This method converts an object of class mtar into a list of
mcmc objects, each corresponding to a Markov chain produced during
Bayesian estimation.
Arguments
- x
an object of class
mtarobtained from a call tomtar().- ...
additional arguments passed to specific coercion methods.
Value
A list of mcmc objects containing the posterior simulation draws
generated by the mtar() routine.
Examples
# \donttest{
###### Example 1: Returns of the closing prices of three financial indexes
data(returns)
fit1 <- mtar(~ COLCAP + BOVESPA | SP500, data=returns, row.names=Date,
subset={Date<="2015-12-07"}, dist="Student-t",
ars=ars(nregim=3,p=c(1,1,2)), n.burnin=100, n.sim=200,
n.thin=2, ssvs=TRUE)
fit1.mcmc <- coda::as.mcmc(fit1)
summary(fit1.mcmc)
#>
#>
#> Iterations = 101:499
#>
#> Thinning interval = 2
#>
#> Sample size per chain = 200
#>
#>
#> Thresholds:
#> Mean Sd Sd(Mean) 2.5% 25% 50%
#> Threshold.1 -0.0032633 0.00204645 0.00205577 -0.0062766 -0.0056319 -0.0020219
#> Threshold.2 0.0075539 0.00036781 0.00013627 0.0069881 0.0074070 0.0075601
#> 75% 97.5%
#> Threshold.1 -0.0012605 -0.0011679
#> Threshold.2 0.0076811 0.0085914
#>
#>
#> Regime 1
#>
#>
#> Autoregressive coefficients:
#> Mean Sd Sd(Mean) 2.5% 25%
#> COLCAP:(Intercept) -0.0040111 0.0012798 0.0006314 -0.0065490 -0.0051373
#> COLCAP:COLCAP.lag(1) 0.1649665 0.0689562 0.0060477 0.0548244 0.1128312
#> COLCAP:BOVESPA.lag(1) 0.0775207 0.0390196 0.0027591 0.0056815 0.0491333
#> BOVESPA:(Intercept) -0.0090429 0.0020337 0.0013875 -0.0128886 -0.0110790
#> BOVESPA:COLCAP.lag(1) -0.0100751 0.0963406 0.0272727 -0.1875211 -0.0638798
#> BOVESPA:BOVESPA.lag(1) 0.0203058 0.0576634 0.0065665 -0.0830870 -0.0164095
#> 50% 75% 97.5%
#> COLCAP:(Intercept) -0.0035320 -0.0030621 -0.0023876
#> COLCAP:COLCAP.lag(1) 0.1599718 0.2123679 0.2997001
#> COLCAP:BOVESPA.lag(1) 0.0773847 0.1005416 0.1579631
#> BOVESPA:(Intercept) -0.0083261 -0.0073594 -0.0064845
#> BOVESPA:COLCAP.lag(1) -0.0021389 0.0497719 0.1747427
#> BOVESPA:BOVESPA.lag(1) 0.0171241 0.0578784 0.1395162
#>
#>
#> Scale parameter:
#> Mean Sd Sd(Mean) 2.5% 25%
#> COLCAP.COLCAP 6.7126e-05 9.0715e-06 3.8578e-06 5.3300e-05 6.0157e-05
#> COLCAP.BOVESPA 3.6543e-05 7.4389e-06 2.3499e-06 2.4428e-05 3.1362e-05
#> BOVESPA.BOVESPA 1.3420e-04 1.6345e-05 3.7590e-06 1.0809e-04 1.2241e-04
#> 50% 75% 97.5%
#> COLCAP.COLCAP 6.5228e-05 7.2787e-05 8.8545e-05
#> COLCAP.BOVESPA 3.6185e-05 4.0620e-05 5.2086e-05
#> BOVESPA.BOVESPA 1.3231e-04 1.4464e-04 1.7317e-04
#>
#>
#> Regime 2
#>
#>
#> Autoregressive coefficients:
#> Mean Sd Sd(Mean) 2.5%
#> COLCAP:(Intercept) 0.00029170 0.00030676 6.4065e-05 -0.00028597
#> COLCAP:COLCAP.lag(1) 0.07190691 0.03294205 2.3294e-03 0.00418045
#> COLCAP:BOVESPA.lag(1) 0.08147656 0.02124026 3.4288e-03 0.04580615
#> BOVESPA:(Intercept) 0.00025408 0.00065069 3.1513e-04 -0.00095336
#> BOVESPA:COLCAP.lag(1) 0.05981546 0.04616000 3.2718e-03 -0.02494411
#> BOVESPA:BOVESPA.lag(1) -0.04192015 0.02933647 2.1962e-03 -0.09414007
#> 25% 50% 75% 97.5%
#> COLCAP:(Intercept) 0.00010437 0.00029305 0.00050150 0.00089092
#> COLCAP:COLCAP.lag(1) 0.05094025 0.07111368 0.09554430 0.13178400
#> COLCAP:BOVESPA.lag(1) 0.06641560 0.08165828 0.09592064 0.11887269
#> BOVESPA:(Intercept) -0.00019958 0.00030706 0.00072692 0.00140899
#> BOVESPA:COLCAP.lag(1) 0.02836742 0.05794963 0.09522793 0.16653438
#> BOVESPA:BOVESPA.lag(1) -0.06170658 -0.04370606 -0.02015080 0.01418482
#>
#>
#> Scale parameter:
#> Mean Sd Sd(Mean) 2.5% 25%
#> COLCAP.COLCAP 4.1046e-05 2.6957e-06 4.8888e-07 3.5516e-05 3.9173e-05
#> COLCAP.BOVESPA 1.1236e-05 2.7873e-06 8.0873e-07 5.4037e-06 9.2464e-06
#> BOVESPA.BOVESPA 8.3488e-05 6.5583e-06 1.3921e-06 7.2043e-05 7.9214e-05
#> 50% 75% 97.5%
#> COLCAP.COLCAP 4.1209e-05 4.2955e-05 4.6347e-05
#> COLCAP.BOVESPA 1.1439e-05 1.3182e-05 1.5951e-05
#> BOVESPA.BOVESPA 8.2406e-05 8.7453e-05 9.7360e-05
#>
#>
#> Regime 3
#>
#>
#> Autoregressive coefficients:
#> Mean Sd Sd(Mean) 2.5% 25%
#> COLCAP:(Intercept) 0.0048878 0.00054873 5.8798e-05 0.0036875 0.0045449
#> COLCAP:COLCAP.lag(1) 0.0509644 0.06496957 5.3949e-03 -0.0744603 0.0088231
#> COLCAP:BOVESPA.lag(1) 0.0729914 0.04667791 4.0536e-03 -0.0171404 0.0455978
#> COLCAP:COLCAP.lag(2) 0.0536864 0.05724897 4.0481e-03 -0.0524903 0.0139236
#> COLCAP:BOVESPA.lag(2) -0.0670312 0.03657777 2.5864e-03 -0.1421984 -0.0890717
#> BOVESPA:(Intercept) 0.0113719 0.00097590 1.3366e-04 0.0096076 0.0105994
#> BOVESPA:COLCAP.lag(1) 0.1522318 0.09032303 6.3868e-03 -0.0397454 0.0993301
#> BOVESPA:BOVESPA.lag(1) -0.1093142 0.07048181 5.5421e-03 -0.2427404 -0.1595007
#> BOVESPA:COLCAP.lag(2) -0.0775529 0.09084758 6.4239e-03 -0.2775178 -0.1351824
#> BOVESPA:BOVESPA.lag(2) -0.0518336 0.06278550 5.6799e-03 -0.1577880 -0.0993907
#> 50% 75% 97.5%
#> COLCAP:(Intercept) 0.0048966 0.0052596 0.0058483
#> COLCAP:COLCAP.lag(1) 0.0501113 0.0941849 0.1747570
#> COLCAP:BOVESPA.lag(1) 0.0740895 0.0994478 0.1567424
#> COLCAP:COLCAP.lag(2) 0.0538258 0.0922435 0.1780201
#> COLCAP:BOVESPA.lag(2) -0.0654872 -0.0455865 0.0083543
#> BOVESPA:(Intercept) 0.0113315 0.0120043 0.0130783
#> BOVESPA:COLCAP.lag(1) 0.1516646 0.2034911 0.3195698
#> BOVESPA:BOVESPA.lag(1) -0.1062808 -0.0599649 0.0195261
#> BOVESPA:COLCAP.lag(2) -0.0709825 -0.0167992 0.0903136
#> BOVESPA:BOVESPA.lag(2) -0.0536160 -0.0067657 0.0667547
#>
#>
#> Scale parameter:
