.0274980968 0.013910792 -0.049313714 -0.014313460
#> lag1_var20 0.0252572067 0.008227037 0.017141706 0.039814770
#> const -2.2323367666 1.967682273 -4.672906348 0.712222157
#>
#> $A$equation4
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.092750368 0.09562933 -0.230960556 0.025562073
#> lag1_var2 -0.029091415 0.15940281 -0.174120404 0.241607206
#> lag1_var3 0.018131613 0.12778283 -0.164419310 0.180016477
#> lag1_var4 0.632318185 0.05001132 0.565939198 0.704222461
#> lag1_var5 0.088022186 0.06630738 0.004784234 0.170009191
#> lag1_var6 0.076856904 0.07124314 -0.003262389 0.186933257
#> lag1_var7 -0.057445839 0.05141180 -0.123000719 0.007862422
#> lag1_var8 0.501484812 0.15505743 0.307020192 0.717027764
#> lag1_var9 0.814232626 0.71358714 -0.014110657 1.716617282
#> lag1_var10 -0.036309173 0.03751104 -0.088323460 0.017634913
#> lag1_var11 0.145711916 0.29191950 -0.303758507 0.539094498
#> lag1_var12 0.032959677 0.04239409 -0.021846897 0.094549048
#> lag1_var13 -0.132142962 0.04534807 -0.191810280 -0.066756750
#> lag1_var14 -0.202842458 0.15569746 -0.389782410 0.006830091
#> lag1_var15 -0.008874423 0.01985666 -0.029396731 0.021763898
#> lag1_var16 0.180669784 0.13379493 -0.010908735 0.361419256
#> lag1_var17 0.016473496 0.06695200 -0.076130586 0.104342030
#> lag1_var18 -0.081692399 0.04225086 -0.135005180 -0.028018823
#> lag1_var19 0.040616883 0.09277125 -0.078265259 0.158296296
#> lag1_var20 0.010250206 0.02665738 -0.027567034 0.042319878
#> const -1.999058128 4.96240354 -8.775603877 4.552082875
#>
#> $A$equation5
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.04275951 0.10973634 -0.180042668 0.107212548
#> lag1_var2 -0.04443485 0.16449291 -0.269138499 0.153038483
#> lag1_var3 0.05825640 0.13161022 -0.141512827 0.198340704
#> lag1_var4 0.06390232 0.07129973 -0.045826562 0.143508133
#> lag1_var5 0.12790218 0.03117969 0.094833055 0.170710394
#> lag1_var6 0.13837197 0.08276764 0.032228456 0.258273819
#> lag1_var7 -0.07270700 0.04624966 -0.137179127 -0.013976327
#> lag1_var8 0.32350099 0.17362650 0.129931529 0.585829052
#> lag1_var9 1.01530902 0.76780403 -0.240325757 1.887883940
#> lag1_var10 0.02923935 0.06445928 -0.067248960 0.112321177
#> lag1_var11 0.35066928 0.22444016 0.074788629 0.670174216
#> lag1_var12 0.11927603 0.09737084 -0.020418517 0.255648286
#> lag1_var13 -0.09644726 0.03194593 -0.142913219 -0.055506536
#> lag1_var14 0.06148041 0.19453625 -0.132341246 0.353845916
#> lag1_var15 -0.01915309 0.01033654 -0.034609796 -0.006004937
#> lag1_var16 0.31531472 0.11152098 0.127688610 0.408175085
#> lag1_var17 0.14601316 0.08972047 0.011871985 0.242471418
#> lag1_var18 -0.01169536 0.06136998 -0.079366581 0.079288667
#> lag1_var19 0.06849585 0.07887940 -0.037921968 0.173503644
#> lag1_var20 0.03372189 0.04440989 -0.009754993 0.105345675
#> const -13.70190564 4.58857697 -18.526562450 -6.500648688
#>
#> $A$equation6
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.129956834 0.11843035 -0.309086268 -0.02555552
#> lag1_var2 -0.228979441 0.10531881 -0.384293744 -0.10983824
#> lag1_var3 -0.339072699 0.09525812 -0.455870757 -0.20059472
#> lag1_var4 0.122395774 0.05352510 0.052864741 0.19454637
#> lag1_var5 0.089170270 0.04887238 0.032456457 0.16260728
#> lag1_var6 0.132702433 0.07601133 0.025538474 0.23715776
#> lag1_var7 -0.053258621 0.04788754 -0.102930294 0.02136912
#> lag1_var8 0.231251198 0.12281956 0.072331750 0.41116697
#> lag1_var9 1.494093711 0.52890061 0.730210166 2.14042058
#> lag1_var10 -0.091267468 0.04393996 -0.148514379 -0.03246608
#> lag1_var11 0.157093078 0.16090751 -0.078600414 0.34870742
#> lag1_var12 0.004906817 0.06763304 -0.083331643 0.09008315
#> lag1_var13 -0.097717031 0.04087295 -0.137975777 -0.02915588
#> lag1_var14 0.297698447 0.19194540 0.039513040 0.55810770
#> lag1_var15 0.021240779 0.01267959 0.006792764 0.03963073
#> lag1_var16 0.294379708 0.17253295 0.038839583 0.49422670
#> lag1_var17 0.038471708 0.07315609 -0.059329232 0.12530023
#> lag1_var18 -0.043907860 0.04276176 -0.093184519 0.01022896
#> lag1_var19 0.034281021 0.08334989 -0.076552770 0.14312458
#> lag1_var20 0.068231714 0.01531775 0.042524026 0.08451540
#> const -9.455154355 3.17552954 -12.898636899 -4.20127308
#>
#> $A$equation7
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.24664672 0.15765702 -0.479076887 -0.02891070
#> lag1_var2 -0.03209439 0.30152338 -0.380837035 0.39177709
#> lag1_var3 -0.40718899 0.40006853 -0.823462495 0.19181912
#> lag1_var4 0.29983873 0.05911104 0.207985085 0.38058559
#> lag1_var5 0.13082163 0.16744224 -0.087028451 0.36790563
#> lag1_var6 0.13796304 0.14519887 -0.073151365 0.32647054
#> lag1_var7 0.43259972 0.05879793 0.357209554 0.50707319
#> lag1_var8 0.33805193 0.33888036 0.009656142 0.93834044
#> lag1_var9 0.92030274 1.24967471 -0.862620575 2.63936953
#> lag1_var10 -0.12020885 0.07415036 -0.242283108 -0.04712017
#> lag1_var11 0.30132336 0.32216981 -0.062935577 0.76305628
#> lag1_var12 -0.33362864 0.13368285 -0.552488202 -0.20149718
#> lag1_var13 -0.12699249 0.09161103 -0.267541399 -0.01535424
#> lag1_var14 0.31789953 0.51052234 -0.427948649 0.85143364
#> lag1_var15 -0.03407176 0.03100027 -0.068014709 0.01680385
#> lag1_var16 -0.04170498 0.24832732 -0.378088396 0.35060620
#> lag1_var17 0.08635743 0.15109114 -0.076442512 0.31476911
#> lag1_var18 0.17533005 0.12623499 -0.014251557 0.34201569
#> lag1_var19 0.02067282 0.13894329 -0.160566661 0.21639299
#> lag1_var20 0.24749305 0.05810175 0.167548072 0.31864230
#> const -22.39953577 7.24970102 -32.646722244 -13.44298039
#>
#> $A$equation8
#> mean sd 5% quantile 95% quantile
#> lag1_var1 0.0004124076 0.006630665 -0.0089621407 0.0098109468
#> lag1_var2 0.0131489693 0.012767828 -0.0027343423 0.0302252666
#> lag1_var3 0.0098600985 0.017004173 -0.0136355643 0.0327593422
#> lag1_var4 -0.0036543669 0.003107241 -0.0072182631 0.0014671234
#> lag1_var5 -0.0026502681 0.006777222 -0.0144068294 0.0036212186
#> lag1_var6 -0.0128948723 0.007221602 -0.0222021619 -0.0019137081
#> lag1_var7 -0.0087132786 0.003183460 -0.0125109169 -0.0041417888
#> lag1_var8 0.9253123970 0.014974152 0.9039377340 0.9436177035
#> lag1_var9 -0.1841405304 0.061964871 -0.2784358010 -0.1201409332
#> lag1_var10 -0.0034503863 0.003528276 -0.0081956361 0.0009837926
#> lag1_var11 -0.0104846499 0.017309284 -0.0312733230 0.0167775300
#> lag1_var12 0.0180779868 0.005723344 0.0117572640 0.0257333028
#> lag1_var13 0.0032363970 0.004562802 -0.0003398126 0.0113092442
#> lag1_var14 0.0084434288 0.020337918 -0.0223047112 0.0324282028
#> lag1_var15 0.0010188428 0.001139512 -0.0008899512 0.0022438131
#> lag1_var16 -0.0621735669 0.014288848 -0.0806585901 -0.0401219807
#> lag1_var17 0.0009022824 0.005398840 -0.0071332331 0.0080345501
#> lag1_var18 -0.0052019479 0.005259728 -0.0102299370 0.0038989652
#> lag1_var19 0.0081318289 0.007022147 -0.0035680182 0.0159203881
#> lag1_var20 -0.0106184336 0.002206712 -0.0131291740 -0.0075157825
#> const 2.0344221857 0.425776959 1.5352562528 2.6644359382
#>
#> $A$equation9
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.0060797584 0.0034314899 -1.106175e-02 -1.611690e-03
#> lag1_var2 0.0001856269 0.0067513770 -1.084521e-02 8.026682e-03
#> lag1_var3 -0.0162907792 0.0052302753 -2.304987e-02 -8.086772e-03
#> lag1_var4 0.0038520876 0.0020843681 1.019782e-03 6.405968e-03
#> lag1_var5 0.0026915090 0.0026228276 -1.734607e-03 5.357624e-03
#> lag1_var6 0.0032928550 0.0031996675 -1.031660e-03 7.481206e-03
#> lag1_var7 -0.0018759496 0.0024855929 -4.849041e-03 1.893317e-03
#> lag1_var8 0.0086360373 0.0065725423 -6.692062e-04 1.628412e-02
#> lag1_var9 0.9879603062 0.0455788308 9.368075e-01 1.057708e+00
#> lag1_var10 -0.0005797765 0.0023607581 -4.327636e-03 1.843865e-03
#> lag1_var11 0.0011776256 0.0097241710 -1.323160e-02 1.296239e-02
#> lag1_var12 -0.0014555026 0.0020475540 -4.686795e-03 6.567160e-04
#> lag1_var13 -0.0022399126 0.0017201474 -4.686154e-03 -6.486133e-05
#> lag1_var14 0.0144766518 0.0073254863 3.379746e-03 2.384598e-02
#> lag1_var15 0.0008239220 0.0006163463 2.546006e-05 1.605107e-03
#> lag1_var16 0.0091513196 0.0070446758 -1.008845e-03 1.691191e-02
#> lag1_var17 -0.0045037106 0.0026872601 -8.445641e-03 -8.762126e-04
#> lag1_var18 0.0003661522 0.0015859648 -1.753509e-03 2.587347e-03
#> lag1_var19 0.0019564538 0.0016705746 1.131556e-04 4.334187e-03
#> lag1_var20 0.0024431260 0.0007826173 1.407368e-03 3.605120e-03
#> const 0.2039056947 0.3168141962 -3.327033e-01 5.178114e-01
#>
#> $A$equation10
#> mean sd 5% quantile 95% quantile
#> lag1_var1 0.02591895 0.25497176 -0.35233248 0.337682603
#> lag1_var2 0.20233779 0.29790586 -0.20282189 0.535302809
#> lag1_var3 0.65730283 0.31114045 0.24517220 1.027449400
#> lag1_var4 0.00114317 0.04929073 -0.07935261 0.049573949
#> lag1_var5 0.20282341 0.16844684 -0.06662570 0.379358276
#> lag1_var6 0.18855057 0.13771821 0.02646512 0.350341403
#> lag1_var7 0.02832629 0.07242831 -0.05758138 0.128722157
#> lag1_var8 0.82685769 0.33232293 0.42402255 1.250502706
#> lag1_var9 1.69521684 1.29578321 0.09198579 3.735523477
#> lag1_var10 0.32807547 0.07596055 0.23233689 0.438191507
#> lag1_var11 0.08992885 0.33925730 -0.32315595 0.618326768
#> lag1_var12 0.14141826 0.08189946 0.06106409 0.273768334
#> lag1_var13 -0.07502527 0.07345252 -0.17239920 0.025225930
#> lag1_var14 -1.11518412 0.42819957 -1.56053653 -0.501759651
#> lag1_var15 -0.03330320 0.02411639 -0.05938233 0.004399135
#> lag1_var16 -0.28748315 0.24789545 -0.66694888 0.003776529
#> lag1_var17 0.14220655 0.13812628 -0.03858438 0.336550693
#> lag1_var18 -0.05431729 0.09687387 -0.20284237 0.069821878
#> lag1_var19 0.10656190 0.11757366 -0.05767706 0.262891796
#> lag1_var20 -0.04595432 0.04457127 -0.10949269 0.013395655
#> const -18.95839296 8.70038970 -31.58236238 -9.404525909
#>
#> $A$equation11
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.020467590 0.061988685 -0.110974282 0.0636139198
#> lag1_var2 -0.005587384 0.052107702 -0.064846600 0.0783826698