#> Mean Sd Sd(Mean) 2.5% 25%
#> COLCAP.COLCAP 5.6085e-05 7.0540e-06 6.2274e-07 4.2955e-05 5.0820e-05
#> COLCAP.BOVESPA 2.5742e-05 6.4496e-06 5.3667e-07 1.3933e-05 2.1283e-05
#> BOVESPA.BOVESPA 1.3598e-04 1.5963e-05 1.5463e-06 1.0942e-04 1.2543e-04
#> 50% 75% 97.5%
#> COLCAP.COLCAP 5.5752e-05 6.1287e-05 6.9593e-05
#> COLCAP.BOVESPA 2.4733e-05 2.9569e-05 3.9837e-05
#> BOVESPA.BOVESPA 1.3454e-04 1.4547e-04 1.7068e-04
#>
#>
#> Extra parameter:
#> Mean Sd Sd(Mean) 2.5% 25% 50% 75% 97.5%
#> nu 6.0913 0.81123 0.23293 4.7685 5.4594 6.0523 6.6795 7.8557
#plot(fit1.mcmc)
###### Example 2: Rainfall and two river flows in Colombia
data(riverflows)
fit2 <- mtar(~ Bedon + LaPlata | Rainfall, data=riverflows, row.names=Date,
subset={Date<="2009-02-13"}, dist="Laplace",
ars=ars(nregim=3,p=5), n.burnin=100, n.sim=200, n.thin=2)
fit2.mcmc <- coda::as.mcmc(fit2)
summary(fit2.mcmc)
#>
#>
#> Iterations = 101:499
#>
#> Thinning interval = 2
#>
#> Sample size per chain = 200
#>
#>
#> Thresholds:
#> Mean Sd Sd(Mean) 2.5% 25% 50% 75% 97.5%
#> Threshold.1 3.026 0.0433821 0.0300934 3 3 3 3.0981 3.0981
#> Threshold.2 10.004 0.0061631 0.0042752 10 10 10 10.0139 10.0139
#>
#>
#> Regime 1
#>
#>
#> Autoregressive coefficients:
#> Mean Sd Sd(Mean) 2.5% 25%
#> Bedon:(Intercept) 1.3263361 0.1119401 0.01091341 1.1353877 1.2456164
#> Bedon:Bedon.lag(1) 0.5650208 0.0344949 0.00351298 0.5027368 0.5419639
#> Bedon:LaPlata.lag(1) 0.0440013 0.0156314 0.00164295 0.0120199 0.0334174
#> Bedon:Bedon.lag(2) 0.0480389 0.0327929 0.00379232 -0.0246206 0.0255715
#> Bedon:LaPlata.lag(2) -0.0174564 0.0121027 0.00115934 -0.0440817 -0.0256149
#> Bedon:Bedon.lag(3) 0.0267378 0.0311043 0.00348603 -0.0262251 0.0055129
#> Bedon:LaPlata.lag(3) 0.0023923 0.0115537 0.00126342 -0.0207066 -0.0062340
#> Bedon:Bedon.lag(4) 0.0363536 0.0312001 0.00278455 -0.0252625 0.0148668
#> Bedon:LaPlata.lag(4) -0.0157276 0.0093116 0.00086573 -0.0337990 -0.0220705
#> Bedon:Bedon.lag(5) 0.0823471 0.0253253 0.00259814 0.0325072 0.0670221
#> Bedon:LaPlata.lag(5) -0.0063663 0.0069921 0.00056255 -0.0194006 -0.0112191
#> LaPlata:(Intercept) 3.4577154 0.3541327 0.04306812 2.8028516 3.2189720
#> LaPlata:Bedon.lag(1) 0.1571491 0.0983607 0.01071078 -0.0388148 0.0835014
#> LaPlata:LaPlata.lag(1) 0.6267787 0.0408616 0.00448569 0.5503184 0.6017877
#> LaPlata:Bedon.lag(2) -0.0448745 0.0837210 0.00864358 -0.2021332 -0.1003584
#> LaPlata:LaPlata.lag(2) -0.0635786 0.0346859 0.00357316 -0.1270740 -0.0879111
#> LaPlata:Bedon.lag(3) 0.0168143 0.0646625 0.00520161 -0.1021400 -0.0261434
#> LaPlata:LaPlata.lag(3) 0.0658315 0.0289243 0.00298018 0.0072065 0.0475842
#> LaPlata:Bedon.lag(4) -0.0769915 0.0762439 0.00750363 -0.2491168 -0.1231024
#> LaPlata:LaPlata.lag(4) 0.0046764 0.0281731 0.00310171 -0.0410747 -0.0165500
#> LaPlata:Bedon.lag(5) 0.1376886 0.0592346 0.00547194 0.0220538 0.1029823
#> LaPlata:LaPlata.lag(5) 0.0294151 0.0212047 0.00197432 -0.0161434 0.0172946
#> 50% 75% 97.5%
#> Bedon:(Intercept) 1.3136414 1.3997095 1.5412575
#> Bedon:Bedon.lag(1) 0.5635970 0.5902108 0.6328029
#> Bedon:LaPlata.lag(1) 0.0431536 0.0560077 0.0725852
#> Bedon:Bedon.lag(2) 0.0485074 0.0722729 0.1117650
#> Bedon:LaPlata.lag(2) -0.0170128 -0.0089957 0.0033845
#> Bedon:Bedon.lag(3) 0.0257698 0.0499449 0.0856332
#> Bedon:LaPlata.lag(3) 0.0034692 0.0107995 0.0221273
#> Bedon:Bedon.lag(4) 0.0364835 0.0571420 0.0922157
#> Bedon:LaPlata.lag(4) -0.0160227 -0.0102018 0.0050029
#> Bedon:Bedon.lag(5) 0.0817374 0.0997405 0.1312570
#> Bedon:LaPlata.lag(5) -0.0068401 -0.0013747 0.0072500
#> LaPlata:(Intercept) 3.4537652 3.6756441 4.3154744
#> LaPlata:Bedon.lag(1) 0.1630910 0.2319518 0.3084857
#> LaPlata:LaPlata.lag(1) 0.6255404 0.6550420 0.7011373
#> LaPlata:Bedon.lag(2) -0.0385039 0.0142144 0.1061221
#> LaPlata:LaPlata.lag(2) -0.0651415 -0.0394819 0.0040026
#> LaPlata:Bedon.lag(3) 0.0182393 0.0659936 0.1457359
#> LaPlata:LaPlata.lag(3) 0.0675773 0.0851664 0.1147958
#> LaPlata:Bedon.lag(4) -0.0764732 -0.0274476 0.0639455
#> LaPlata:LaPlata.lag(4) 0.0030253 0.0255099 0.0565357
#> LaPlata:Bedon.lag(5) 0.1363488 0.1707403 0.2613932
#> LaPlata:LaPlata.lag(5) 0.0311540 0.0425327 0.0716608
#>
#>
#> Scale parameter:
#> Mean Sd Sd(Mean) 2.5% 25% 50% 75%
#> Bedon.Bedon 0.32573 0.030332 0.0029826 0.27542 0.30209 0.32485 0.34982
#> Bedon.LaPlata 0.36547 0.057605 0.0043241 0.25732 0.32167 0.36778 0.41004
#> LaPlata.LaPlata 2.34178 0.237389 0.0197894 1.90043 2.16362 2.33477 2.47205
#> 97.5%
#> Bedon.Bedon 0.38389
#> Bedon.LaPlata 0.46292
#> LaPlata.LaPlata 2.84057
#>
#>
#> Regime 2
#>
#>
#> Autoregressive coefficients:
#> Mean Sd Sd(Mean) 2.5% 25%
#> Bedon:(Intercept) 2.0901413 0.448815 0.0500516 1.2721444 1.7212590
#> Bedon:Bedon.lag(1) 0.5796506 0.045653 0.0042450 0.4854426 0.5510907
#> Bedon:LaPlata.lag(1) 0.0207756 0.013792 0.0013271 -0.0061785 0.0124392
#> Bedon:Bedon.lag(2) 0.0983530 0.064210 0.0072201 -0.0346337 0.0523763
#> Bedon:LaPlata.lag(2) -0.0179113 0.017192 0.0017451 -0.0473864 -0.0304392
#> Bedon:Bedon.lag(3) -0.0260077 0.060441 0.0072691 -0.1426571 -0.0674385
#> Bedon:LaPlata.lag(3) -0.0092837 0.015241 0.0011684 -0.0375889 -0.0210545
#> Bedon:Bedon.lag(4) 0.1034415 0.060201 0.0081147 -0.0043601 0.0583517
#> Bedon:LaPlata.lag(4) 0.0083872 0.017784 0.0020167 -0.0281609 -0.0018485