#> lag1_var3 0.231878858 0.098099682 0.097989704 0.3570437232
#> lag1_var4 0.005410865 0.017835026 -0.015864428 0.0335836844
#> lag1_var5 0.056929501 0.045020326 -0.008461710 0.1079036535
#> lag1_var6 0.009511692 0.049721376 -0.056954349 0.0807514090
#> lag1_var7 -0.011619351 0.020956133 -0.043301958 0.0081132504
#> lag1_var8 0.164889554 0.079927389 0.080648887 0.2874557828
#> lag1_var9 0.404541652 0.273292051 0.039110524 0.7840929538
#> lag1_var10 -0.010400964 0.021534631 -0.037702731 0.0141901528
#> lag1_var11 0.649946894 0.071410030 0.550561065 0.7596750785
#> lag1_var12 0.112007994 0.035251669 0.071716159 0.1635212980
#> lag1_var13 0.019135393 0.019626997 -0.005902121 0.0465860754
#> lag1_var14 -0.236236715 0.115398169 -0.348185331 -0.0619325843
#> lag1_var15 -0.008754652 0.007291469 -0.017817746 0.0006885076
#> lag1_var16 0.029899168 0.086890017 -0.083128802 0.1452517299
#> lag1_var17 0.021907465 0.043689134 -0.036716659 0.0803863898
#> lag1_var18 0.005972599 0.030561411 -0.026350362 0.0543853650
#> lag1_var19 0.027875703 0.035542332 -0.016078588 0.0829280482
#> lag1_var20 0.000336497 0.013133687 -0.017369459 0.0170254035
#> const -4.919480865 2.086011033 -7.895000284 -2.3176095228
#>
#> $A$equation12
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.084003334 0.05311851 -0.16954634 -0.025166596
#> lag1_var2 0.183330369 0.16270520 -0.05291341 0.388193266
#> lag1_var3 -0.083886683 0.09899357 -0.20743316 0.065103538
#> lag1_var4 0.177074819 0.06153347 0.09278007 0.254676196
#> lag1_var5 0.056201984 0.08503781 -0.06535484 0.148984755
#> lag1_var6 0.002918037 0.09650256 -0.12120818 0.139894762
#> lag1_var7 -0.012758748 0.03392046 -0.05751825 0.033296829
#> lag1_var8 -0.080304962 0.16168157 -0.27383105 0.145283890
#> lag1_var9 0.645302429 0.51331610 -0.11259754 1.371093071
#> lag1_var10 -0.137054324 0.05210843 -0.22622933 -0.080395380
#> lag1_var11 0.543330244 0.14978576 0.37599824 0.747004644
#> lag1_var12 0.231715788 0.08886223 0.08812668 0.331585182
#> lag1_var13 -0.026111791 0.01991632 -0.04803327 0.005662619
#> lag1_var14 0.020136052 0.16991924 -0.19467415 0.276962789
#> lag1_var15 -0.007240917 0.01418793 -0.02448716 0.015351203
#> lag1_var16 -0.038149221 0.09625800 -0.18603935 0.066020023
#> lag1_var17 0.053758453 0.05366921 -0.02193014 0.129420889
#> lag1_var18 -0.004681185 0.04762874 -0.07208765 0.052004823
#> lag1_var19 0.059619373 0.06765482 -0.03569944 0.147801709
#> lag1_var20 -0.014344388 0.01564532 -0.03788930 0.001684893
#> const -6.527434319 3.39037038 -10.86250381 -1.761832367
#>
#> $A$equation13
#> mean sd 5% quantile 95% quantile
#> lag1_var1 0.0025406005 0.17849910 -0.216557128 0.28728234
#> lag1_var2 0.2350603048 0.20096759 -0.067855785 0.45965301
#> lag1_var3 -0.4163764795 0.14684087 -0.590666253 -0.22618220
#> lag1_var4 -0.0439620442 0.08969069 -0.174995387 0.05860575
#> lag1_var5 -0.1166646820 0.08673993 -0.208603170 0.01088606
#> lag1_var6 0.1203143628 0.14973550 -0.074188271 0.30642950
#> lag1_var7 -0.1445278569 0.05683757 -0.219432772 -0.06097674
#> lag1_var8 0.6393566643 0.36884803 0.068600509 1.13601901
#> lag1_var9 -0.1270163417 1.61791612 -2.100816439 2.36210297
#> lag1_var10 -0.0004350951 0.10553596 -0.146075661 0.15116288
#> lag1_var11 0.0468000430 0.39773525 -0.332429846 0.70906277
#> lag1_var12 0.0240933456 0.08860758 -0.129082109 0.09797820
#> lag1_var13 0.5474603522 0.06919941 0.434197380 0.61608943
#> lag1_var14 0.2761440947 0.24242330 0.008291203 0.68009988
#> lag1_var15 0.0019771846 0.02394863 -0.034706029 0.03088619
#> lag1_var16 0.3009234381 0.27472834 -0.061458733 0.68948223
#> lag1_var17 0.1286862716 0.10281798 -0.016624719 0.26624483
#> lag1_var18 -0.1697734044 0.14944090 -0.379216033 0.04610592
#> lag1_var19 0.0201740817 0.09918834 -0.103159355 0.17736489
#> lag1_var20 -0.0162442010 0.02056537 -0.044849741 0.01374636
#> const 2.0181330884 9.74453861 -13.864639730 12.52384040
#>
#> $A$equation14
#> mean sd 5% quantile 95% quantile
#> lag1_var1 0.0150659185 0.019063453 -0.0130624921 0.036605710
#> lag1_var2 0.0172073269 0.017617321 -0.0090059645 0.039904032
#> lag1_var3 0.0594529600 0.038388566 0.0178830993 0.115080323
#> lag1_var4 0.0008778420 0.005749101 -0.0061158099 0.009901907
#> lag1_var5 0.0033409805 0.012819918 -0.0098983314 0.022873276
#> lag1_var6 -0.0053663800 0.022541050 -0.0260292722 0.030361293
#> lag1_var7 -0.0149697909 0.006093171 -0.0221267819 -0.005348161
#> lag1_var8 0.0278310190 0.040588824 -0.0383778872 0.075291048
#> lag1_var9 0.0309151694 0.115856767 -0.1137028325 0.196921156
#> lag1_var10 0.0009313069 0.007298469 -0.0080905671 0.011444267
#> lag1_var11 -0.0114354288 0.033032384 -0.0611240506 0.035040033
#> lag1_var12 0.0309126288 0.013605031 0.0137327636 0.045866306
#> lag1_var13 0.0073363615 0.004333032 0.0025835463 0.014105656
#> lag1_var14 0.8923543533 0.045150233 0.8318529668 0.954494614
#> lag1_var15 -0.0040777326 0.002181552 -0.0068616394 -0.001319067
#> lag1_var16 0.0366984851 0.027131555 -0.0009166515 0.070788650
#> lag1_var17 0.0058881948 0.016628464 -0.0108876828 0.033128190
#> lag1_var18 0.0055716178 0.013053845 -0.0174104227 0.017380020
#> lag1_var19 0.0055192867 0.008573570 -0.0061101961 0.016420983
#> lag1_var20 0.0130513220 0.003834081 0.0087448535 0.018769215
#> const -0.9262155520 0.835038341 -1.9786520710 0.114652443
#>
#> $A$equation15
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -1.54649073 0.29821716 -1.98218856 -1.1362077
#> lag1_var2 0.40598521 0.76290665 -0.71191146 1.2698323
#> lag1_var3 -0.77389148 0.97157916 -1.94459453 0.7089167
#> lag1_var4 0.50525054 0.18618805 0.30273384 0.7746230
#> lag1_var5 0.12258499 0.33130104 -0.32298698 0.5648115
#> lag1_var6 2.28761201 0.32053032 1.85799674 2.6880991
#> lag1_var7 0.28832672 0.27578405 -0.14150217 0.6145886
#> lag1_var8 1.27246417 0.80764290 0.61056695 2.6267611
#> lag1_var9 2.78473919 4.85022511 -3.30867610 8.9370018
#> lag1_var10 -0.09504287 0.13949372 -0.23721226 0.1137852
#> lag1_var11 0.12183134 0.71573749 -0.88627075 1.0729383
#> lag1_var12 -0.01343685 0.24326175 -0.31180203 0.3598755
#> lag1_var13 -0.16314120 0.19935753 -0.42473864 0.1425204
#> lag1_var14 0.33030699 1.10470370 -1.24327093 1.5690758
#> lag1_var15 0.25717336 0.08557728 0.11479821 0.3541115
#> lag1_var16 -0.85034198 0.50226389 -1.54267012 -0.1630625
#> lag1_var17 -0.02525218 0.32105986 -0.42768711 0.4690208
#> lag1_var18 0.61593970 0.35253887 0.04620528 0.9872413
#> lag1_var19 -0.75072867 0.44980745 -1.46158411 -0.2283866
#> lag1_var20 0.60109551 0.10561133 0.46197993 0.7442308
#> const -61.71360760 37.91638427 -121.46662310 -23.3113132
#>
#> $A$equation16
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.070681191 0.056097374 -0.124865095 0.0062359239
#> lag1_var2 -0.069089856 0.054710327 -0.132474495 0.0110997235
#> lag1_var3 -0.119451150 0.066557119 -0.216202699 -0.0392776027
#> lag1_var4 0.057725669 0.014942829 0.044579895 0.0809071342
#> lag1_var5 0.027120948 0.033965545 -0.018702274 0.0709669520
#> lag1_var6 0.072819632 0.047089340 0.007275183 0.1420340116
#> lag1_var7 0.010427274 0.012445799 -0.001856770 0.0290517113
#> lag1_var8 0.110787716 0.050948020 0.037015508 0.1798230706
#> lag1_var9 0.441250645 0.309646486 0.007875196 0.8713048451
#> lag1_var10 -0.015768923 0.017874556 -0.038385117 0.0088094110
#> lag1_var11 0.136984208 0.070748906 0.033019994 0.2030517177
#> lag1_var12 -0.027687534 0.031885996 -0.077643709 0.0005198616
#> lag1_var13 -0.018314765 0.015693551 -0.043474415 -0.0026543723
#> lag1_var14 0.083074001 0.106204066 -0.045184676 0.1980274979
#> lag1_var15 -0.006502467 0.005512051 -0.013166839 0.0019231692
#> lag1_var16 0.722825521 0.058955830 0.648008656 0.8086634399
#> lag1_var17 0.023908597 0.036308177 -0.018450584 0.0793535953
#> lag1_var18 0.022602175 0.026019372 -0.011613348 0.0600087647
#> lag1_var19 0.004591672 0.037923370 -0.054169883 0.0495486917
#> lag1_var20 0.055325705 0.010287021 0.040171101 0.0667473530
#> const -6.400188396 1.572262702 -8.195826283 -3.9452094062
#>
#> $A$equation17
#> mean sd 5% quantile 95% quantile
#> lag1_var1 0.09528958 0.14299107 -0.06417373 0.322273969
#> lag1_var2 -0.02742160 0.19210142 -0.35958934 0.173240609
#> lag1_var3 -0.34984759 0.13044900 -0.56054922 -0.194436877
#> lag1_var4 0.11568326 0.05491900 0.04141556 0.183899474
#> lag1_var5 0.08493488 0.16396370 -0.11878551 0.346889387
#> lag1_var6 0.09498583 0.12264339 -0.05413523 0.291124713
#> lag1_var7 -0.06096157 0.03561049 -0.09842134 -0.005495028
#> lag1_var8 0.52036237 0.21254496 0.18075864 0.754730290
#> lag1_var9 2.42461976 0.61385768 1.48800360 3.139858973
#> lag1_var10 -0.06753488 0.04996088 -0.13448450 -0.010925242
#> lag1_var11 0.16863249 0.28061542 -0.18379068 0.520457854
#> lag1_var12 -0.04834024 0.10785137 -0.20371776 0.109479441
#> lag1_var13 -0.02419105 0.03956924 -0.07900595 0.026136841
#> lag1_var14 0.02288001 0.18107567 -0.19531868 0.316071856
#> lag1_var15 -0.03775170 0.02218664 -0.07345790 -0.014447662
#> lag1_var16 -0.14105829 0.12855394 -0.27267734 0.046661906
#> lag1_var17 0.79656013 0.06846283 0.70505594 0.886647427
#> lag1_var18 0.04548359 0.07270437 -0.05422364 0.133291152
#> lag1_var19 0.04285568 0.08831195 -0.08096791 0.164596887
#> lag1_var20 0.16337521 0.03405850 0.11254631 0.206041473
#> const -12.27112755 5.56711140 -19.31003192 -4.444308517
#>
#> $A$equation18
#> mean sd 5% quantile 95% quantile
#> lag1_var1 0.10303822 0.18347279 -0.03343237 0.437863153
#> lag1_var2 -0.09292317 0.24940467 -0.44236667 0.248371734
#> lag1_var3 -0.45984001 0.19582440 -0.76333304 -0.225422152
#> lag1_var4 0.13437381 0.08962463 0.02568225 0.258298114
#> lag1_var5 0.11412469 0.18435759 -0.13118204 0.408656477
#> lag1_var6 -0.00571924 0.17238576 -0.28761211 0.219941446
#> lag1_var7 -0.10425606 0.05098749 -0.16350107 -0.025343797
#> lag1_var8 0.92230354 0.34679526 0.35577543 1.325824568
#> lag1_var9 4.19349802 0.94011531 2.91182663 5.354938661
#> lag1_var10 -0.14467926 0.08343515 -0.26120208 -0.041167029
#> lag1_var11 0.25688008 0.32609851 -0.17496547 0.700814064
#> lag1_var12 -0.03820904 0.12396104 -0.22692872 0.129739115
#> lag1_var13 -0.04453459 0.04262023 -0.10754604 0.000754335
#> lag1_var14 -0.12730677 0.22188480 -0.44530255 0.167587131
#> lag1_var15 -0.04559811 0.02836054 -0.08511610 -0.011606323
#> lag1_var16 0.08086579 0.23625087 -0.19539840 0.449462004
#> lag1_var17 -0.10371042 0.07069968 -0.20338157 -0.001111373
#> lag1_var18 0.74204894 0.07963663 0.62325832 0.825818355
#> lag1_var19 0.11853373 0.10726260 -0.03572334 0.252895929
#> lag1_var20 0.16643439 0.04180766 0.10281281 0.217023118
#> const -14.56782782 8.55739697 -24.30220732 -2.992734597
#>
#> $A$equation19
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.27163918 0.12666577 -0.45974162 -0.12286700
#> lag1_var2 -0.06970842 0.20646061 -0.35833235 0.14127778
#> lag1_var3 -0.27488533 0.31893054 -0.67861147 0.15269200
#> lag1_var4 0.16133558 0.07294953 0.07454031 0.27345810
#> lag1_var5 0.16070105 0.04957570 0.08631813 0.21751726
#> lag1_var6 -0.15493920 0.08503284 -0.26411071 -0.03817760
#> lag1_var7 0.04657679 0.08740143 -0.06714258 0.17696230
#> lag1_var8 0.11717594 0.28367183 -0.18425790 0.54249067
#> lag1_var9 1.12861566 1.11667974 -0.30338906 2.72598945
#> lag1_var10 -0.04999956 0.04562147 -0.11357066 0.01811492
#> lag1_var11 -0.14313530 0.26251694 -0.50747491 0.10757816
#> lag1_var12 0.07399609 0.08870724 -0.05896932 0.16597744
#> lag1_var13 -0.09063807 0.05179995 -0.16128804 -0.02392218
#> lag1_var14 0.17006397 0.38423869 -0.38720599 0.59810346
#> lag1_var15 -0.03691969 0.02377912 -0.07569685 -0.01133743
#> lag1_var16 -0.07515164 0.25914495 -0.43778334 0.31138148
#> lag1_var17 0.03594174 0.11018900 -0.10519574 0.19304491
#> lag1_var18 -0.00129585 0.10997288 -0.14531374 0.14456919
#> lag1_var19 0.27674446 0.10259924 0.12291314 0.39695927
#> lag1_var20 0.06905636 0.03472215 0.02836874 0.12123654
#> const -8.26497338 7.87981441 -18.74266912 0.24971518
#>
#> $A$equation20
#> mean sd 5% quantile 95% quantile
#> lag1_var1 0.049974651 0.22568543 -0.23534673 0.37524690
#> lag1_var2 0.067707847 0.33372415 -0.49068353 0.44897406
#> lag1_var3 -0.195497962 0.37546110 -0.68294713 0.20194168
#> lag1_var4 -0.136240713 0.21945026 -0.47007623 0.11501706
#> lag1_var5 0.043543117 0.22883434 -0.27277352 0.36192018
#> lag1_var6 -0.041479686 0.23375962 -0.33833535 0.27698834
#> lag1_var7 0.020438095 0.10726965 -0.10214140 0.19630240
#> lag1_var8 1.075661108 0.46286462 0.42565269 1.65207302
#> lag1_var9 3.558081266 2.67699349 0.19259945 7.41853154
#> lag1_var10 -0.040628741 0.11508244 -0.16250710 0.13867419
#> lag1_var11 -0.327924094 0.38709415 -0.97384943 0.08216318
#> lag1_var12 0.053735144 0.19553092 -0.18362659 0.34055695
#> lag1_var13 -0.093297634 0.06974003 -0.17189543 0.01357544
#> lag1_var14 -0.122241414 0.39563900 -0.73152477 0.32726686
#> lag1_var15 -0.008091921 0.04530104 -0.05890435 0.06628940
#> lag1_var16 0.425120571 0.41706114 -0.11402573 1.03442121
#> lag1_var17 -0.207101830 0.12489009 -0.39117611 -0.05461351
#> lag1_var18 -0.164509882 0.17427814 -0.38263726 0.07083722
#> lag1_var19 0.044176970 0.17815118 -0.19000064 0.29984651
#> lag1_var20 0.371716072 0.03828080 0.32569100 0.42850818
#> const -8.873843639 17.31270796 -33.77623730 13.57184191
#>
#>
#> $Sigma
#> $Sigma$equation1
#> mean sd 5% quantile 95% quantile
#> Sigma[1,1] 7.413292 0.7154813 6.582579 8.36803
#>
#> $Sigma$equation2
#> mean sd 5% quantile 95% quantile
#> Sigma[2,1] -0.03844276 0.4069480 -0.5724351 0.5321264
#> Sigma[2,2] 3.10437703 0.5924297 2.6761229 4.0503296
#>
#> $Sigma$equation3
#> mean sd 5% quantile 95% quantile
#> Sigma[3,1] 0.1335689 0.19711181 -0.1799316 0.3281224
#> Sigma[3,2] 0.3653324 0.08588461 0.2751085 0.4961856
#> Sigma[3,3] 0.5711259 0.06193658 0.5132313 0.6681668
#>
#> $Sigma$equation4
#> mean sd 5% quantile 95% quantile
#> Sigma[4,1] -0.1457497 0.50068719 -0.8204389 0.5159207
#> Sigma[4,2] -1.2329990 0.29556505 -1.7094610 -0.9121450
#> Sigma[4,3] -0.4624663 0.07518661 -0.5752525 -0.3699053
#> Sigma[4,4] 5.4455894 0.46075085 4.8708998 6.0024319
#>
#> $Sigma$equation5
#> mean sd 5% quantile 95% quantile
#> Sigma[5,1] 2.29520566 0.5253712 1.7235565 3.0264052
#> Sigma[5,2] 1.05410029 0.3593039 0.6636401 1.6142939
#> Sigma[5,3] 0.28165353 0.1279016 0.1295851 0.4634986
#> Sigma[5,4] -0.02422082 0.5249175 -0.5813284 0.6546987
#> Sigma[5,5] 7.22925341 0.6678268 6.4419650 8.1487067
#>
#> $Sigma$equation6
#> mean sd 5% quantile 95% quantile
#> Sigma[6,1] 3.18697123 0.3931781 2.6525074575 3.77027234
#> Sigma[6,2] -0.38507382 0.3268220 -0.8818966162 0.06067955
#> Sigma[6,3] 0.03806831 0.1502393 -0.1123355665 0.29554014
#> Sigma[6,4] 0.46757743 0.3197781 -0.0008519541 0.84581595
#> Sigma[6,5] 2.26373030 0.3406683 1.7614170712 2.73041741
#> Sigma[6,6] 5.34461575 0.4805253 4.6875036689 5.93144978
#>
#> $Sigma$equation7
#> mean sd 5% quantile 95% quantile
#> Sigma[7,1] 6.6364850 1.1668199 5.4647802 8.399879
#> Sigma[7,2] 0.4306646 0.5105530 -0.1725787 1.107444
#> Sigma[7,3] 0.9036004 0.2010450 0.6298576 1.174184
#> Sigma[7,4] -0.7924827 0.9332299 -2.0342278 0.596330
#> Sigma[7,5] 4.8748972 0.9669891 3.6573161 6.299566
#> Sigma[7,6] 3.6820551 0.5339996 2.9376903 4.412172
#> Sigma[7,7] 19.5450698 1.8733355 17.8734188 22.809867
#>
#> $Sigma$equation8
#> mean sd 5% quantile 95% quantile
#> Sigma[8,1] -0.20122533 0.04433612 -0.27622932 -0.153078747
#> Sigma[8,2] -0.01411808 0.01586856 -0.03836829 0.004058617
#> Sigma[8,3] -0.04103159 0.01135593 -0.05298016 -0.024718423
#> Sigma[8,4] 0.01631114 0.03076761 -0.02742114 0.051802609
#> Sigma[8,5] -0.14283679 0.04607623 -0.20688605 -0.083431484
#> Sigma[8,6] -0.12636820 0.03242947 -0.16935771 -0.089361913
#> Sigma[8,7] -0.44001496 0.07529611 -0.53543050 -0.320022334
#> Sigma[8,8] 0.04018838 0.00310520 0.03498130 0.043537517
#>
#> $Sigma$equation9
#> mean sd 5% quantile 95% quantile
#> Sigma[9,1] 0.048501870 0.0189256545 0.024273275 0.071607214
#> Sigma[9,2] 0.003501677 0.0146914693 -0.015867983 0.024305084
#> Sigma[9,3] -0.006747986 0.0030910069 -0.010981560 -0.002863749
#> Sigma[9,4] 0.036793402 0.0115695795 0.019132663 0.050654686
#> Sigma[9,5] 0.058614648 0.0231862154 0.022925216 0.084913689
#> Sigma[9,6] 0.050372529 0.0179746812 0.024314743 0.073137062
#> Sigma[9,7] 0.082222644 0.0295749303 0.036027951 0.115057510
#> Sigma[9,8] -0.004519136 0.0015357778 -0.006899363 -0.002570876
#> Sigma[9,9] 0.009840341 0.0006238785 0.008882931 0.010515976
#>
#> $Sigma$equation10
#> mean sd 5% quantile 95% quantile
#> Sigma[10,1] -0.59031117 0.96569414 -1.87107330 0.66193298
#> Sigma[10,2] 5.45657092 1.34462526 4.27827841 7.72630639
#> Sigma[10,3] 0.55758368 0.21825842 0.31536790 0.88168261
#> Sigma[10,4] -2.42215149 0.70457323 -3.43284966 -1.56094460
#> Sigma[10,5] 1.98971402 0.83087040 1.02057382 3.28555329
#> Sigma[10,6] -0.47582649 0.99047566 -1.83640955 0.92840419
#> Sigma[10,7] 1.08960321 1.24080136 -0.80354897 2.41653156
#> Sigma[10,8] -0.06324168 0.05859988 -0.14637068 0.01441531
#> Sigma[10,9] 0.03527099 0.03165836 -0.01694858 0.07137792
#> Sigma[10,10] 18.91633436 3.00914452 15.79114767 24.13311491
#>
#> $Sigma$equation11
#> mean sd 5% quantile 95% quantile
#> Sigma[11,1] -0.09796035 0.260211096 -0.437510673 0.24724630
#> Sigma[11,2] 1.90516289 0.390973680 1.597490013 2.52695178
#> Sigma[11,3] 0.17180972 0.051850477 0.093505525 0.24184617
#> Sigma[11,4] -0.63154656 0.221091636 -0.979004389 -0.43304778
#> Sigma[11,5] 0.78231696 0.278242387 0.449689585 1.19918329
#> Sigma[11,6] -0.21123203 0.262636701 -0.585423525 0.12851874
#> Sigma[11,7] 0.38203202 0.480838620 -0.283875548 1.00564419
#> Sigma[11,8] -0.01043271 0.014642281 -0.025290815 0.01252973
#> Sigma[11,9] 0.01603583 0.009750047 0.001414747 0.02743974
#> Sigma[11,10] 4.13099740 0.868163915 3.309260694 5.57012611
#> Sigma[11,11] 1.64588776 0.256867752 1.411025873 2.04605462
#>
#> $Sigma$equation12
#> mean sd 5% quantile 95% quantile
#> Sigma[12,1] 0.98109113 0.40364813 0.544116755 1.62648669
#> Sigma[12,2] 0.19516793 0.37384853 -0.212325145 0.78806183
#> Sigma[12,3] 0.06494057 0.10787518 -0.073319622 0.21159996
#> Sigma[12,4] -0.01886418 0.49227111 -0.798697994 0.44865090
#> Sigma[12,5] 1.83473216 0.42766348 1.296178040 2.43219384
#> Sigma[12,6] 1.07372914 0.32372393 0.706576918 1.54280250
#> Sigma[12,7] 4.17565477 0.48431397 3.499312806 4.83409774
#> Sigma[12,8] -0.09191539 0.03156704 -0.133738769 -0.04515786
#> Sigma[12,9] 0.01515717 0.01542510 -0.001437679 0.03734110
#> Sigma[12,10] 0.92643552 0.94603973 -0.107945983 2.25393775
#> Sigma[12,11] 0.21170482 0.25098346 -0.101127705 0.59219409
#> Sigma[12,12] 4.90396296 0.59824765 4.303678480 5.91327761
#>
#> $Sigma$equation13
#> mean sd 5% quantile 95% quantile
#> Sigma[13,1] 0.14486069 0.86221155 -0.81919622 1.41336664
#> Sigma[13,2] -1.40139403 0.39703263 -1.96834909 -0.88071468
#> Sigma[13,3] -0.38771394 0.13682696 -0.51629261 -0.16675308
#> Sigma[13,4] 4.21418051 0.94658437 3.20496306 5.59657124
#> Sigma[13,5] 0.68007459 0.62008390 -0.17195573 1.48137874
#> Sigma[13,6] 0.84374870 0.53488769 0.09392834 1.52130838
#> Sigma[13,7] -0.01572477 1.42933843 -1.57993621 2.26789840
#> Sigma[13,8] -0.02484664 0.05534632 -0.09804504 0.05292033
#> Sigma[13,9] 0.03182085 0.02724624 -0.01114580 0.06179334
#> Sigma[13,10] -2.15854870 1.32841993 -4.16478090 -0.77489111
#> Sigma[13,11] -0.56750922 0.30675829 -0.97590140 -0.13892891
#> Sigma[13,12] -0.12991222 0.90658595 -1.49646221 0.95857970
#> Sigma[13,13] 13.15043703 1.63704982 11.32350509 15.75479772
#>
#> $Sigma$equation14
#> mean sd 5% quantile 95% quantile
#> Sigma[14,1] 0.123212924 0.114811210 -0.004702428 0.310116930
#> Sigma[14,2] 0.220774896 0.058206739 0.138900849 0.294965753
#> Sigma[14,3] 0.170355176 0.025043660 0.134389198 0.206089807
#> Sigma[14,4] -0.254810990 0.071718409 -0.360922395 -0.170412775