#> Bedon:Bedon.lag(5) 0.0191588 0.044757 0.0066557 -0.0615284 -0.0108821
#> Bedon:LaPlata.lag(5) 0.0057790 0.014979 0.0015064 -0.0216804 -0.0053849
#> LaPlata:(Intercept) 6.7924065 1.044097 0.1162270 4.9224005 6.0110870
#> LaPlata:Bedon.lag(1) 0.1462528 0.102395 0.0100347 -0.0372265 0.0720045
#> LaPlata:LaPlata.lag(1) 0.5246536 0.041794 0.0049636 0.4448871 0.4956671
#> LaPlata:Bedon.lag(2) 0.0012900 0.124805 0.0109253 -0.2570708 -0.0804959
#> LaPlata:LaPlata.lag(2) 0.0355301 0.037383 0.0034563 -0.0509692 0.0127207
#> LaPlata:Bedon.lag(3) -0.0585389 0.111192 0.0118525 -0.2806787 -0.1363642
#> LaPlata:LaPlata.lag(3) 0.0420448 0.030552 0.0030546 -0.0120441 0.0202405
#> LaPlata:Bedon.lag(4) 0.2208690 0.134966 0.0129446 -0.0314236 0.1191283
#> LaPlata:LaPlata.lag(4) -0.0438973 0.040347 0.0042126 -0.1148359 -0.0729232
#> LaPlata:Bedon.lag(5) -0.2694943 0.113779 0.0098496 -0.4685395 -0.3429293
#> LaPlata:LaPlata.lag(5) 0.1183315 0.042720 0.0049824 0.0349275 0.0914981
#> 50% 75% 97.5%
#> Bedon:(Intercept) 2.0838162 2.41749585 2.983490
#> Bedon:Bedon.lag(1) 0.5790116 0.60910295 0.660550
#> Bedon:LaPlata.lag(1) 0.0201319 0.03087145 0.048938
#> Bedon:Bedon.lag(2) 0.1049092 0.14086732 0.204705
#> Bedon:LaPlata.lag(2) -0.0190815 -0.00303609 0.011546
#> Bedon:Bedon.lag(3) -0.0249634 0.01455329 0.079968
#> Bedon:LaPlata.lag(3) -0.0090022 -0.00047109 0.020641
#> Bedon:Bedon.lag(4) 0.1053701 0.14605400 0.215616
#> Bedon:LaPlata.lag(4) 0.0079078 0.01956083 0.045199
#> Bedon:Bedon.lag(5) 0.0183559 0.04719693 0.113739
#> Bedon:LaPlata.lag(5) 0.0058328 0.01517325 0.035502
#> LaPlata:(Intercept) 6.7860605 7.55824666 8.745831
#> LaPlata:Bedon.lag(1) 0.1435381 0.20833582 0.343430
#> LaPlata:LaPlata.lag(1) 0.5280016 0.55376325 0.596631
#> LaPlata:Bedon.lag(2) 0.0015926 0.07932802 0.251273
#> LaPlata:LaPlata.lag(2) 0.0365990 0.05952563 0.107607
#> LaPlata:Bedon.lag(3) -0.0502738 0.01135774 0.139689
#> LaPlata:LaPlata.lag(3) 0.0439495 0.05988409 0.105686
#> LaPlata:Bedon.lag(4) 0.2287663 0.31605335 0.462880
#> LaPlata:LaPlata.lag(4) -0.0442119 -0.01347804 0.048467
#> LaPlata:Bedon.lag(5) -0.2718373 -0.20001668 -0.052741
#> LaPlata:LaPlata.lag(5) 0.1229004 0.14491911 0.199927
#>
#>
#> Scale parameter:
#> Mean Sd Sd(Mean) 2.5% 25% 50% 75% 97.5%
#> Bedon.Bedon 1.0979 0.12587 0.011688 0.86740 1.0111 1.0893 1.1837 1.3699
#> Bedon.LaPlata 1.3261 0.19819 0.017958 0.99338 1.1876 1.3130 1.4354 1.7607
#> LaPlata.LaPlata 6.4808 0.64504 0.063394 5.43585 5.9937 6.3801 6.9312 7.8860
#>
#>
#> Regime 3
#>
#>
#> Autoregressive coefficients:
#> Mean Sd Sd(Mean) 2.5% 25%
#> Bedon:(Intercept) 5.7246303 0.803034 0.0736335 4.2485443 5.1753318
#> Bedon:Bedon.lag(1) 0.4552767 0.088057 0.0101792 0.2875636 0.3889481
#> Bedon:LaPlata.lag(1) 0.0452820 0.016225 0.0019632 0.0157154 0.0351546
#> Bedon:Bedon.lag(2) 0.0850427 0.075437 0.0068484 -0.0494261 0.0293901
#> Bedon:LaPlata.lag(2) -0.0011437 0.018205 0.0016435 -0.0374175 -0.0128195
#> Bedon:Bedon.lag(3) -0.0931942 0.062245 0.0059193 -0.2040973 -0.1308777
#> Bedon:LaPlata.lag(3) 0.0321278 0.018212 0.0017322 -0.0054082 0.0212128
#> Bedon:Bedon.lag(4) -0.0042984 0.068667 0.0070719 -0.1236375 -0.0531644
#> Bedon:LaPlata.lag(4) 0.0044136 0.020007 0.0022328 -0.0321187 -0.0082318
#> Bedon:Bedon.lag(5) 0.1906821 0.068484 0.0066371 0.0704656 0.1408764
#> Bedon:LaPlata.lag(5) -0.0139646 0.016516 0.0027483 -0.0481332 -0.0238568
#> LaPlata:(Intercept) 17.3347149 2.993367 0.2733791 11.8178416 15.1954986
#> LaPlata:Bedon.lag(1) 0.4831105 0.251622 0.0236822 0.0411294 0.3132401
#> LaPlata:LaPlata.lag(1) 0.3328200 0.064177 0.0067902 0.2053928 0.2897544
#> LaPlata:Bedon.lag(2) -0.5549851 0.283760 0.0296837 -1.0494585 -0.7787602
#> LaPlata:LaPlata.lag(2) 0.1278156 0.070818 0.0076932 0.0049879 0.0790013
#> LaPlata:Bedon.lag(3) -0.5794237 0.235672 0.0193542 -1.0366461 -0.7605889
#> LaPlata:LaPlata.lag(3) 0.2797343 0.082561 0.0085675 0.1040718 0.2275418
#> LaPlata:Bedon.lag(4) 0.0105755 0.298062 0.0343586 -0.5606337 -0.1944424
#> LaPlata:LaPlata.lag(4) -0.0071711 0.075434 0.0078117 -0.1605965 -0.0575582
#> LaPlata:Bedon.lag(5) 0.3222044 0.255771 0.0281877 -0.2243294 0.1588703
#> LaPlata:LaPlata.lag(5) 0.0652834 0.061864 0.0054488 -0.0527165 0.0217019
#> 50% 75% 97.5%
#> Bedon:(Intercept) 5.69198235 6.2787616 7.364283
#> Bedon:Bedon.lag(1) 0.45509178 0.5150297 0.642577
#> Bedon:LaPlata.lag(1) 0.04470012 0.0549151 0.078968
#> Bedon:Bedon.lag(2) 0.08343278 0.1341359 0.236820
#> Bedon:LaPlata.lag(2) -0.00052599 0.0094767 0.033822
#> Bedon:Bedon.lag(3) -0.09848641 -0.0550215 0.032365
#> Bedon:LaPlata.lag(3) 0.03330632 0.0436873 0.064642
#> Bedon:Bedon.lag(4) -0.00398724 0.0423601 0.126334
#> Bedon:LaPlata.lag(4) 0.00233287 0.0165776 0.044557
#> Bedon:Bedon.lag(5) 0.19084273 0.2349515 0.322748
#> Bedon:LaPlata.lag(5) -0.01411361 -0.0047528 0.021367
#> LaPlata:(Intercept) 17.26968612 19.4832380 22.761366
#> LaPlata:Bedon.lag(1) 0.48726570 0.6489693 0.968823
#> LaPlata:LaPlata.lag(1) 0.33095477 0.3790037 0.458355
#> LaPlata:Bedon.lag(2) -0.55849281 -0.3531028 0.039680
#> LaPlata:LaPlata.lag(2) 0.12498666 0.1659485 0.285965
#> LaPlata:Bedon.lag(3) -0.57583777 -0.4295905 -0.093438
#> LaPlata:LaPlata.lag(3) 0.28100137 0.3402798 0.430171
#> LaPlata:Bedon.lag(4) 0.00327710 0.1986016 0.618417
#> LaPlata:LaPlata.lag(4) -0.00830032 0.0432333 0.146253
#> LaPlata:Bedon.lag(5) 0.33107759 0.4873765 0.806392
#> LaPlata:LaPlata.lag(5) 0.06132628 0.1051924 0.177252
#>
#>
#> Scale parameter:
#> Mean Sd Sd(Mean) 2.5% 25% 50% 75%
#> Bedon.Bedon 2.7546 0.29406 0.027869 2.2206 2.5649 2.7200 2.9452
#> Bedon.LaPlata 7.0782 0.91609 0.084649 5.3303 6.4014 7.0909 7.6865
#> LaPlata.LaPlata 42.8940 4.65825 0.481227 34.0608 39.5116 43.1305 46.1918
#> 97.5%
#> Bedon.Bedon 3.3379
#> Bedon.LaPlata 8.7387
#> LaPlata.LaPlata 51.5446
#plot(fit2.mcmc)
###### Example 3: Temperature, precipitation, and two river flows in Iceland
data(iceland.rf)
fit3 <- mtar(~ Jokulsa + Vatnsdalsa | Temperature | Precipitation,
data=iceland.rf, subset={Date<="1974-11-06"}, row.names=Date,
ars=ars(nregim=2,p=15,q=4,d=2), n.burnin=100, n.sim=200,
n.thin=2, dist="Slash")
fit3.mcmc <- coda::as.mcmc(fit3)
summary(fit3.mcmc)
#>
#>
#> Iterations = 101:499
#>
#> Thinning interval = 2
#>
#> Sample size per chain = 200
#>
#>
#> Thresholds:
#> Mean Sd Sd(Mean) 2.5% 25% 50% 75% 97.5%
#> threshold 0.6419 0.044011 0.0087852 0.59845 0.62093 0.63938 0.66426 0.75651
#>
#>
#> Regime 1
#>
#>
#> Autoregressive coefficients:
#> Mean Sd Sd(Mean) 2.5%
#> Jokulsa:(Intercept) 3.37291575 0.3738113 0.05132478 2.72796577
#> Jokulsa:Jokulsa.lag( 1) 0.87491337 0.0356429 0.00606073 0.78602067
#> Jokulsa:Vatnsdalsa.lag( 1) 0.26284150 0.0676909 0.00837514 0.09989323
#> Jokulsa:Jokulsa.lag( 2) -0.05613492 0.0278168 0.00378241 -0.10635128
#> Jokulsa:Vatnsdalsa.lag( 2) -0.26422034 0.0828826 0.01051590 -0.40268043
#> Jokulsa:Jokulsa.lag( 3) -0.00502408 0.0204680 0.00185515 -0.04486862
#> Jokulsa:Vatnsdalsa.lag( 3) 0.09482147 0.0481523 0.00515505 -0.00063473
#> Jokulsa:Jokulsa.lag( 4) 0.00188572 0.0238723 0.00291808 -0.04080924
#> Jokulsa:Vatnsdalsa.lag( 4) -0.01751335 0.0455507 0.00551960 -0.10440792
#> Jokulsa:Jokulsa.lag( 5) -0.00700057 0.0294971 0.00485288 -0.06516815
#> Jokulsa:Vatnsdalsa.lag( 5) -0.02948134 0.0344369 0.00309998 -0.11202005
#> Jokulsa:Jokulsa.lag( 6) 0.02037479 0.0306703 0.00437353 -0.04886117
#> Jokulsa:Vatnsdalsa.lag( 6) -0.01948110 0.0431356 0.00376958 -0.09145434
#> Jokulsa:Jokulsa.lag( 7) 0.00842426 0.0321651 0.00363731 -0.05407921
#> Jokulsa:Vatnsdalsa.lag( 7) 0.01774714 0.0363720 0.00312848 -0.04709370
#> Jokulsa:Jokulsa.lag( 8) -0.00359778 0.0245993 0.00231723 -0.05985398
#> Jokulsa:Vatnsdalsa.lag( 8) -0.00757565 0.0302789 0.00241052 -0.06575341
#> Jokulsa:Jokulsa.lag( 9) 0.00067841 0.0229990 0.00274483 -0.04600539
#> Jokulsa:Vatnsdalsa.lag( 9) -0.01414938 0.0382265 0.00466781 -0.08226343
#> Jokulsa:Jokulsa.lag(10) 0.02033506 0.0188401 0.00204999 -0.01894286
#> Jokulsa:Vatnsdalsa.lag(10) 0.02425402 0.0317041 0.00292033 -0.04157495
#> Jokulsa:Jokulsa.lag(11) -0.01045031 0.0149179 0.00135785 -0.03869200
#> Jokulsa:Vatnsdalsa.lag(11) -0.01204913 0.0268765 0.00219763 -0.06096264
#> Jokulsa:Jokulsa.lag(12) 0.00619938 0.0142500 0.00117377 -0.02367890
#> Jokulsa:Vatnsdalsa.lag(12) 0.00397570 0.0255946 0.00224973 -0.05561005
#> Jokulsa:Jokulsa.lag(13) -0.01346337 0.0186535 0.00295062 -0.04872400
#> Jokulsa:Vatnsdalsa.lag(13) -0.01316897 0.0293369 0.00227486 -0.07331761
#> Jokulsa:Jokulsa.lag(14) 0.00262397 0.0145345 0.00142251 -0.02272183
#> Jokulsa:Vatnsdalsa.lag(14) 0.00940603 0.0319871 0.00335960 -0.04634493
#> Jokulsa:Jokulsa.lag(15) 0.01902433 0.0157158 0.00244726 -0.00727573
#> Jokulsa:Vatnsdalsa.lag(15) -0.01743824 0.0222495 0.00278425 -0.06168464
#> Jokulsa:Precipitation.lag(1) 0.00506774 0.0083477 0.00086266 -0.00977571
#> Jokulsa:Precipitation.lag(2) 0.00639657 0.0078152 0.00083301 -0.00894865
#> Jokulsa:Precipitation.lag(3) -0.01089198 0.0064382 0.00071678 -0.02320853
#> Jokulsa:Precipitation.lag(4) 0.01905336 0.0068085 0.00057274 0.00757450
#> Jokulsa:Temperature.lag(1) 0.01668385 0.0107009 0.00085716 -0.00317323
#> Jokulsa:Temperature.lag(2) -0.03275620 0.0103536 0.00074442 -0.05125429
#> Vatnsdalsa:(Intercept) 0.71012159 0.2034522 0.03222098 0.34334393
#> Vatnsdalsa:Jokulsa.lag( 1) -0.05172657 0.0205848 0.00358538 -0.09973940
#> Vatnsdalsa:Vatnsdalsa.lag( 1) 1.17069309 0.0524854 0.00850959 1.06110198
#> Vatnsdalsa:Jokulsa.lag( 2) 0.04976420 0.0173753 0.00282729 0.02027858
#> Vatnsdalsa:Vatnsdalsa.lag( 2) -0.32317848 0.0611721 0.00864549 -0.43367638
#> Vatnsdalsa:Jokulsa.lag( 3) -0.03115881 0.0138961 0.00161844 -0.05707707
#> Vatnsdalsa:Vatnsdalsa.lag( 3) 0.07646332 0.0398256 0.00486392 0.00170481
#> Vatnsdalsa:Jokulsa.lag( 4) 0.01261010 0.0136904 0.00132165 -0.01356353
#> Vatnsdalsa:Vatnsdalsa.lag( 4) -0.02653970 0.0353705 0.00528902 -0.09984629
#> Vatnsdalsa:Jokulsa.lag( 5) 0.00915004 0.0161340 0.00162285 -0.02035812
#> Vatnsdalsa:Vatnsdalsa.lag( 5) -0.00503993 0.0232417 0.00235570 -0.05091455
#> Vatnsdalsa:Jokulsa.lag( 6) 0.00323919 0.0160352 0.00243798 -0.03141680
#> Vatnsdalsa:Vatnsdalsa.lag( 6) -0.01851798 0.0221049 0.00179521 -0.06450978
#> Vatnsdalsa:Jokulsa.lag( 7) 0.00290876 0.0165645 0.00250058 -0.02524519
#> Vatnsdalsa:Vatnsdalsa.lag( 7) 0.01616759 0.0203089 0.00143606 -0.02304288
#> Vatnsdalsa:Jokulsa.lag( 8) -0.01700727 0.0130230 0.00123568 -0.04202431
#> Vatnsdalsa:Vatnsdalsa.lag( 8) 0.01022249 0.0169499 0.00119854 -0.02122039
#> Vatnsdalsa:Jokulsa.lag( 9) 0.02135234 0.0144114 0.00192882 -0.00762940
#> Vatnsdalsa:Vatnsdalsa.lag( 9) 0.00140855 0.0176913 0.00125097 -0.03723757