#> Sigma[14,5] 0.252361407 0.093587043 0.147209501 0.394400224
#> Sigma[14,6] 0.042905593 0.057008196 -0.039920433 0.101524285
#> Sigma[14,7] 0.582601389 0.171819076 0.296944160 0.781550098
#> Sigma[14,8] -0.026315796 0.006002370 -0.032797974 -0.017838472
#> Sigma[14,9] -0.001023969 0.003648462 -0.007001906 0.003029446
#> Sigma[14,10] 0.454245735 0.138099504 0.261568238 0.599760562
#> Sigma[14,11] 0.158873177 0.029135073 0.119533369 0.198612515
#> Sigma[14,12] 0.094475929 0.060247266 0.016798756 0.180229473
#> Sigma[14,13] -0.237596791 0.159360936 -0.413909803 0.001800730
#> Sigma[14,14] 0.194433388 0.016258319 0.176976667 0.218496184
#>
#> $Sigma$equation15
#> mean sd 5% quantile 95% quantile
#> Sigma[15,1] 24.2952200 3.80833001 20.326006401 30.4059409
#> Sigma[15,2] 0.7488056 1.67887903 -1.272326191 3.1679164
#> Sigma[15,3] 1.3086451 0.79725664 0.042580360 2.2670716
#> Sigma[15,4] -2.7724334 1.28095515 -4.284767492 -0.8897656
#> Sigma[15,5] 6.4360365 2.25031816 4.034957716 9.7707962
#> Sigma[15,6] 0.6450806 1.39767176 -1.362366703 2.5112769
#> Sigma[15,7] 31.2100654 5.75104715 26.510244679 40.4978029
#> Sigma[15,8] -0.9600663 0.22449657 -1.243910549 -0.6061383
#> Sigma[15,9] 0.0878317 0.05605431 -0.002979348 0.1493205
#> Sigma[15,10] -0.5702982 3.43234541 -4.950355826 4.1611547
#> Sigma[15,11] -0.2070623 1.09284586 -1.485314184 1.5750815
#> Sigma[15,12] 5.5537112 1.81625589 3.222077886 8.0861581
#> Sigma[15,13] -2.1429537 3.63793313 -5.552050401 3.8448476
#> Sigma[15,14] 1.0977212 0.48714712 0.381846387 1.7939196
#> Sigma[15,15] 165.2082375 18.68385705 147.228423988 194.0607534
#>
#> $Sigma$equation16
#> mean sd 5% quantile 95% quantile
#> Sigma[16,1] 1.49758853 0.282387256 1.116969262 1.89414160
#> Sigma[16,2] 0.17708751 0.138956968 0.017667051 0.38818045
#> Sigma[16,3] 0.15969792 0.054170070 0.087128491 0.23236814
#> Sigma[16,4] -0.05130294 0.135369913 -0.205929707 0.16979017
#> Sigma[16,5] 1.18652202 0.268966585 0.890698732 1.58872039
#> Sigma[16,6] 0.80705122 0.218020043 0.452223004 1.05671470
#> Sigma[16,7] 3.18319246 0.406047312 2.832192612 3.80789415
#> Sigma[16,8] -0.11330716 0.020098357 -0.139880809 -0.08675290
#> Sigma[16,9] 0.01914402 0.008634485 0.008069537 0.03021317
#> Sigma[16,10] 0.30138951 0.334504601 -0.106548141 0.80354179
#> Sigma[16,11] 0.08959040 0.104399547 -0.050553383 0.22955582
#> Sigma[16,12] 0.67056240 0.138062326 0.491202189 0.87177588
#> Sigma[16,13] 0.13811416 0.297037503 -0.199070555 0.61956512
#> Sigma[16,14] 0.08598079 0.037463119 0.046281252 0.14696528
#> Sigma[16,15] 6.19062527 1.241288886 4.936968146 8.26121227
#> Sigma[16,16] 1.00868772 0.119563543 0.905066097 1.19700652
#>
#> $Sigma$equation17
#> mean sd 5% quantile 95% quantile
#> Sigma[17,1] 3.29162897 0.69591708 2.33524240 4.28985082
#> Sigma[17,2] 0.64912325 0.31015023 0.28284326 1.13167563
#> Sigma[17,3] 0.53321725 0.15648451 0.31105118 0.73350180
#> Sigma[17,4] -0.58698372 0.67730667 -1.56463355 0.22605923
#> Sigma[17,5] 2.89628082 0.50244745 2.29259647 3.68828254
#> Sigma[17,6] 2.42133324 0.52417450 1.71367188 3.03381459
#> Sigma[17,7] 8.48172110 1.01188790 6.70280430 9.41798873
#> Sigma[17,8] -0.26466055 0.05773976 -0.34482103 -0.18188984
#> Sigma[17,9] 0.05156481 0.01559336 0.02852411 0.07023098
#> Sigma[17,10] 2.33464495 0.93890231 0.98892854 3.40847411
#> Sigma[17,11] 0.77296629 0.24078429 0.49147822 1.15346093
#> Sigma[17,12] 2.34376173 0.34070094 1.89314937 2.75855915
#> Sigma[17,13] 0.73680448 0.92326578 -0.39687236 2.16109957
#> Sigma[17,14] 0.56355663 0.10102544 0.40382225 0.69893650
#> Sigma[17,15] 13.92642963 2.74037424 10.60834160 17.87571727
#> Sigma[17,16] 1.75767696 0.25636567 1.46464261 2.15761126
#> Sigma[17,17] 9.12867140 0.95812817 7.76585686 10.30029233
#>
#> $Sigma$equation18
#> mean sd 5% quantile 95% quantile
#> Sigma[18,1] 4.55467860 0.90741998 3.24076536 5.79005096
#> Sigma[18,2] 1.01067361 0.48209631 0.46575816 1.77690861
#> Sigma[18,3] 0.52129448 0.24120868 0.21429524 0.85450288
#> Sigma[18,4] -1.17203482 0.99319382 -2.62596610 0.02945775
#> Sigma[18,5] 4.26147635 0.63981934 3.43769776 5.26563230
#> Sigma[18,6] 3.68094089 0.70161836 2.70354217 4.51879163
#> Sigma[18,7] 10.55263342 1.79356403 7.53687911 12.41311646
#> Sigma[18,8] -0.33017482 0.08010738 -0.43204891 -0.20783493
#> Sigma[18,9] 0.08520939 0.02316251 0.05245571 0.11710735
#> Sigma[18,10] 3.48841160 1.42134183 1.60117376 5.37810545
#> Sigma[18,11] 1.07436707 0.36666793 0.66162841 1.61335076
#> Sigma[18,12] 3.14676850 0.67871371 2.23593537 3.92567718
#> Sigma[18,13] 0.19614432 1.36609641 -1.59567496 2.02448574
#> Sigma[18,14] 0.78217271 0.12557717 0.61102062 0.95964790
#> Sigma[18,15] 16.89229277 3.51188745 12.80668089 22.42264419
#> Sigma[18,16] 2.17421805 0.37233856 1.72871287 2.73420635
#> Sigma[18,17] 11.35910270 1.32974465 9.56202897 12.87920688
#> Sigma[18,18] 17.16257398 1.95305198 14.92672967 19.87451729
#>
#> $Sigma$equation19
#> mean sd 5% quantile 95% quantile
#> Sigma[19,1] 6.68668498 0.69218471 5.79167994 7.62184624
#> Sigma[19,2] -0.74438482 0.41878903 -1.33404605 -0.20457978
#> Sigma[19,3] -0.03981262 0.19587341 -0.38097592 0.15382026
#> Sigma[19,4] -0.28527820 0.52519455 -0.93523940 0.42113417
#> Sigma[19,5] 1.07709149 0.54089096 0.49493044 1.88336051
#> Sigma[19,6] 2.97298388 0.50278235 2.31477587 3.73927214
#> Sigma[19,7] 4.62760277 1.09088125 3.44151451 6.44365933
#> Sigma[19,8] -0.10048089 0.04651191 -0.16442680 -0.04748144
#> Sigma[19,9] 0.01551264 0.02481490 -0.01521197 0.04918908
#> Sigma[19,10] -2.19328968 1.17906633 -3.96263042 -0.60854757
#> Sigma[19,11] -0.63027729 0.23525551 -0.96594351 -0.32920258
#> Sigma[19,12] 0.73865132 0.61664454 0.03751536 1.69907051
#> Sigma[19,13] 0.28302173 0.87313648 -0.73150482 1.59619246
#> Sigma[19,14] 0.03955571 0.10887308 -0.10049776 0.18967469
#> Sigma[19,15] 22.48704243 3.35870974 18.61412296 27.65436009
#> Sigma[19,16] 0.79877621 0.26154695 0.43650713 1.14477419
#> Sigma[19,17] 2.34287067 0.63690510 1.42053560 3.29359340
#> Sigma[19,18] 3.47692804 0.72836692 2.36372332 4.35824844
#> Sigma[19,19] 10.06141332 0.64113602 9.12480724 10.76137505
#>
#> $Sigma$equation20
#> mean sd 5% quantile 95% quantile
#> Sigma[20,1] 3.35333762 0.96088895 2.0181900 4.64665661
#> Sigma[20,2] 0.10644121 0.61396579 -0.8407382 0.73615355
#> Sigma[20,3] -0.17686156 0.35566537 -0.7021450 0.22331450
#> Sigma[20,4] -1.13791064 1.18125332 -2.9148428 0.09943390
#> Sigma[20,5] 2.50499811 1.05706713 1.3072006 4.09940157
#> Sigma[20,6] 3.51685964 0.84061917 2.4437604 4.85494028
#> Sigma[20,7] 1.84322728 1.77536002 -0.3487489 4.20948765
#> Sigma[20,8] -0.03300006 0.07030585 -0.1408836 0.05516828
#> Sigma[20,9] 0.08275343 0.04023947 0.0370710 0.14105406
#> Sigma[20,10] 1.42806266 1.91874312 -1.6606915 3.54986286
#> Sigma[20,11] -0.01186117 0.56671348 -0.9232361 0.54637418
#> Sigma[20,12] -0.04817238 0.99252939 -1.2032055 1.32868995
#> Sigma[20,13] -1.20754267 2.46115418 -5.0518271 1.34786639
#> Sigma[20,14] -0.27474085 0.11330401 -0.3832908 -0.10327252
#> Sigma[20,15] -0.29261571 6.22172038 -7.9263128 8.34551858
#> Sigma[20,16] 0.66153051 0.30418055 0.2673394 1.04411679
#> Sigma[20,17] 3.94609976 1.34799128 2.7651072 6.15777876
#> Sigma[20,18] 7.81709534 1.86660042 5.9891691 10.73447073
#> Sigma[20,19] 2.91311522 1.11776924 1.2704661 4.41168847
#> Sigma[20,20] 33.18038889 3.09536664 29.4582578 37.97053261
#>
#>
# workflow with the pipe |>
############################################################
us_macro_chan |>
specify_bvar$new() |>
estimate(S = 5) |>
estimate(S = 10) |>
summary()
#> **************************************************|
#> bvars: Forecasting with Large |
#> Bayesian Vector Autoregressions |
#> **************************************************|
#> Gibbs sampler for the BVAR model |
#> **************************************************|
#> Progress of the MCMC simulation for 5 draws
#> Every draw is saved via MCMC thinning
#> Press Esc to interrupt the computations
#> **************************************************|
#> **************************************************|
#> bvars: Forecasting with Large |
#> Bayesian Vector Autoregressions |
#> **************************************************|
#> Gibbs sampler for the BVAR model |
#> **************************************************|
#> Progress of the MCMC simulation for 10 draws
#> Every draw is saved via MCMC thinning
#> Press Esc to interrupt the computations
#> **************************************************|
#> $A
#> $A$equation1
#> mean sd 5% quantile 95% quantile
#> lag1_var1 3.182168e-01 0.09538114 0.150124140 0.41011423
#> lag1_var2 -1.383983e-01 0.09457902 -0.269423542 -0.02313075
#> lag1_var3 -3.302695e-01 0.16776764 -0.566027479 -0.10491087
#> lag1_var4 1.391474e-01 0.08445395 0.040889076 0.26328459
#> lag1_var5 7.749178e-02 0.09304165 -0.084321810 0.17628890
#> lag1_var6 1.019700e-01 0.09089422 -0.025194964 0.22826334
#> lag1_var7 2.500499e-02 0.05392116 -0.042106802 0.10440419
#> lag1_var8 1.738991e-01 0.27010419 -0.173699144 0.56848945
#> lag1_var9 1.401251e+00 0.93969983 -0.121364779 2.45303578
#> lag1_var10 -4.669271e-02 0.05151915 -0.108493245 0.01211875
#> lag1_var11 4.388871e-02 0.24096710 -0.244210152 0.41468733
#> lag1_var12 8.443598e-02 0.08522032 -0.009977851 0.22201634
#> lag1_var13 -5.775009e-02 0.04150074 -0.095555991 0.01374594
#> lag1_var14 2.332674e-01 0.18797681 -0.058669935 0.45193619
#> lag1_var15 -3.915113e-02 0.01480444 -0.052858995 -0.01299000
#> lag1_var16 9.504979e-04 0.14446353 -0.173867958 0.19137072
#> lag1_var17 4.005921e-03 0.06231723 -0.059737369 0.09751179
#> lag1_var18 6.174044e-02 0.05585477 -0.007804018 0.14128286
#> lag1_var19 -2.288993e-01 0.05622990 -0.320409829 -0.16850621
#> lag1_var20 1.037602e-01 0.02982358 0.070442928 0.14899724
#> const -1.314638e+01 7.39651525 -20.937731408 -1.68534341
#>
#> $A$equation2
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.033701233 0.05492644 -0.097703990 0.037902277
#> lag1_var2 0.533845180 0.11589124 0.373888390 0.687972260
#> lag1_var3 0.372610966 0.07398846 0.282870913 0.480606344
#> lag1_var4 0.024457050 0.03875575 -0.017644662 0.085339553
#> lag1_var5 0.102141599 0.04063544 0.051912517 0.159976839
#> lag1_var6 0.010495033 0.07523407 -0.069580256 0.138732925
#> lag1_var7 0.004379586 0.02609028 -0.029527125 0.038677318
#> lag1_var8 0.031394760 0.16381115 -0.148156785 0.280332755
#> lag1_var9 0.027426087 0.46774736 -0.576304371 0.676333123
#> lag1_var10 -0.008038135 0.04222323 -0.063572201 0.051916717
#> lag1_var11 0.020948014 0.10683520 -0.111106715 0.176051918
#> lag1_var12 0.111466826 0.02825756 0.071022067 0.145050459
#> lag1_var13 0.061884789 0.03317628 0.007931354 0.098136572
#> lag1_var14 -0.287772318 0.10802349 -0.425858090 -0.139973356
#> lag1_var15 -0.015064301 0.01241558 -0.030254106 0.003419282
#> lag1_var16 -0.060613633 0.14326593 -0.245094704 0.150726638
#> lag1_var17 0.048487971 0.05599491 -0.025733099 0.112923719
#> lag1_var18 0.025961480 0.03922900 -0.015283508 0.088428730
#> lag1_var19 0.038500735 0.03661764 -0.009543594 0.089500795
#> lag1_var20 -0.001650516 0.01201395 -0.017250762 0.014932694
#> const -4.274986449 5.25161281 -12.141997010 1.643047014
#>
#> $A$equation3
#> mean sd 5% quantile 95% quantile
#> lag1_var1 0.041426492 0.034915931 0.0003691746 0.089359882
#> lag1_var2 -0.136319414 0.027128576 -0.1682407052 -0.092879177
#> lag1_var3 0.893245686 0.058677751 0.8150635647 0.970667756
#> lag1_var4 0.018905687 0.015423397 -0.0017096120 0.039489471
#> lag1_var5 -0.009897614 0.020985297 -0.0320119170 0.020037534
#> lag1_var6 0.013353365 0.030863852 -0.0281630120 0.058079991
#> lag1_var7 -0.009548305 0.010713381 -0.0196662905 0.006878557
#> lag1_var8 -0.134017946 0.064680789 -0.2396567802 -0.067244840
#> lag1_var9 0.022094744 0.292706607 -0.4149144452 0.420603986
#> lag1_var10 0.006985622 0.019097729 -0.0231812220 0.029087235
#> lag1_var11 0.215986047 0.051828149 0.1567755654 0.290642624
#> lag1_var12 0.017460263 0.023136926 -0.0114524163 0.050041284
#> lag1_var13 0.024032912 0.010421590 0.0133990580 0.042571929
#> lag1_var14 0.089965916 0.063247471 0.0162861753 0.191687566
#> lag1_var15 -0.003617496 0.005504807 -0.0121106283 0.003515826
#> lag1_var16 -0.011691709 0.036397503 -0.0663772921 0.029636625
#> lag1_var17 0.031076343 0.024393511 -0.0112285317 0.051997130
#> lag1_var18 0.013775662 0.022696678 -0.0095857887 0.046157242
#> lag1_var19 -0.041023441 0.031103277 -0.0845880765 -0.002571139
#> lag1_var20 0.024168625 0.008602512 0.0131773465 0.036897837
#> const -2.271163748 2.271800106 -4.7507831589 1.243194791
#>
#> $A$equation4
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.040587462 0.11689831 -0.205726477 0.10546097
#> lag1_var2 -0.077224604 0.16085623 -0.293610776 0.13087017
#> lag1_var3 -0.059189090 0.13153170 -0.274232837 0.09885272
#> lag1_var4 0.645001687 0.09041304 0.532083530 0.74233087
#> lag1_var5 0.092113318 0.07474417 0.002536159 0.18498404
#> lag1_var6 0.095792178 0.08487797 -0.018196342 0.21075433
#> lag1_var7 -0.093895263 0.04800610 -0.144012214 -0.01446000
#> lag1_var8 0.592988313 0.16786542 0.322304500 0.79628266
#> lag1_var9 1.331542775 0.99264002 0.191438056 2.65145630
#> lag1_var10 0.004985461 0.04453143 -0.054137631 0.06704708
#> lag1_var11 0.103802619 0.20434671 -0.212572305 0.36371971
#> lag1_var12 0.025591813 0.04618862 -0.044047533 0.08682344
#> lag1_var13 -0.152536500 0.03548251 -0.206658286 -0.11024765
#> lag1_var14 -0.082399982 0.17937289 -0.326321424 0.12176524
#> lag1_var15 -0.007816220 0.01546662 -0.026233729 0.01491256
#> lag1_var16 0.188266216 0.11550728 0.027521672 0.34900404
#> lag1_var17 0.046365969 0.05902164 -0.044041333 0.12186287
#> lag1_var18 -0.102844972 0.04439997 -0.168088159 -0.05995243
#> lag1_var19 0.078788899 0.10116788 -0.049568634 0.22797393
#> lag1_var20 -0.011911723 0.03182787 -0.052178406 0.03312993
#> const -7.179292516 7.14466860 -16.968920444 1.64806237
#>
#> $A$equation5
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.07061094 0.10867753 -0.189276729 0.107782885
#> lag1_var2 -0.12486806 0.18885025 -0.426909192 0.097956715
#> lag1_var3 0.16773687 0.08201352 0.051280496 0.284994539
#> lag1_var4 0.08002834 0.08512587 -0.034055190 0.179887351
#> lag1_var5 0.13757820 0.07475274 0.023463179 0.227796659
#> lag1_var6 0.09950184 0.12390002 -0.050739685 0.252180412
#> lag1_var7 -0.10812598 0.03766148 -0.164173559 -0.071195146
#> lag1_var8 0.15934062 0.20353347 -0.137476264 0.390142680
#> lag1_var9 0.67765091 0.49134475 0.121350673 1.428350585
#> lag1_var10 0.06203120 0.04386985 -0.001119006 0.119020652
#> lag1_var11 0.28841907 0.24786670 -0.029697773 0.555337296
#> lag1_var12 0.17866533 0.06880767 0.087362120 0.286840969
#> lag1_var13 -0.07535598 0.04301970 -0.132028001 -0.013789262
#> lag1_var14 0.06104066 0.09137866 -0.060016598 0.177932590
#> lag1_var15 -0.01052972 0.01587620 -0.033397648 0.006190298
#> lag1_var16 0.35140721 0.17864219 0.112652389 0.602395326
#> lag1_var17 0.09706639 0.06131382 0.001688710 0.171909145
#> lag1_var18 0.06299661 0.05273816 -0.001090619 0.138951660
#> lag1_var19 0.07433228 0.08933646 -0.021416896 0.221324125
#> lag1_var20 0.05262302 0.01754878 0.027147352 0.077640993
#> const -12.22524518 3.07921890 -14.975410600 -6.840026536
#>
#> $A$equation6
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.161384307 0.06010591 -0.253408062 -0.09421414
#> lag1_var2 -0.254980936 0.15908907 -0.435735886 0.01769720
#> lag1_var3 -0.377849071 0.19212675 -0.665178457 -0.20386536
#> lag1_var4 0.101678157 0.04770882 0.035202083 0.16184617
#> lag1_var5 0.098182959 0.08818726 -0.004779921 0.21286625
#> lag1_var6 0.218836278 0.08975170 0.086011117 0.32579011
#> lag1_var7 -0.050919087 0.04120380 -0.099919272 0.01128324
#> lag1_var8 0.063967034 0.20974551 -0.232423481 0.33465816
#> lag1_var9 1.567535424 0.74724976 0.426509390 2.35720674
#> lag1_var10 -0.080150489 0.04616030 -0.139102816 -0.02009342
#> lag1_var11 0.162802408 0.22369486 -0.156250161 0.47153975
#> lag1_var12 0.012784948 0.08375568 -0.090299467 0.13961558
#> lag1_var13 -0.071275987 0.03950538 -0.118791686 -0.01701338
#> lag1_var14 0.381368288 0.22794781 0.153226446 0.71437651
#> lag1_var15 0.032663297 0.01768025 0.006207289 0.05313837
#> lag1_var16 0.197601028 0.10338555 0.065304861 0.33620726
#> lag1_var17 0.025954760 0.05955756 -0.065584237 0.09083107
#> lag1_var18 -0.025347311 0.03849024 -0.071258224 0.03154686
#> lag1_var19 -0.004038652 0.05652899 -0.093141145 0.05789616
#> lag1_var20 0.061152825 0.03068821 0.013724991 0.09186270
#> const -9.704922000 6.78147906 -16.936803985 1.00304659
#>
#> $A$equation7
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.16022816 0.19682757 -0.39427397 0.0961402302
#> lag1_var2 -0.06060291 0.24801933 -0.35712770 0.3218626752
#> lag1_var3 -0.38573316 0.24437554 -0.70376836 -0.0586669661
#> lag1_var4 0.31445074 0.10674689 0.17467369 0.4735655125
#> lag1_var5 0.11295767 0.13860720 -0.07850107 0.2893668954
#> lag1_var6 0.21695290 0.11854970 0.04361552 0.3600354728
#> lag1_var7 0.35899667 0.10805192 0.20034400 0.4950618108
#> lag1_var8 0.40823817 0.47721858 -0.17533024 1.1366722553
#> lag1_var9 1.59266837 1.58908995 -0.23353576 4.1116589108
#> lag1_var10 -0.14194797 0.11537424 -0.30250802 -0.0061103037
#> lag1_var11 0.36459492 0.45412350 -0.25841129 0.9837195134
#> lag1_var12 -0.31111954 0.22143026 -0.59107426 0.0008318448
#> lag1_var13 -0.14057298 0.06682625 -0.23171785 -0.0480329794
#> lag1_var14 0.22629186 0.34699893 -0.25757245 0.7094336961
#> lag1_var15 -0.01742991 0.01775270 -0.04174909 0.0080956844
#> lag1_var16 -0.11734988 0.20081556 -0.35825471 0.2001573770
#> lag1_var17 0.05591215 0.13761612 -0.10009134 0.2712788201
#> lag1_var18 0.18589664 0.14481087 -0.02324625 0.3506205757
#> lag1_var19 -0.13614047 0.15624356 -0.30578331 0.0807091621
#> lag1_var20 0.24028100 0.06832975 0.13708182 0.3140907834
#> const -25.88078717 13.09254393 -44.48654820 -8.6274816428
#>
#> $A$equation8
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.0038737759 0.006893719 -1.376029e-02 0.004365001
#> lag1_var2 0.0147278631 0.011859429 -9.274279e-05 0.031240277
#> lag1_var3 0.0097542021 0.011418857 -4.409813e-03 0.025681200
#> lag1_var4 -0.0045868975 0.004714173 -1.092497e-02 0.001484098
#> lag1_var5 -0.0042589918 0.005126691 -9.464722e-03 0.003985135
#> lag1_var6 -0.0158705630 0.007846601 -2.676880e-02 -0.006215272
#> lag1_var7 -0.0074969247 0.001797167 -1.018385e-02 -0.005443088
#> lag1_var8 0.9296217529 0.019304112 9.075523e-01 0.960835774
#> lag1_var9 -0.1964934469 0.060161441 -2.576589e-01 -0.108802947
#> lag1_var10 -0.0035264709 0.004786878 -8.150975e-03 0.004504304
#> lag1_var11 -0.0059788925 0.019682337 -3.529643e-02 0.015965762
#> lag1_var12 0.0197478175 0.008056511 6.434535e-03 0.028463498
#> lag1_var13 0.0029541928 0.003661226 -1.624720e-03 0.007852174
#> lag1_var14 0.0068762776 0.012962028 -8.396681e-03 0.027175273
#> lag1_var15 0.0004942908 0.001188024 -1.189577e-03 0.001855202
#> lag1_var16 -0.0520395233 0.012441992 -7.037770e-02 -0.036953848
#> lag1_var17 -0.0003877905 0.004951651 -6.526257e-03 0.006474283
#> lag1_var18 -0.0058115170 0.003258307 -1.009335e-02 -0.001936737
#> lag1_var19 0.0119627253 0.005303806 4.528944e-03 0.019809255
#> lag1_var20 -0.0091415578 0.002118865 -1.201907e-02 -0.006232698
#> const 2.1822884863 0.537178392 1.239874e+00 2.699340452
#>
#> $A$equation9
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.0011415161 0.0043549644 -0.0050662886 0.0059070031
#> lag1_var2 -0.0018510292 0.0071509874 -0.0120426700 0.0068447481
#> lag1_var3 -0.0160382212 0.0046023237 -0.0223863332 -0.0099998620
#> lag1_var4 0.0040878090 0.0017113024 0.0019496220 0.0065827091
#> lag1_var5 0.0007256286 0.0035851736 -0.0051643483 0.0039230082
#> lag1_var6 0.0030677503 0.0024357404 0.0002416211 0.0064197376