#> Vatnsdalsa:Jokulsa.lag(10) -0.01746462 0.0123124 0.00172894 -0.04202078
#> Vatnsdalsa:Vatnsdalsa.lag(10) 0.00943483 0.0185416 0.00145489 -0.02069355
#> Vatnsdalsa:Jokulsa.lag(11) 0.01217450 0.0092289 0.00074830 -0.00615017
#> Vatnsdalsa:Vatnsdalsa.lag(11) 0.00131612 0.0199306 0.00192239 -0.03132154
#> Vatnsdalsa:Jokulsa.lag(12) -0.01167575 0.0094818 0.00079459 -0.02755721
#> Vatnsdalsa:Vatnsdalsa.lag(12) -0.00695448 0.0182509 0.00144275 -0.04571646
#> Vatnsdalsa:Jokulsa.lag(13) 0.00667601 0.0105540 0.00113520 -0.01404492
#> Vatnsdalsa:Vatnsdalsa.lag(13) -0.01888670 0.0221481 0.00225939 -0.06437729
#> Vatnsdalsa:Jokulsa.lag(14) -0.00944722 0.0090079 0.00077033 -0.02476557
#> Vatnsdalsa:Vatnsdalsa.lag(14) 0.03897104 0.0200668 0.00196846 0.00514587
#> Vatnsdalsa:Jokulsa.lag(15) 0.00649461 0.0064170 0.00059136 -0.00570876
#> Vatnsdalsa:Vatnsdalsa.lag(15) 0.00033076 0.0136080 0.00128547 -0.02655419
#> Vatnsdalsa:Precipitation.lag(1) 0.00124755 0.0059270 0.00056165 -0.00962589
#> Vatnsdalsa:Precipitation.lag(2) 0.00159092 0.0047918 0.00044806 -0.00756886
#> Vatnsdalsa:Precipitation.lag(3) -0.00307203 0.0040052 0.00031192 -0.01090243
#> Vatnsdalsa:Precipitation.lag(4) 0.00626564 0.0040930 0.00037787 -0.00161143
#> Vatnsdalsa:Temperature.lag(1) -0.00026353 0.0067803 0.00054544 -0.01304071
#> Vatnsdalsa:Temperature.lag(2) -0.01089012 0.0065559 0.00063726 -0.02332996
#> 25% 50% 75% 97.5%
#> Jokulsa:(Intercept) 3.1232e+00 3.31585412 3.57676338 4.1833769
#> Jokulsa:Jokulsa.lag( 1) 8.6568e-01 0.88469442 0.89641355 0.9223210
#> Jokulsa:Vatnsdalsa.lag( 1) 2.2785e-01 0.26586936 0.30084568 0.3898561
#> Jokulsa:Jokulsa.lag( 2) -7.4913e-02 -0.05868010 -0.03846602 0.0066228
#> Jokulsa:Vatnsdalsa.lag( 2) -3.1598e-01 -0.27502887 -0.21226232 -0.0897327
#> Jokulsa:Jokulsa.lag( 3) -1.8750e-02 -0.00475182 0.00779293 0.0362135
#> Jokulsa:Vatnsdalsa.lag( 3) 6.2739e-02 0.09482959 0.12874968 0.1898428
#> Jokulsa:Jokulsa.lag( 4) -1.6787e-02 0.00110311 0.02057007 0.0442602
#> Jokulsa:Vatnsdalsa.lag( 4) -4.7551e-02 -0.01947778 0.01316886 0.0757773
#> Jokulsa:Jokulsa.lag( 5) -3.0314e-02 -0.00321849 0.01517453 0.0414271
#> Jokulsa:Vatnsdalsa.lag( 5) -4.9870e-02 -0.02663273 -0.00355843 0.0286329
#> Jokulsa:Jokulsa.lag( 6) 9.5706e-05 0.02088125 0.03991166 0.0729072
#> Jokulsa:Vatnsdalsa.lag( 6) -5.2081e-02 -0.01914658 0.01022812 0.0614701
#> Jokulsa:Jokulsa.lag( 7) -1.4354e-02 0.00774643 0.03131492 0.0680924
#> Jokulsa:Vatnsdalsa.lag( 7) -4.7244e-03 0.01646274 0.03874024 0.1012682
#> Jokulsa:Jokulsa.lag( 8) -1.8053e-02 -0.00337333 0.01394319 0.0409669
#> Jokulsa:Vatnsdalsa.lag( 8) -2.5524e-02 -0.00745951 0.01111329 0.0477656
#> Jokulsa:Jokulsa.lag( 9) -1.4657e-02 0.00137752 0.01686143 0.0457200
#> Jokulsa:Vatnsdalsa.lag( 9) -3.9685e-02 -0.01511651 0.00495208 0.0652370
#> Jokulsa:Jokulsa.lag(10) 8.2819e-03 0.02130108 0.03444052 0.0538484
#> Jokulsa:Vatnsdalsa.lag(10) 5.0559e-03 0.02358550 0.04343333 0.0857164
#> Jokulsa:Jokulsa.lag(11) -2.1232e-02 -0.01083202 -0.00053478 0.0169181
#> Jokulsa:Vatnsdalsa.lag(11) -3.0510e-02 -0.01200847 0.00550415 0.0363403
#> Jokulsa:Jokulsa.lag(12) -3.4870e-03 0.00723734 0.01542781 0.0342641
#> Jokulsa:Vatnsdalsa.lag(12) -7.2360e-03 0.00449510 0.02080096 0.0545482
#> Jokulsa:Jokulsa.lag(13) -2.6921e-02 -0.01537925 -0.00154964 0.0267790
#> Jokulsa:Vatnsdalsa.lag(13) -2.9241e-02 -0.01197876 0.00475868 0.0396736
#> Jokulsa:Jokulsa.lag(14) -7.9948e-03 0.00337213 0.01293791 0.0333742
#> Jokulsa:Vatnsdalsa.lag(14) -1.3008e-02 0.00542900 0.02913682 0.0778155
#> Jokulsa:Jokulsa.lag(15) 8.6979e-03 0.01927268 0.02938486 0.0479431
#> Jokulsa:Vatnsdalsa.lag(15) -3.2533e-02 -0.01545048 -0.00266891 0.0240450
#> Jokulsa:Precipitation.lag(1) -1.2895e-03 0.00561001 0.01083407 0.0202622
#> Jokulsa:Precipitation.lag(2) 1.1407e-03 0.00655843 0.01203310 0.0202010
#> Jokulsa:Precipitation.lag(3) -1.5524e-02 -0.01143159 -0.00639027 0.0011404
#> Jokulsa:Precipitation.lag(4) 1.4170e-02 0.01918836 0.02329972 0.0316750
#> Jokulsa:Temperature.lag(1) 9.5678e-03 0.01707629 0.02387060 0.0379787
#> Jokulsa:Temperature.lag(2) -3.9802e-02 -0.03229739 -0.02629234 -0.0127513
#> Vatnsdalsa:(Intercept) 5.7701e-01 0.68672931 0.85071756 1.1342337
#> Vatnsdalsa:Jokulsa.lag( 1) -5.9644e-02 -0.04790714 -0.03787230 -0.0249713
#> Vatnsdalsa:Vatnsdalsa.lag( 1) 1.1331e+00 1.17728444 1.20854612 1.2681691
#> Vatnsdalsa:Jokulsa.lag( 2) 3.8173e-02 0.04773358 0.06358155 0.0794864
#> Vatnsdalsa:Vatnsdalsa.lag( 2) -3.6593e-01 -0.32595178 -0.28175452 -0.2058046
#> Vatnsdalsa:Jokulsa.lag( 3) -3.9659e-02 -0.03085246 -0.02212687 -0.0015599
#> Vatnsdalsa:Vatnsdalsa.lag( 3) 5.3222e-02 0.07287489 0.10416951 0.1542969
#> Vatnsdalsa:Jokulsa.lag( 4) 3.7894e-03 0.01296854 0.02055931 0.0388915
#> Vatnsdalsa:Vatnsdalsa.lag( 4) -4.9444e-02 -0.02405697 -0.00093230 0.0385285
#> Vatnsdalsa:Jokulsa.lag( 5) -1.3144e-03 0.00733527 0.01882352 0.0421015
#> Vatnsdalsa:Vatnsdalsa.lag( 5) -2.0142e-02 -0.00532002 0.00965363 0.0422823
#> Vatnsdalsa:Jokulsa.lag( 6) -6.7635e-03 0.00390342 0.01424034 0.0307880
#> Vatnsdalsa:Vatnsdalsa.lag( 6) -3.3248e-02 -0.02054370 -0.00232702 0.0250487
#> Vatnsdalsa:Jokulsa.lag( 7) -9.9365e-03 0.00361009 0.01410497 0.0331650
#> Vatnsdalsa:Vatnsdalsa.lag( 7) 3.0686e-03 0.01740167 0.02988881 0.0520834
#> Vatnsdalsa:Jokulsa.lag( 8) -2.5318e-02 -0.01746571 -0.00730081 0.0078062