#> lag1_var7 -0.0028355105 0.0016653793 -0.0049218302 -0.0006177949
#> lag1_var8 0.0091016077 0.0080490291 -0.0020496716 0.0196339781
#> lag1_var9 0.9851726171 0.0263851794 0.9464985443 1.0200949021
#> lag1_var10 0.0004326654 0.0018462335 -0.0017493499 0.0029292290
#> lag1_var11 0.0008824117 0.0049850558 -0.0051732879 0.0084860344
#> lag1_var12 -0.0006881897 0.0033533651 -0.0061759220 0.0028179383
#> lag1_var13 -0.0028259108 0.0009333287 -0.0041118164 -0.0015882203
#> lag1_var14 0.0140400384 0.0057155822 0.0053329457 0.0205992701
#> lag1_var15 0.0003695626 0.0003810721 -0.0002067626 0.0008227278
#> lag1_var16 0.0110443715 0.0069135174 0.0010248006 0.0193993589
#> lag1_var17 -0.0032542771 0.0021074719 -0.0066600965 -0.0009055906
#> lag1_var18 -0.0005312241 0.0019919333 -0.0037835691 0.0017887145
#> lag1_var19 0.0019898861 0.0040107832 -0.0039040838 0.0069746766
#> lag1_var20 0.0020460506 0.0016017167 0.0002765009 0.0041101863
#> const 0.2125820116 0.1769719200 -0.0106520692 0.4482100355
#>
#> $A$equation10
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.025470989 0.14137896 -0.177720891 0.201761915
#> lag1_var2 0.056266893 0.15921149 -0.162596023 0.246910956
#> lag1_var3 0.663008676 0.24867322 0.311877156 0.967613262
#> lag1_var4 0.004451750 0.09592710 -0.130310122 0.122715123
#> lag1_var5 0.196696530 0.15741722 0.024324151 0.470971051
#> lag1_var6 0.123600764 0.18347192 -0.161609975 0.358228639
#> lag1_var7 0.021997385 0.09551180 -0.122627826 0.136365113
#> lag1_var8 0.664608787 0.28023234 0.277676702 1.090593494
#> lag1_var9 0.470225934 1.39197725 -1.460101902 2.323122952
#> lag1_var10 0.357335665 0.10070970 0.196872906 0.472780916
#> lag1_var11 0.123796448 0.27677322 -0.193120279 0.562918166
#> lag1_var12 0.147388587 0.10045805 -0.014038312 0.260547579
#> lag1_var13 -0.024604145 0.07525673 -0.138294306 0.047727969
#> lag1_var14 -0.931110574 0.32589639 -1.365791481 -0.479285285
#> lag1_var15 -0.041380574 0.02642106 -0.074074471 -0.007105064
#> lag1_var16 -0.145081311 0.31382277 -0.533556313 0.289054298
#> lag1_var17 0.135088337 0.14440897 -0.074856749 0.305934664
#> lag1_var18 -0.002875559 0.10362311 -0.114577762 0.158836727
#> lag1_var19 0.146938704 0.10449394 0.004429062 0.274813696
#> lag1_var20 -0.028296377 0.04587732 -0.085844073 0.033376137
#> const -12.353241155 11.76099762 -28.948652528 1.993039097
#>
#> $A$equation11
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.041420698 0.039526621 -0.087095166 0.012961054
#> lag1_var2 -0.035262280 0.102440691 -0.184187583 0.076491027
#> lag1_var3 0.237054585 0.062413943 0.163435776 0.334025963
#> lag1_var4 0.013534140 0.032713114 -0.022699912 0.065526560
#> lag1_var5 0.070938948 0.021159275 0.043437075 0.101726389
#> lag1_var6 -0.004891330 0.050538099 -0.059053910 0.079920225
#> lag1_var7 -0.011860617 0.026923367 -0.053864590 0.018594336
#> lag1_var8 0.087421291 0.108568181 -0.051833371 0.245022913
#> lag1_var9 0.128319551 0.348555968 -0.382178744 0.546182553
#> lag1_var10 -0.014693056 0.029193580 -0.053081973 0.020286230
#> lag1_var11 0.673201888 0.111179184 0.543220494 0.843919450
#> lag1_var12 0.101401653 0.030237355 0.062172478 0.139395848
#> lag1_var13 0.023273805 0.031906485 -0.029259107 0.055922538
#> lag1_var14 -0.189344978 0.090302130 -0.327278549 -0.081243456
#> lag1_var15 -0.006916884 0.008749398 -0.018300821 0.005169665
#> lag1_var16 -0.008355874 0.102613295 -0.147255364 0.119447597
#> lag1_var17 0.041315409 0.053968685 -0.028497726 0.114177084
#> lag1_var18 0.009948808 0.037780013 -0.038297513 0.059771482
#> lag1_var19 0.034012610 0.027384638 -0.005431161 0.063852751
#> lag1_var20 0.004827010 0.014702650 -0.011960730 0.028061936
#> const -3.936767628 3.549065566 -8.768906556 0.616998439
#>
#> $A$equation12
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.096166081 0.06403652 -0.19497917 -0.03376096
#> lag1_var2 0.159404081 0.09912043 0.01431213 0.26959076
#> lag1_var3 0.011811690 0.10355419 -0.13763170 0.13114648
#> lag1_var4 0.148070992 0.06260754 0.05835901 0.21890454
#> lag1_var5 0.068459683 0.07594418 -0.02900705 0.17111624
#> lag1_var6 -0.019412028 0.08602253 -0.14100423 0.07653800
#> lag1_var7 -0.042527984 0.04388588 -0.09644118 0.02096853
#> lag1_var8 0.067370183 0.07805016 -0.05287456 0.15236828
#> lag1_var9 0.908636469 0.63181353 0.04919965 1.61020412
#> lag1_var10 -0.105616682 0.03860075 -0.17207193 -0.07302570
#> lag1_var11 0.446278603 0.13063990 0.24056326 0.60899757
#> lag1_var12 0.232056500 0.07887945 0.12793317 0.33399946
#> lag1_var13 -0.022135591 0.02873195 -0.06739115 0.01337463
#> lag1_var14 -0.088404134 0.10308083 -0.20927824 0.06436287
#> lag1_var15 -0.007628343 0.01208868 -0.02788885 0.00640508
#> lag1_var16 0.063574471 0.11878452 -0.07706421 0.22997129
#> lag1_var17 0.071214775 0.03234121 0.03034788 0.11583461
#> lag1_var18 -0.008724107 0.02920885 -0.04366831 0.03471888
#> lag1_var19 0.038140149 0.08631694 -0.06974814 0.17081891
#> lag1_var20 -0.006321529 0.02066403 -0.03317621 0.01852241
#> const -9.347527101 4.51693708 -14.12001685 -1.98696695
#>
#> $A$equation13
#> mean sd 5% quantile 95% quantile
#> lag1_var1 0.056428359 0.21547640 -0.21099751 0.36989759
#> lag1_var2 0.132507950 0.21381081 -0.19755739 0.37665385
#> lag1_var3 -0.503960293 0.14875547 -0.72864944 -0.33693343
#> lag1_var4 0.003273978 0.09955220 -0.14624461 0.12122396
#> lag1_var5 -0.132166829 0.08463286 -0.21931523 0.01029107
#> lag1_var6 0.091238285 0.18079888 -0.14189708 0.33011602
#> lag1_var7 -0.175606930 0.06723914 -0.28416308 -0.12079857
#> lag1_var8 0.603908789 0.22037912 0.35440989 0.94496022
#> lag1_var9 -0.178458398 0.88715209 -1.19129268 1.13093670
#> lag1_var10 0.039719741 0.06428535 -0.06007636 0.11254727
#> lag1_var11 0.099139444 0.27558104 -0.24377626 0.52330110
#> lag1_var12 0.024810166 0.07769550 -0.07638025 0.13621447
#> lag1_var13 0.555720534 0.07000993 0.46118367 0.65946686
#> lag1_var14 0.368215132 0.16919538 0.22201897 0.62153960
#> lag1_var15 -0.004841753 0.03566758 -0.06523961 0.03425421
#> lag1_var16 0.481498532 0.23491458 0.13458757 0.74496046
#> lag1_var17 0.089757665 0.09311655 -0.01271721 0.20870808
#> lag1_var18 -0.155129560 0.08084008 -0.24356387 -0.04202543
#> lag1_var19 0.042934554 0.12685513 -0.13809194 0.20657957
#> lag1_var20 -0.025685159 0.05670029 -0.08243302 0.06323297
#> const 3.099248815 7.69227828 -9.41564708 10.49411253
#>
#> $A$equation14
#> mean sd 5% quantile 95% quantile
#> lag1_var1 0.0073422644 0.016051148 -0.009807517 0.027968404
#> lag1_var2 0.0214201134 0.020332691 -0.005927566 0.048449093
#> lag1_var3 0.0572132566 0.021658673 0.025481636 0.085597446
#> lag1_var4 0.0085918505 0.010456632 -0.003943014 0.024356250
#> lag1_var5 0.0001819657 0.011040099 -0.014805963 0.013832432
#> lag1_var6 -0.0014647300 0.021563284 -0.024893595 0.035232150
#> lag1_var7 -0.0154434120 0.008921216 -0.027187061 -0.002135273
#> lag1_var8 0.0258600801 0.022825892 -0.004092008 0.058693915
#> lag1_var9 0.0725609453 0.092822598 -0.014682808 0.226289245
#> lag1_var10 -0.0043703926 0.012683498 -0.024426764 0.008001082
#> lag1_var11 -0.0033076279 0.033087322 -0.050896889 0.040083032
#> lag1_var12 0.0308164746 0.018441017 0.006214709 0.057242544
#> lag1_var13 0.0066883022 0.009921316 -0.005544011 0.019720393
#> lag1_var14 0.8918404026 0.029612950 0.850250107 0.933764331
#> lag1_var15 -0.0024906439 0.003770508 -0.007286161 0.002933672
#> lag1_var16 0.0352279349 0.023804827 0.005592898 0.068676413
#> lag1_var17 0.0011104816 0.013628640 -0.014205464 0.020139608
#> lag1_var18 0.0089880999 0.007598857 -0.001245093 0.019255530
#> lag1_var19 0.0012941107 0.015287902 -0.021964000 0.020597557
#> lag1_var20 0.0132512423 0.005070152 0.005894807 0.019109361
#> const -1.1712143078 0.855738995 -2.416720110 -0.312369270
#>
#> $A$equation15
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -1.58227097 0.47079331 -2.31387152 -0.9463497
#> lag1_var2 0.39187098 0.90480404 -1.10107204 1.3035723
#> lag1_var3 -0.78042426 0.59690993 -1.74202751 -0.1977235
#> lag1_var4 0.47687740 0.47768394 -0.04950014 1.1996076
#> lag1_var5 0.06803414 0.40624768 -0.53756099 0.5712428
#> lag1_var6 2.49643039 0.28864888 2.16181982 2.9172378
#> lag1_var7 0.17453548 0.27379485 -0.18173776 0.5489468
#> lag1_var8 1.19853093 1.40706930 -0.61539810 3.0724473
#> lag1_var9 2.46568996 3.94268171 -3.31150665 7.1840718
#> lag1_var10 -0.05922658 0.25868151 -0.31017084 0.3458787
#> lag1_var11 0.18207045 1.36953652 -1.00161873 2.5492134
#> lag1_var12 -0.04216234 0.41914095 -0.54029140 0.4903807
#> lag1_var13 -0.11026167 0.20342367 -0.42206418 0.1404592
#> lag1_var14 0.20866681 1.06588495 -0.80695263 2.1294059
#> lag1_var15 0.27190390 0.07483332 0.18887172 0.3538152
#> lag1_var16 -0.59681324 0.67969466 -1.22396335 0.4624735
#> lag1_var17 -0.15112120 0.32359172 -0.60188132 0.2476398
#> lag1_var18 0.64319039 0.27632203 0.28976515 0.9976302
#> lag1_var19 -0.83976573 0.34159454 -1.23082483 -0.3118414
#> lag1_var20 0.63627774 0.12576402 0.47730111 0.8141650
#> const -52.83493805 32.20547321 -91.84009075 -5.4204916
#>
#> $A$equation16
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.045809759 0.039387713 -0.103695118 0.0069752525
#> lag1_var2 -0.133220345 0.057977417 -0.203595852 -0.0490629173
#> lag1_var3 -0.113845077 0.050562721 -0.165627278 -0.0389640203
#> lag1_var4 0.046804297 0.026133591 0.016483874 0.0837385979
#> lag1_var5 0.024938432 0.024150832 -0.014615513 0.0513432462
#> lag1_var6 0.094502631 0.036707331 0.059074345 0.1534994732
#> lag1_var7 -0.009888826 0.012698914 -0.025169901 0.0083234701
#> lag1_var8 0.115029394 0.095742297 -0.002421411 0.2661286282
#> lag1_var9 0.589172522 0.455019517 0.095468981 1.3047585827
#> lag1_var10 -0.007296021 0.022040786 -0.042262013 0.0221687847
#> lag1_var11 0.177907119 0.099217641 0.063331533 0.3280481780
#> lag1_var12 -0.015261754 0.031903397 -0.050911333 0.0296538766
#> lag1_var13 -0.020222473 0.009149821 -0.030443718 -0.0054159281
#> lag1_var14 0.079567202 0.077029933 -0.026083288 0.1731598748
#> lag1_var15 -0.003398497 0.003169374 -0.007487741 0.0008572693
#> lag1_var16 0.703985756 0.067419703 0.637369389 0.8216031027
#> lag1_var17 0.028049395 0.022909467 0.001824365 0.0619130209
#> lag1_var18 0.025958737 0.025675846 -0.018116887 0.0519990365
#> lag1_var19 -0.025193456 0.022375934 -0.056757069 0.0043102644
#> lag1_var20 0.054310824 0.011199521 0.039288216 0.0690673611
#> const -7.697878041 3.364954796 -13.183431961 -3.5824544555
#>
#> $A$equation17
#> mean sd 5% quantile 95% quantile
#> lag1_var1 0.08133496 0.08979003 -0.06223394 0.178706098
#> lag1_var2 -0.14886052 0.16899176 -0.35113306 0.101712143
#> lag1_var3 -0.31472042 0.18113361 -0.52929949 -0.041310698
#> lag1_var4 0.11731378 0.04087457 0.05908526 0.169400271
#> lag1_var5 0.13320336 0.09365144 -0.02881168 0.219533659
#> lag1_var6 0.15271862 0.11690033 -0.01276689 0.301870857
#> lag1_var7 -0.09855539 0.06352317 -0.19277850 -0.023799858
#> lag1_var8 0.71166799 0.32759418 0.39110578 1.197530939
#> lag1_var9 3.28182176 1.18717725 2.00227467 4.974923742
#> lag1_var10 -0.04786078 0.07698685 -0.16089170 0.051549546
#> lag1_var11 0.19671211 0.18448100 -0.10756208 0.406084689
#> lag1_var12 -0.03050769 0.09196049 -0.14140017 0.118046091
#> lag1_var13 -0.02148811 0.04456711 -0.09178003 0.024777689
#> lag1_var14 -0.08741646 0.26549415 -0.49992826 0.220467662
#> lag1_var15 -0.02175188 0.01606026 -0.04082297 0.003007679
#> lag1_var16 -0.14076289 0.17187632 -0.39117043 0.082210968
#> lag1_var17 0.79280910 0.08450370 0.64791017 0.890977677
#> lag1_var18 0.01737994 0.07011293 -0.08545846 0.109200979
#> lag1_var19 -0.03687771 0.07925348 -0.14518885 0.068769246
#> lag1_var20 0.16464357 0.03920706 0.10452062 0.202136386
#> const -17.33271659 9.39038284 -29.93860746 -6.453495586
#>
#> $A$equation18
#> mean sd 5% quantile 95% quantile
#> lag1_var1 0.05757457 0.14403657 -0.18919208 0.1982974021
#> lag1_var2 -0.26921822 0.28112900 -0.64889162 0.1071166077
#> lag1_var3 -0.39632862 0.27870327 -0.69981546 0.0183213118
#> lag1_var4 0.10398478 0.06984527 0.02792760 0.2116608444
#> lag1_var5 0.17191061 0.12849245 -0.03542874 0.3240086394
#> lag1_var6 0.08460615 0.19963796 -0.16413985 0.3445444476
#> lag1_var7 -0.15513436 0.05954232 -0.23440501 -0.0766966126
#> lag1_var8 1.10090112 0.48397936 0.60572298 1.8445587689
#> lag1_var9 5.34990274 1.66701236 3.41502441 7.8687693886
#> lag1_var10 -0.10539225 0.10367392 -0.25663561 0.0220315973
#> lag1_var11 0.30575227 0.28769815 -0.10152373 0.6372778202
#> lag1_var12 -0.01276969 0.13188062 -0.17446002 0.1991270783
#> lag1_var13 -0.01713456 0.05192451 -0.09398181 0.0392076519
#> lag1_var14 -0.26279874 0.42751204 -0.94799017 0.2431132260
#> lag1_var15 -0.02853049 0.02190691 -0.05708126 -0.0020371025
#> lag1_var16 0.11198142 0.18479579 -0.19593592 0.3061227002
#> lag1_var17 -0.11226793 0.12736836 -0.33942996 0.0006387823
#> lag1_var18 0.71591615 0.09280462 0.60573038 0.8537371409
#> lag1_var19 0.04239554 0.10440857 -0.10717227 0.1764870720
#> lag1_var20 0.16998800 0.05408635 0.08966419 0.2312550311
#> const -21.55863284 13.22791768 -39.95094986 -4.6604848430
#>
#> $A$equation19
#> mean sd 5% quantile 95% quantile
#> lag1_var1 -0.32125998 0.07368266 -0.41938679 -0.240225300
#> lag1_var2 -0.07178162 0.14189637 -0.26801494 0.118335591
#> lag1_var3 -0.38092989 0.19655412 -0.66952495 -0.137121078
#> lag1_var4 0.14426508 0.06685297 0.04215046 0.225978143
#> lag1_var5 0.15876407 0.11664695 -0.03163380 0.279817734
#> lag1_var6 -0.02911826 0.11246899 -0.20595098 0.113597712
#> lag1_var7 0.03282545 0.07321669 -0.06608608 0.129870287
#> lag1_var8 -0.07830334 0.34106648 -0.52360597 0.423084352
#> lag1_var9 0.92976776 1.18626204 -0.87267162 2.296098091
#> lag1_var10 -0.07063850 0.05352696 -0.15163529 -0.011223703
#> lag1_var11 -0.03332561 0.26739416 -0.38589006 0.368940315
#> lag1_var12 0.06380997 0.08300869 -0.02189165 0.190259244
#> lag1_var13 -0.05820766 0.05742163 -0.11629800 0.034990251
#> lag1_var14 0.26746011 0.24496701 -0.10120228 0.587184347
#> lag1_var15 -0.01797276 0.01800487 -0.04213316 0.007048836
#> lag1_var16 -0.12559267 0.21156984 -0.40835732 0.188625407
#> lag1_var17 -0.01138843 0.08022620 -0.12760277 0.100120753
#> lag1_var18 0.01181731 0.07470870 -0.06746612 0.135722279
#> lag1_var19 0.18508048 0.09803858 0.04997223 0.301425325
#> lag1_var20 0.07817969 0.03796921 0.02294994 0.120410915
#> const -4.21768794 9.40703894 -16.09381022 9.776412121
#>
#> $A$equation20
#> mean sd 5% quantile 95% quantile
#> lag1_var1 0.092370550 0.18453334 -0.14799353 0.34390998
#> lag1_var2 -0.286279171 0.38909949 -0.83061413 0.19461621
#> lag1_var3 -0.196983350 0.36501196 -0.73348370 0.25512507
#> lag1_var4 -0.156204152 0.12094774 -0.32987132 -0.01372455
#> lag1_var5 0.125076272 0.15984268 -0.09526952 0.31977256
#> lag1_var6 -0.038074710 0.14446500 -0.19917931 0.17115494
#> lag1_var7 0.050461125 0.11234392 -0.11037731 0.18678024
#> lag1_var8 1.022070349 0.57009666 0.37824506 1.91262668
#> lag1_var9 3.715666773 2.02039484 1.42214165 6.42487580
#> lag1_var10 0.015452975 0.06829929 -0.09376219 0.09002775
#> lag1_var11 -0.129603155 0.51284594 -0.58299957 0.79487183
#> lag1_var12 0.120263509 0.19341861 -0.11074749 0.38594970
#> lag1_var13 -0.086151494 0.15359781 -0.26763950 0.12574206
#> lag1_var14 -0.132919050 0.45967823 -0.77964162 0.53419494
#> lag1_var15 -0.002002395 0.02931907 -0.03230655 0.04366083
#> lag1_var16 0.267021365 0.29224028 -0.03868256 0.71429866
#> lag1_var17 -0.222462380 0.12518854 -0.41638694 -0.07483028
#> lag1_var18 -0.201796376 0.10306883 -0.35579503 -0.05980548
#> lag1_var19 -0.044073395 0.12433490 -0.24570222 0.09926798
#> lag1_var20 0.356766149 0.04927324 0.29770252 0.41948983
#> const -6.697792082 13.43345512 -24.96128351 11.04097397
#>
#>
#> $Sigma
#> $Sigma$equation1
#> mean sd 5% quantile 95% quantile
#> Sigma[1,1] 7.676585 0.6381177 6.955966 8.623669
#>
#> $Sigma$equation2
#> mean sd 5% quantile 95% quantile
#> Sigma[2,1] -0.006837949 0.3488633 -0.4779196 0.3737556
#> Sigma[2,2] 3.033294391 0.2803420 2.6355816 3.4387728
#>
#> $Sigma$equation3
#> mean sd 5% quantile 95% quantile
#> Sigma[3,1] 0.1911624 0.13717338 -0.008858676 0.3779436
#> Sigma[3,2] 0.2850606 0.04644157 0.238958735 0.3605873
#> Sigma[3,3] 0.5784500 0.05167712 0.505403992 0.6382369
#>
#> $Sigma$equation4
#> mean sd 5% quantile 95% quantile
#> Sigma[4,1] -0.2205312 0.4985949 -0.8171517 0.5473643
#> Sigma[4,2] -1.1470408 0.1816361 -1.4007587 -0.9261815
#> Sigma[4,3] -0.4413150 0.1232366 -0.6198950 -0.3076563
#> Sigma[4,4] 5.5822005 0.4788942 4.9566869 6.1607760
#>
#> $Sigma$equation5
#> mean sd 5% quantile 95% quantile
#> Sigma[5,1] 2.4574964 0.5241984 1.7892878 3.1819597
#> Sigma[5,2] 0.7684987 0.1079028 0.5920680 0.8866517
#> Sigma[5,3] 0.3597232 0.1421296 0.2168526 0.5737786
#> Sigma[5,4] -0.0139834 0.5621721 -0.6771862 0.8877344
#> Sigma[5,5] 7.1469514 0.6205564 6.4371751 8.1081452
#>
#> $Sigma$equation6
#> mean sd 5% quantile 95% quantile
#> Sigma[6,1] 3.20157435 0.4044978 2.625587461 3.6934568
#> Sigma[6,2] -0.50089383 0.1583009 -0.702393634 -0.2645729
#> Sigma[6,3] 0.09886588 0.1190828 0.007324942 0.2924639
#> Sigma[6,4] 0.74665747 0.4159702 0.062905794 1.1364396
#> Sigma[6,5] 2.15766226 0.3307691 1.663030906 2.5678104
#> Sigma[6,6] 5.57513300 0.3157777 5.215107351 6.0149600
#>
#> $Sigma$equation7
#> mean sd 5% quantile 95% quantile
#> Sigma[7,1] 7.4954352 1.0124615 6.3443597 8.9208572
#> Sigma[7,2] 0.6189666 0.6212456 -0.1567394 1.4493426
#> Sigma[7,3] 1.1532460 0.1871147 0.9113499 1.3830774
#> Sigma[7,4] -1.0088031 0.8637974 -2.1232353 0.2046339
#> Sigma[7,5] 5.4231483 1.3745775 3.6511582 7.3734382
#> Sigma[7,6] 3.7269379 0.5580936 2.7823276 4.2135916
#> Sigma[7,7] 21.7337171 1.9320933 18.9830208 24.1233991
#>
#> $Sigma$equation8
#> mean sd 5% quantile 95% quantile
#> Sigma[8,1] -0.238099122 0.038934475 -0.28987174 -0.18774599
#> Sigma[8,2] -0.015821449 0.027720373 -0.05440586 0.02039750
#> Sigma[8,3] -0.050966848 0.009486677 -0.06234641 -0.03624000
#> Sigma[8,4] 0.008638712 0.037187336 -0.05832897 0.04283110
#> Sigma[8,5] -0.182151909 0.041240722 -0.22624088 -0.11982192
#> Sigma[8,6] -0.153344547 0.027013876 -0.18647906 -0.11863003
#> Sigma[8,7] -0.554810207 0.064755092 -0.63001789 -0.44979827
#> Sigma[8,8] 0.044452566 0.002899129 0.04004772 0.04816866
#>
#> $Sigma$equation9
#> mean sd 5% quantile 95% quantile
#> Sigma[9,1] 0.060445951 0.014925761 0.044175837 0.084088600
#> Sigma[9,2] 0.014928622 0.005924274 0.008617460 0.023665498
#> Sigma[9,3] -0.003470202 0.004019238 -0.008751036 0.002214714
#> Sigma[9,4] 0.031176885 0.010610326 0.016131756 0.044667771
#> Sigma[9,5] 0.058448076 0.017672838 0.037121526 0.082679481
#> Sigma[9,6] 0.051073698 0.014815457 0.036233201 0.075442556
#> Sigma[9,7] 0.093269533 0.022676894 0.060812477 0.120794520
#> Sigma[9,8] -0.004331342 0.001546082 -0.006173812 -0.002094344
#> Sigma[9,9] 0.009255955 0.001016024 0.007953586 0.010538483
#>
#> $Sigma$equation10
#> mean sd 5% quantile 95% quantile
#> Sigma[10,1] -0.11230257 0.8350112 -1.28931204 0.896683053
#> Sigma[10,2] 5.43916771 0.6398043 4.76016914 6.297290426
#> Sigma[10,3] 0.39121044 0.2246835 0.08692610 0.718060945
#> Sigma[10,4] -2.47830015 0.5508063 -3.28016407 -1.756336707
#> Sigma[10,5] 1.19382523 0.5608165 0.29649916 1.860627591
#> Sigma[10,6] -0.56902502 0.3614391 -1.01630479 -0.024181989
#> Sigma[10,7] 1.44035986 1.3187669 -0.14793464 3.445879341
#> Sigma[10,8] -0.04902669 0.0488558 -0.12473199 0.005151918
#> Sigma[10,9] 0.05157701 0.0116986 0.03509729 0.065815674
#> Sigma[10,10] 19.22285666 1.5955453 16.86561182 21.154783733
#>
#> $Sigma$equation11
#> mean sd 5% quantile 95% quantile
#> Sigma[11,1] 0.010738006 0.188201727 -0.24976914 0.25715246
#> Sigma[11,2] 1.950727078 0.206905150 1.69587830 2.19698409