#> Vatnsdalsa:Vatnsdalsa.lag( 8) -2.2735e-03 0.00790521 0.02185566 0.0461805
#> Vatnsdalsa:Jokulsa.lag( 9) 1.1833e-02 0.02088711 0.03124905 0.0501290
#> Vatnsdalsa:Vatnsdalsa.lag( 9) -1.0473e-02 0.00057228 0.01403004 0.0326078
#> Vatnsdalsa:Jokulsa.lag(10) -2.4853e-02 -0.01772502 -0.00948569 0.0044632
#> Vatnsdalsa:Vatnsdalsa.lag(10) -3.3047e-03 0.00776815 0.02190461 0.0480684
#> Vatnsdalsa:Jokulsa.lag(11) 5.8978e-03 0.01246656 0.01842303 0.0294750
#> Vatnsdalsa:Vatnsdalsa.lag(11) -1.3513e-02 0.00162054 0.01309339 0.0479783
#> Vatnsdalsa:Jokulsa.lag(12) -1.8631e-02 -0.01221785 -0.00352147 0.0059534
#> Vatnsdalsa:Vatnsdalsa.lag(12) -1.8114e-02 -0.00696944 0.00400220 0.0314360
#> Vatnsdalsa:Jokulsa.lag(13) -8.4117e-04 0.00673139 0.01410530 0.0280838
#> Vatnsdalsa:Vatnsdalsa.lag(13) -3.2711e-02 -0.02020859 -0.00495528 0.0252039
#> Vatnsdalsa:Jokulsa.lag(14) -1.6210e-02 -0.00958042 -0.00265606 0.0081827
#> Vatnsdalsa:Vatnsdalsa.lag(14) 2.3882e-02 0.03886761 0.05161025 0.0819466
#> Vatnsdalsa:Jokulsa.lag(15) 1.7620e-03 0.00625772 0.01115805 0.0195166
#> Vatnsdalsa:Vatnsdalsa.lag(15) -8.3403e-03 0.00071663 0.00960602 0.0286874
#> Vatnsdalsa:Precipitation.lag(1) -2.8756e-03 0.00052284 0.00569072 0.0122665
#> Vatnsdalsa:Precipitation.lag(2) -2.0222e-03 0.00188445 0.00459225 0.0112668
#> Vatnsdalsa:Precipitation.lag(3) -5.3109e-03 -0.00295810 -0.00062936 0.0043428
#> Vatnsdalsa:Precipitation.lag(4) 3.5833e-03 0.00641008 0.00931899 0.0138380
#> Vatnsdalsa:Temperature.lag(1) -4.8543e-03 -0.00056457 0.00361515 0.0133736
#> Vatnsdalsa:Temperature.lag(2) -1.5594e-02 -0.01048790 -0.00626582 0.0017879
#>
#>
#> Scale parameter:
#> Mean Sd Sd(Mean) 2.5% 25%
#> Jokulsa.Jokulsa 0.0616958 0.0093814 0.0055090 0.0471549 0.0547605
#> Jokulsa.Vatnsdalsa 0.0093599 0.0026730 0.0002961 0.0045145 0.0075118
#> Vatnsdalsa.Vatnsdalsa 0.0255409 0.0042312 0.0010186 0.0197014 0.0223950
#> 50% 75% 97.5%
#> Jokulsa.Jokulsa 0.0600786 0.067348 0.082543
#> Jokulsa.Vatnsdalsa 0.0094483 0.010854 0.014837
#> Vatnsdalsa.Vatnsdalsa 0.0246808 0.027954 0.034469
#>
#>
#> Regime 2
#>
#>
#> Autoregressive coefficients:
#> Mean Sd Sd(Mean) 2.5%
#> Jokulsa:(Intercept) -1.8628e-01 0.6086418 0.06146337 -1.3622523
#> Jokulsa:Jokulsa.lag( 1) 1.0143e+00 0.0360634 0.00414208 0.9449417
#> Jokulsa:Vatnsdalsa.lag( 1) 9.3359e-01 0.1905381 0.01421920 0.6130703
#> Jokulsa:Jokulsa.lag( 2) -1.4158e-01 0.0599955 0.00811708 -0.2579148
#> Jokulsa:Vatnsdalsa.lag( 2) -4.4981e-01 0.2530974 0.01534829 -0.8897757
#> Jokulsa:Jokulsa.lag( 3) -1.3719e-02 0.0512823 0.00534690 -0.1154048
#> Jokulsa:Vatnsdalsa.lag( 3) 2.0359e-04 0.2626756 0.01905984 -0.5631316
#> Jokulsa:Jokulsa.lag( 4) -6.3720e-02 0.0411794 0.00431242 -0.1399417
#> Jokulsa:Vatnsdalsa.lag( 4) -1.5419e-01 0.2257499 0.02356129 -0.5460150
#> Jokulsa:Jokulsa.lag( 5) 3.8814e-02 0.0418485 0.00397702 -0.0319338
#> Jokulsa:Vatnsdalsa.lag( 5) 2.3713e-01 0.2367160 0.03803587 -0.2439795
#> Jokulsa:Jokulsa.lag( 6) -5.0873e-02 0.0314224 0.00268151 -0.1128538
#> Jokulsa:Vatnsdalsa.lag( 6) -2.4332e-01 0.1850594 0.02071091 -0.6353037
#> Jokulsa:Jokulsa.lag( 7) 2.5038e-03 0.0320123 0.00305005 -0.0510948
#> Jokulsa:Vatnsdalsa.lag( 7) 2.7970e-01 0.1977890 0.02019248 -0.1484696
#> Jokulsa:Jokulsa.lag( 8) 2.4920e-02 0.0310049 0.00280411 -0.0298921
#> Jokulsa:Vatnsdalsa.lag( 8) -3.2285e-01 0.1794351 0.01849281 -0.6857614
#> Jokulsa:Jokulsa.lag( 9) 3.7904e-02 0.0304925 0.00233901 -0.0164951
#> Jokulsa:Vatnsdalsa.lag( 9) 1.7903e-01 0.2020422 0.02086834 -0.1606341
#> Jokulsa:Jokulsa.lag(10) -3.0798e-02 0.0370712 0.00319887 -0.1010589
#> Jokulsa:Vatnsdalsa.lag(10) -1.3154e-01 0.1921724 0.02506801 -0.4950745
#> Jokulsa:Jokulsa.lag(11) -5.3212e-03 0.0377360 0.00334861 -0.0884362
#> Jokulsa:Vatnsdalsa.lag(11) 2.2943e-01 0.2473356 0.02824452 -0.2445946
#> Jokulsa:Jokulsa.lag(12) -8.0168e-04 0.0354020 0.00288222 -0.0667795
#> Jokulsa:Vatnsdalsa.lag(12) 5.8144e-03 0.2894549 0.03873901 -0.5672255
#> Jokulsa:Jokulsa.lag(13) 1.2546e-02 0.0410687 0.00404633 -0.0608658
#> Jokulsa:Vatnsdalsa.lag(13) 8.3506e-02 0.2767332 0.04705010 -0.3928599
#> Jokulsa:Jokulsa.lag(14) -1.8778e-02 0.0419955 0.00453120 -0.0972333
#> Jokulsa:Vatnsdalsa.lag(14) 3.0659e-01 0.1791051 0.01777681 -0.0629945
#> Jokulsa:Jokulsa.lag(15) 4.7401e-02 0.0227636 0.00217728 0.0051060
#> Jokulsa:Vatnsdalsa.lag(15) -4.0259e-01 0.1421977 0.01514542 -0.6863235
#> Jokulsa:Precipitation.lag(1) -1.1737e-01 0.0380790 0.00374484 -0.1859762
#> Jokulsa:Precipitation.lag(2) 6.7409e-03 0.0536971 0.00694123 -0.0960993
#> Jokulsa:Precipitation.lag(3) 4.6716e-02 0.0309735 0.00250208 -0.0065277
#> Jokulsa:Precipitation.lag(4) 1.8258e-02 0.0321797 0.00227545 -0.0332241
#> Jokulsa:Temperature.lag(1) 1.0648e+00 0.1011374 0.00952753 0.8625988
#> Jokulsa:Temperature.lag(2) -5.3918e-01 0.0973184 0.00996832 -0.7321167
#> Vatnsdalsa:(Intercept) 4.8203e-01 0.0966346 0.01078166 0.2957685
#> Vatnsdalsa:Jokulsa.lag( 1) -5.7963e-03 0.0041423 0.00039471 -0.0138838
#> Vatnsdalsa:Vatnsdalsa.lag( 1) 1.2004e+00 0.0286024 0.00329634 1.1497046
#> Vatnsdalsa:Jokulsa.lag( 2) 1.6087e-02 0.0062607 0.00067632 0.0050350
#> Vatnsdalsa:Vatnsdalsa.lag( 2) -3.1691e-01 0.0431858 0.00812267 -0.4032342
#> Vatnsdalsa:Jokulsa.lag( 3) -1.5261e-02 0.0057680 0.00059184 -0.0260280