#> Sigma[11,3] 0.111376472 0.057488961 0.01742743 0.17585303
#> Sigma[11,4] -0.622444718 0.173252924 -0.92097064 -0.44499248
#> Sigma[11,5] 0.630557691 0.139886344 0.42544905 0.78768964
#> Sigma[11,6] -0.276002122 0.174164378 -0.50215246 -0.03820853
#> Sigma[11,7] 0.498668622 0.285498000 0.08229323 0.87238455
#> Sigma[11,8] -0.008150764 0.017705308 -0.02755406 0.01827955
#> Sigma[11,9] 0.023894178 0.005661889 0.01773278 0.03208475
#> Sigma[11,10] 4.136065126 0.497330050 3.55202521 4.76604296
#> Sigma[11,11] 1.720244829 0.157516671 1.45954137 1.87599466
#>
#> $Sigma$equation12
#> mean sd 5% quantile 95% quantile
#> Sigma[12,1] 1.4198759 0.44918279 0.77573728 1.99057146
#> Sigma[12,2] 0.2800701 0.31889882 -0.12171563 0.72369699
#> Sigma[12,3] 0.1156677 0.06458056 0.01952236 0.18758419
#> Sigma[12,4] 0.1898037 0.40190436 -0.30080036 0.72878467
#> Sigma[12,5] 1.7439419 0.64140885 1.08379256 2.86549296
#> Sigma[12,6] 1.0662136 0.43916732 0.32494844 1.45203727
#> Sigma[12,7] 4.2863536 0.93245950 2.94731717 5.46104914
#> Sigma[12,8] -0.1177303 0.02421350 -0.14684322 -0.08309255
#> Sigma[12,9] 0.0167301 0.01194733 0.00240509 0.03297540
#> Sigma[12,10] 0.9607799 0.68184068 0.02812031 1.75578358
#> Sigma[12,11] 0.2062863 0.23140806 -0.06119458 0.54898608
#> Sigma[12,12] 4.5495393 0.57926777 4.14005620 5.48227543
#>
#> $Sigma$equation13
#> mean sd 5% quantile 95% quantile
#> Sigma[13,1] -0.241963438 0.72831360 -0.9295546045 0.90325501
#> Sigma[13,2] -1.310724653 0.40402971 -1.7937579355 -0.82470418
#> Sigma[13,3] -0.429213905 0.25587962 -0.7248829057 -0.04498285
#> Sigma[13,4] 4.133071383 0.76334689 3.0860502469 5.21120974
#> Sigma[13,5] 0.449775378 0.76676924 -0.6995556065 1.35625890
#> Sigma[13,6] 0.572859907 0.40959390 -0.0533589940 1.05484856
#> Sigma[13,7] -0.687536222 0.98262238 -1.8519884076 0.77399313
#> Sigma[13,8] 0.008027874 0.04575397 -0.0588794044 0.07000776
#> Sigma[13,9] 0.027065028 0.01959425 0.0008379641 0.05461986
#> Sigma[13,10] -1.948411962 0.85532355 -3.3005490141 -0.90059424
#> Sigma[13,11] -0.492253909 0.31483559 -0.8351869900 -0.01033982
#> Sigma[13,12] -0.483246326 0.33098017 -0.8841946468 0.04838927
#> Sigma[13,13] 13.333215782 1.24575089 11.6327757586 15.01595811
#>
#> $Sigma$equation14
#> mean sd 5% quantile 95% quantile
#> Sigma[14,1] 0.221629332 0.087556859 0.108668411 0.338425871
#> Sigma[14,2] 0.182857150 0.051698288 0.113029762 0.247929331
#> Sigma[14,3] 0.179367864 0.016569238 0.154385048 0.197206351
#> Sigma[14,4] -0.246247005 0.093400237 -0.383463194 -0.134206835
#> Sigma[14,5] 0.339919875 0.107611733 0.221479676 0.513538454
#> Sigma[14,6] 0.112310385 0.070864319 0.010130002 0.214721961
#> Sigma[14,7] 0.733133300 0.140023946 0.601814698 0.968360323
#> Sigma[14,8] -0.033090494 0.005148836 -0.038886752 -0.025558534
#> Sigma[14,9] 0.001139999 0.002329783 -0.002704169 0.003344494
#> Sigma[14,10] 0.346364790 0.158584253 0.106611782 0.530967873
#> Sigma[14,11] 0.129336456 0.049719964 0.049505834 0.194481469
#> Sigma[14,12] 0.117149747 0.078205788 0.042167458 0.252746371
#> Sigma[14,13] -0.260196094 0.146025161 -0.468821744 -0.051525821
#> Sigma[14,14] 0.191732784 0.014177562 0.172705871 0.209142382
#>
#> $Sigma$equation15
#> mean sd 5% quantile 95% quantile
#> Sigma[15,1] 25.9341635 3.73895088 22.4428695 31.9484526
#> Sigma[15,2] 1.3544295 1.09313282 -0.4794735 2.4618538
#> Sigma[15,3] 1.4103067 0.46326630 0.8028388 2.1099586
#> Sigma[15,4] -5.1147019 2.71641055 -7.5280027 -0.4651099
#> Sigma[15,5] 8.5486209 3.20080178 4.3074402 12.8799286
#> Sigma[15,6] -0.5268364 1.65173253 -3.0258328 1.4613325
#> Sigma[15,7] 34.4222641 4.99564922 29.2636701 42.2069436
#> Sigma[15,8] -1.1177779 0.24807624 -1.5607616 -0.9132905
#> Sigma[15,9] 0.1108434 0.06000311 0.0253767 0.1818517
#> Sigma[15,10] 0.8701995 3.15508929 -2.5952267 5.4833336
#> Sigma[15,11] 0.2476406 0.85352920 -0.7200717 1.4886435
#> Sigma[15,12] 6.8027535 2.08546728 3.7922917 9.1657840
#> Sigma[15,13] -4.3275090 3.90938710 -8.2820342 1.5658759
#> Sigma[15,14] 1.2859682 0.39687809 0.7980329 1.8654893
#> Sigma[15,15] 178.0339203 25.59937278 150.6729664 222.7645423
#>
#> $Sigma$equation16
#> mean sd 5% quantile 95% quantile
#> Sigma[16,1] 1.62007148 0.163285749 1.43712401 1.89101965
#> Sigma[16,2] 0.23901965 0.119281572 0.10403387 0.40267367
#> Sigma[16,3] 0.17956668 0.047810107 0.10853964 0.24973691
#> Sigma[16,4] -0.09468654 0.182550719 -0.32771014 0.14902229
#> Sigma[16,5] 1.24480137 0.244214817 0.96819439 1.60382891
#> Sigma[16,6] 0.79126841 0.136148122 0.58101500 0.94564977
#> Sigma[16,7] 3.60318733 0.354126268 3.09845268 4.11925309
#> Sigma[16,8] -0.12684552 0.015431519 -0.15124793 -0.10832410
#> Sigma[16,9] 0.02005311 0.004384563 0.01338801 0.02606148
#> Sigma[16,10] 0.42827931 0.278089530 0.03458872 0.78017447
#> Sigma[16,11] 0.15127585 0.054673378 0.07208554 0.22411937
#> Sigma[16,12] 0.69637720 0.158850203 0.46557364 0.91840549
#> Sigma[16,13] 0.04677999 0.229837301 -0.23624296 0.42085940
#> Sigma[16,14] 0.11365576 0.021939552 0.08399254 0.14649528
#> Sigma[16,15] 6.70910371 1.474234225 5.69977550 9.38531270
#> Sigma[16,16] 1.04219557 0.092969727 0.93822275 1.17928413
#>
#> $Sigma$equation17
#> mean sd 5% quantile 95% quantile
#> Sigma[17,1] 3.49429852 0.60038364 2.61222271 4.14174038
#> Sigma[17,2] 0.80121137 0.32783317 0.39036989 1.27971896
#> Sigma[17,3] 0.55401218 0.09639766 0.41828078 0.67109945
#> Sigma[17,4] -0.67416659 0.55630780 -1.30341864 0.16450105
#> Sigma[17,5] 2.93212322 0.47758423 2.22775605 3.47363197
#> Sigma[17,6] 2.24785939 0.40711209 1.85918189 2.97346926
#> Sigma[17,7] 9.20800105 0.98195885 7.71778247 10.27403132
#> Sigma[17,8] -0.30444526 0.04467447 -0.34789374 -0.23312923
#> Sigma[17,9] 0.05747215 0.01646198 0.03794266 0.08065837
#> Sigma[17,10] 2.34967486 0.50320259 1.59440614 2.96597907
#> Sigma[17,11] 0.79240805 0.20951661 0.53204459 1.10490980
#> Sigma[17,12] 2.17964078 0.47242811 1.48341606 2.78611651
#> Sigma[17,13] 0.23808658 1.08179382 -1.00496368 1.84060117
#> Sigma[17,14] 0.54229817 0.08469549 0.44352251 0.67914918
#> Sigma[17,15] 14.89395939 2.40040245 11.91150237 18.27730267
#> Sigma[17,16] 1.82076206 0.22640981 1.50680874 2.04718438
#> Sigma[17,17] 8.94502469 0.56878857 8.06995087 9.65269917
#>
#> $Sigma$equation18
#> mean sd 5% quantile 95% quantile
#> Sigma[18,1] 4.87563422 0.95840573 3.38601082 5.89215645
#> Sigma[18,2] 1.21430995 0.40034674 0.68399383 1.77770370
#> Sigma[18,3] 0.61571336 0.13782607 0.39410116 0.77721003
#> Sigma[18,4] -0.99818141 0.72738456 -1.82548028 -0.03120583
#> Sigma[18,5] 4.14412336 0.68956297 3.17964874 5.16427934
#> Sigma[18,6] 3.52776510 0.45587307 3.09142397 4.32636826
#> Sigma[18,7] 11.33086558 1.07175656 9.52739003 12.45861523
#> Sigma[18,8] -0.38499136 0.06076918 -0.47033028 -0.30186664
#> Sigma[18,9] 0.09330701 0.01958320 0.06667577 0.11780734
#> Sigma[18,10] 3.60274163 0.88743231 2.22451714 4.52758793
#> Sigma[18,11] 1.09090326 0.30529661 0.69489599 1.55337106
#> Sigma[18,12] 2.93636558 0.63345705 1.95283225 3.80754988
#> Sigma[18,13] -0.04603178 1.34272123 -1.81913400 1.75757468
#> Sigma[18,14] 0.73816585 0.11379733 0.60906244 0.91527469
#> Sigma[18,15] 18.37400909 3.71058955 14.64498096 23.92171110
#> Sigma[18,16] 2.31088261 0.27696474 1.97496574 2.67410728
#> Sigma[18,17] 11.13391856 0.78443197 9.96226145 12.25571786
#> Sigma[18,18] 16.70315272 1.33639945 14.92466990 18.54323079
#>
#> $Sigma$equation19
#> mean sd 5% quantile 95% quantile
#> Sigma[19,1] 6.3708002088 0.84201388 5.36359444 7.39455960
#> Sigma[19,2] -0.5551752743 0.34433808 -0.96564679 -0.08937516
#> Sigma[19,3] -0.0006928793 0.09897093 -0.14820264 0.12563667
#> Sigma[19,4] -0.4859984784 0.43839942 -0.97471687 0.18691452
#> Sigma[19,5] 1.1852477853 0.47168432 0.56722159 1.75082087
#> Sigma[19,6] 2.7349492056 0.45775630 2.11407885 3.38399401
#> Sigma[19,7] 4.7244915582 1.00577543 3.35717801 6.11674045
#> Sigma[19,8] -0.1109846357 0.03506831 -0.16410892 -0.06690836
#> Sigma[19,9] 0.0295642180 0.01447584 0.01469002 0.05077896
#> Sigma[19,10] -1.4190241951 0.79917810 -2.62509870 -0.54520401
#> Sigma[19,11] -0.4552506449 0.25252878 -0.80112239 -0.07888503
#> Sigma[19,12] 0.7258781248 0.45711614 0.06875642 1.35477178
#> Sigma[19,13] -0.1921781931 0.49617483 -0.84220433 0.47913726
#> Sigma[19,14] 0.0852640847 0.10228032 -0.04724231 0.23009554
#> Sigma[19,15] 22.4231233938 3.69233515 18.09946585 28.27563152
#> Sigma[19,16] 0.7844821967 0.20083571 0.52935153 1.07982245
#> Sigma[19,17] 2.0369144018 0.57572531 1.35548553 2.86067887
#> Sigma[19,18] 3.0432909463 0.95173132 1.84920135 4.44677604
#> Sigma[19,19] 9.1709665931 0.98426698 7.84398233 10.40676998
#>
#> $Sigma$equation20
#> mean sd 5% quantile 95% quantile
#> Sigma[20,1] 3.22744442 1.35575434 1.83212094 5.38994250
#> Sigma[20,2] 0.11585824 0.74761821 -1.06589580 1.09785113
#> Sigma[20,3] -0.15091268 0.30706916 -0.63867971 0.20625710
#> Sigma[20,4] -0.39366690 0.74148810 -1.35142297 0.73132803
#> Sigma[20,5] 2.35024780 0.95005675 0.80410646 3.30975657
#> Sigma[20,6] 3.57873369 0.76827144 2.77174024 4.79670466
#> Sigma[20,7] 2.30280819 2.73919618 -1.32127054 6.07538846
#> Sigma[20,8] -0.05665738 0.08395535 -0.16774029 0.05796004
#> Sigma[20,9] 0.08829514 0.04551792 0.03658141 0.15319315
#> Sigma[20,10] 1.24924626 1.54053130 -0.74311819 3.39834556
#> Sigma[20,11] 0.06953239 0.46512504 -0.59546242 0.64672318
#> Sigma[20,12] -0.67009520 0.95297700 -2.11156566 0.17889736
#> Sigma[20,13] -0.53514275 1.71339112 -3.42474113 1.31132867
#> Sigma[20,14] -0.30059125 0.14571160 -0.49447319 -0.08441720
#> Sigma[20,15] 1.15207943 6.04963693 -5.40831138 11.06986579
#> Sigma[20,16] 0.65743629 0.40867623 0.17377337 1.22245098
#> Sigma[20,17] 3.64210600 1.43244665 1.33771527 5.30500461
#> Sigma[20,18] 7.06918503 1.85626011 4.56644861 9.91260623
#> Sigma[20,19] 2.76985688 1.08877232 1.91376408 4.68185396
#> Sigma[20,20] 32.16340531 4.09155198 26.87111299 38.05794299
#>
#>