#> Vatnsdalsa:Vatnsdalsa.lag( 3) 1.5714e-01 0.0382559 0.00417478 0.0861319
#> Vatnsdalsa:Jokulsa.lag( 4) 5.3923e-03 0.0048060 0.00041010 -0.0041975
#> Vatnsdalsa:Vatnsdalsa.lag( 4) -8.8597e-02 0.0387034 0.00418457 -0.1469246
#> Vatnsdalsa:Jokulsa.lag( 5) -3.1620e-03 0.0048784 0.00043049 -0.0124780
#> Vatnsdalsa:Vatnsdalsa.lag( 5) -4.1020e-02 0.0396415 0.00628557 -0.1225476
#> Vatnsdalsa:Jokulsa.lag( 6) 2.7361e-03 0.0043212 0.00044016 -0.0051096
#> Vatnsdalsa:Vatnsdalsa.lag( 6) 7.9144e-02 0.0334450 0.00412966 0.0146123
#> Vatnsdalsa:Jokulsa.lag( 7) -4.6415e-03 0.0042723 0.00030210 -0.0135373
#> Vatnsdalsa:Vatnsdalsa.lag( 7) -5.8230e-02 0.0321582 0.00435978 -0.1078781
#> Vatnsdalsa:Jokulsa.lag( 8) 2.6186e-03 0.0041606 0.00029420 -0.0057771
#> Vatnsdalsa:Vatnsdalsa.lag( 8) -8.3269e-02 0.0250550 0.00249271 -0.1333743
#> Vatnsdalsa:Jokulsa.lag( 9) -2.9288e-03 0.0048260 0.00040739 -0.0119615
#> Vatnsdalsa:Vatnsdalsa.lag( 9) 1.3296e-01 0.0328778 0.00373261 0.0595655
#> Vatnsdalsa:Jokulsa.lag(10) 4.9753e-03 0.0051455 0.00052369 -0.0044706
#> Vatnsdalsa:Vatnsdalsa.lag(10) -8.4562e-02 0.0255285 0.00265879 -0.1332019
#> Vatnsdalsa:Jokulsa.lag(11) -7.6967e-03 0.0050422 0.00043837 -0.0165059
#> Vatnsdalsa:Vatnsdalsa.lag(11) 6.8475e-02 0.0312201 0.00366284 0.0064634
#> Vatnsdalsa:Jokulsa.lag(12) 1.0311e-02 0.0048538 0.00039012 0.0022308
#> Vatnsdalsa:Vatnsdalsa.lag(12) -7.2036e-02 0.0314929 0.00378002 -0.1246048
#> Vatnsdalsa:Jokulsa.lag(13) -7.1780e-03 0.0046224 0.00039250 -0.0167060
#> Vatnsdalsa:Vatnsdalsa.lag(13) 1.5388e-01 0.0285874 0.00399424 0.0969662
#> Vatnsdalsa:Jokulsa.lag(14) -2.4066e-03 0.0046487 0.00044944 -0.0109543
#> Vatnsdalsa:Vatnsdalsa.lag(14) -2.8587e-02 0.0274337 0.00337222 -0.0794851
#> Vatnsdalsa:Jokulsa.lag(15) 2.5291e-03 0.0032376 0.00033907 -0.0030222
#> Vatnsdalsa:Vatnsdalsa.lag(15) -4.9258e-02 0.0253598 0.00392791 -0.0937482
#> Vatnsdalsa:Precipitation.lag(1) -4.8133e-05 0.0058824 0.00052165 -0.0120352
#> Vatnsdalsa:Precipitation.lag(2) -9.1107e-03 0.0068472 0.00086504 -0.0222501
#> Vatnsdalsa:Precipitation.lag(3) 4.7330e-03 0.0051702 0.00055655 -0.0042625
#> Vatnsdalsa:Precipitation.lag(4) 5.2818e-03 0.0047848 0.00033834 -0.0054900
#> Vatnsdalsa:Temperature.lag(1) 3.3877e-02 0.0143078 0.00131750 0.0104370
#> Vatnsdalsa:Temperature.lag(2) -4.1055e-02 0.0149566 0.00180798 -0.0758451
#> 25% 50% 75% 97.5%
#> Jokulsa:(Intercept) -0.57441948 -0.20027596 0.21166849 0.9536668
#> Jokulsa:Jokulsa.lag( 1) 0.99165632 1.01355874 1.03354728 1.0992809
#> Jokulsa:Vatnsdalsa.lag( 1) 0.80528361 0.93188378 1.07425219 1.3026318
#> Jokulsa:Jokulsa.lag( 2) -0.17927608 -0.14136260 -0.10768790 -0.0148653
#> Jokulsa:Vatnsdalsa.lag( 2) -0.64252606 -0.44641092 -0.30257106 0.0794116
#> Jokulsa:Jokulsa.lag( 3) -0.04634738 -0.01337258 0.01855162 0.0808097
#> Jokulsa:Vatnsdalsa.lag( 3) -0.14020080 0.01711137 0.19021245 0.4339323
#> Jokulsa:Jokulsa.lag( 4) -0.09275259 -0.06196249 -0.03808089 0.0112230
#> Jokulsa:Vatnsdalsa.lag( 4) -0.30044009 -0.18251125 -0.04195415 0.3865299
#> Jokulsa:Jokulsa.lag( 5) 0.01134262 0.03437925 0.06762060 0.1227047
#> Jokulsa:Vatnsdalsa.lag( 5) 0.09273213 0.24746483 0.37820068 0.6972175
#> Jokulsa:Jokulsa.lag( 6) -0.07226689 -0.05094304 -0.02984340 0.0113001
#> Jokulsa:Vatnsdalsa.lag( 6) -0.35987354 -0.24717518 -0.12730845 0.1025950
#> Jokulsa:Jokulsa.lag( 7) -0.02021422 0.00095280 0.02678446 0.0638608
#> Jokulsa:Vatnsdalsa.lag( 7) 0.15609296 0.30277788 0.40706422 0.6525022
#> Jokulsa:Jokulsa.lag( 8) 0.00171538 0.02252125 0.04472392 0.0853790
#> Jokulsa:Vatnsdalsa.lag( 8) -0.44868381 -0.31216035 -0.21376053 0.0052679
#> Jokulsa:Jokulsa.lag( 9) 0.01611019 0.03633124 0.05979105 0.0976916
#> Jokulsa:Vatnsdalsa.lag( 9) 0.03365028 0.17447646 0.31215535 0.5886839
#> Jokulsa:Jokulsa.lag(10) -0.05725789 -0.03386126 -0.00412644 0.0422444
#> Jokulsa:Vatnsdalsa.lag(10) -0.24465478 -0.12151405 -0.00026805 0.2313221
#> Jokulsa:Jokulsa.lag(11) -0.02647404 -0.00172222 0.01760985 0.0627720
#> Jokulsa:Vatnsdalsa.lag(11) 0.08248429 0.21383943 0.40095809 0.7667670
#> Jokulsa:Jokulsa.lag(12) -0.02586736 -0.00088544 0.02533103 0.0654257
#> Jokulsa:Vatnsdalsa.lag(12) -0.19233802 0.02083880 0.20960617 0.5578367
#> Jokulsa:Jokulsa.lag(13) -0.01728605 0.01299808 0.03989250 0.0874166
#> Jokulsa:Vatnsdalsa.lag(13) -0.13095632 0.09194089 0.28770908 0.5685666
#> Jokulsa:Jokulsa.lag(14) -0.04692667 -0.01873089 0.00762684 0.0594359
#> Jokulsa:Vatnsdalsa.lag(14) 0.19496784 0.30808088 0.41769665 0.6674932
#> Jokulsa:Jokulsa.lag(15) 0.03110400 0.04636449 0.06271562 0.0920085
#> Jokulsa:Vatnsdalsa.lag(15) -0.49288614 -0.40177530 -0.32103291 -0.1117040
#> Jokulsa:Precipitation.lag(1) -0.13802324 -0.11773796 -0.09213786 -0.0448795
#> Jokulsa:Precipitation.lag(2) -0.02828463 0.00500435 0.04268823 0.1086872
#> Jokulsa:Precipitation.lag(3) 0.02605378 0.04592438 0.06536073 0.1110947
#> Jokulsa:Precipitation.lag(4) -0.00518424 0.01650019 0.04192357 0.0773539
#> Jokulsa:Temperature.lag(1) 1.00302032 1.06011202 1.13255140 1.2485744
#> Jokulsa:Temperature.lag(2) -0.59735338 -0.54672048 -0.47169009 -0.3630999
#> Vatnsdalsa:(Intercept) 0.41632182 0.48522747 0.54770213 0.6725832
#> Vatnsdalsa:Jokulsa.lag( 1) -0.00872039 -0.00603976 -0.00274462 0.0019112
#> Vatnsdalsa:Vatnsdalsa.lag( 1) 1.18160003 1.19805045 1.21675690 1.2671941
#> Vatnsdalsa:Jokulsa.lag( 2) 0.01169120 0.01618052 0.02068023 0.0282421
#> Vatnsdalsa:Vatnsdalsa.lag( 2) -0.34991265 -0.31386310 -0.28538035 -0.2343856
#> Vatnsdalsa:Jokulsa.lag( 3) -0.01945705 -0.01497709 -0.01192720 -0.0029657
#> Vatnsdalsa:Vatnsdalsa.lag( 3) 0.12631826 0.15744771 0.18422513 0.2275319
#> Vatnsdalsa:Jokulsa.lag( 4) 0.00227363 0.00570448 0.00871780 0.0143078
#> Vatnsdalsa:Vatnsdalsa.lag( 4) -0.11647186 -0.09190544 -0.06702702 -0.0039360
#> Vatnsdalsa:Jokulsa.lag( 5) -0.00608336 -0.00327737 0.00010245 0.0064856
#> Vatnsdalsa:Vatnsdalsa.lag( 5) -0.06528500 -0.04204333 -0.01539386 0.0370381
#> Vatnsdalsa:Jokulsa.lag( 6) 0.00010277 0.00268258 0.00564162 0.0108047
#> Vatnsdalsa:Vatnsdalsa.lag( 6) 0.05635477 0.08330165 0.10425529 0.1290681
#> Vatnsdalsa:Jokulsa.lag( 7) -0.00739691 -0.00436269 -0.00183864 0.0028890
#> Vatnsdalsa:Vatnsdalsa.lag( 7) -0.08329030 -0.06104954 -0.03636565 0.0145057
#> Vatnsdalsa:Jokulsa.lag( 8) -0.00038695 0.00311210 0.00550466 0.0103230
#> Vatnsdalsa:Vatnsdalsa.lag( 8) -0.09932570 -0.08594064 -0.06929514 -0.0361263
#> Vatnsdalsa:Jokulsa.lag( 9) -0.00604758 -0.00323652 0.00030786 0.0061781
#> Vatnsdalsa:Vatnsdalsa.lag( 9) 0.11199681 0.13347255 0.15699882 0.1876927
#> Vatnsdalsa:Jokulsa.lag(10) 0.00173233 0.00510040 0.00799755 0.0173978
#> Vatnsdalsa:Vatnsdalsa.lag(10) -0.10125396 -0.08657249 -0.06905531 -0.0339878
#> Vatnsdalsa:Jokulsa.lag(11) -0.01165725 -0.00732861 -0.00454206 0.0024889
#> Vatnsdalsa:Vatnsdalsa.lag(11) 0.04730809 0.07138039 0.08910419 0.1234366
#> Vatnsdalsa:Jokulsa.lag(12) 0.00663901 0.00973600 0.01358233 0.0195757
#> Vatnsdalsa:Vatnsdalsa.lag(12) -0.09481793 -0.07273544 -0.05208240 -0.0035770
#> Vatnsdalsa:Jokulsa.lag(13) -0.00999833 -0.00714828 -0.00411195 0.0016040
#> Vatnsdalsa:Vatnsdalsa.lag(13) 0.13497262 0.15471066 0.17426873 0.2031493
#> Vatnsdalsa:Jokulsa.lag(14) -0.00592353 -0.00256366 0.00107274 0.0055315
#> Vatnsdalsa:Vatnsdalsa.lag(14) -0.04926744 -0.02888624 -0.00921426 0.0199468
#> Vatnsdalsa:Jokulsa.lag(15) 0.00016017 0.00235114 0.00494715 0.0090609
#> Vatnsdalsa:Vatnsdalsa.lag(15) -0.06622248 -0.05188470 -0.03217321 0.0017342
#> Vatnsdalsa:Precipitation.lag(1) -0.00393208 -0.00016071 0.00391133 0.0113760
#> Vatnsdalsa:Precipitation.lag(2) -0.01402285 -0.00906952 -0.00432975 0.0043758
#> Vatnsdalsa:Precipitation.lag(3) 0.00099492 0.00417621 0.00827146 0.0151238
#> Vatnsdalsa:Precipitation.lag(4) 0.00205174 0.00541236 0.00864999 0.0137434
#> Vatnsdalsa:Temperature.lag(1) 0.02384017 0.03356178 0.04186060 0.0666896
#> Vatnsdalsa:Temperature.lag(2) -0.04924210 -0.04021970 -0.02954633 -0.0132308
#>
#>
#> Scale parameter:
#> Mean Sd Sd(Mean) 2.5% 25% 50%
#> Jokulsa.Jokulsa 1.405306 0.2200709 0.0573646 0.968679 1.268066 1.414408
#> Jokulsa.Vatnsdalsa 0.045639 0.0121981 0.0012270 0.021664 0.037563 0.045126
#> Vatnsdalsa.Vatnsdalsa 0.029589 0.0050458 0.0012272 0.021092 0.026091 0.029339
#> 75% 97.5%
#> Jokulsa.Jokulsa 1.546303 1.857178
#> Jokulsa.Vatnsdalsa 0.053392 0.070382
#> Vatnsdalsa.Vatnsdalsa 0.032745 0.039306
#>
#>
#> Extra parameter:
#> Mean Sd Sd(Mean) 2.5% 25% 50% 75% 97.5%
#> nu 0.83252 0.046917 0.010546 0.7444 0.79887 0.83198 0.8626 0.91959
#plot(fit3.mcmc)
###### Example 4: U.S. stock returns
data(US.returns)
fit4 <- mtar(~ CCR | dVIX, data=US.returns, subset={Date<="2025-11-28"},
row.names=Date, ars=ars(nregim=2,p=3,d=3), n.burnin=100,
n.sim=200, n.thin=2, dist="Student-t")
fit4.mcmc <- coda::as.mcmc(fit4)
summary(fit4.mcmc)
#>
#>
#> Iterations = 101:499
#>
#> Thinning interval = 2
#>
#> Sample size per chain = 200
#>
#>
#> Thresholds:
#> Mean Sd Sd(Mean) 2.5% 25% 50% 75% 97.5%
#> threshold 1.6084 0.010818 0.0028955 1.5771 1.6007 1.6123 1.6165 1.6165
#>
#>
#> Regime 1
#>
#>
#> Autoregressive coefficients:
#> Mean Sd Sd(Mean) 2.5% 25%
#> CCR:(Intercept) 0.0872668 0.0109352 0.00088288 0.0671703 0.0800671
#> CCR:CCR.lag(1) -0.0438673 0.0107235 0.00075826 -0.0656030 -0.0506341
#> CCR:CCR.lag(2) -0.0519628 0.0251588 0.00223125 -0.1032281 -0.0684437
#> CCR:CCR.lag(3) -0.0077675 0.0210199 0.00148633 -0.0464451 -0.0223339
#> CCR:dVIX.lag(1) -0.0544906 0.0186138 0.00169842 -0.0907523 -0.0677178
#> CCR:dVIX.lag(2) -0.0071310 0.0142997 0.00101114 -0.0322775 -0.0171929
#> CCR:dVIX.lag(3) 0.0135422 0.0083921 0.00075942 -0.0026582 0.0073295
#> 50% 75% 97.5%
#> CCR:(Intercept) 0.0873493 0.0938770 0.10733390
#> CCR:CCR.lag(1) -0.0441748 -0.0371845 -0.02246078
#> CCR:CCR.lag(2) -0.0504755 -0.0347725 -0.00041803
#> CCR:CCR.lag(3) -0.0077388 0.0049452 0.03565698
#> CCR:dVIX.lag(1) -0.0540943 -0.0433743 -0.01654312
#> CCR:dVIX.lag(2) -0.0073259 0.0024214 0.01965513
#> CCR:dVIX.lag(3) 0.0129266 0.0185714 0.03046528
#>
#>
#> Scale parameter:
#> Mean Sd Sd(Mean) 2.5% 25% 50% 75% 97.5%
#> CCR.CCR 0.34951 0.014508 0.002519 0.31979 0.33869 0.3506 0.35954 0.37588
#>
#>
#> Regime 2
#>
#>
#> Autoregressive coefficients:
#> Mean Sd Sd(Mean) 2.5% 25% 50%
#> CCR:(Intercept) 0.171041 0.127584 0.0087914 -0.077589 0.0856168 0.167880
#> CCR:CCR.lag(1) -0.196324 0.051176 0.0062918 -0.290714 -0.2307560 -0.199170
#> CCR:CCR.lag(2) 0.054280 0.084227 0.0082825 -0.111114 -0.0022563 0.054182
#> CCR:CCR.lag(3) -0.088244 0.097945 0.0138458 -0.259022 -0.1606799 -0.092976
#> CCR:dVIX.lag(1) 0.013227 0.038157 0.0038374 -0.064223 -0.0129528 0.015373
#> CCR:dVIX.lag(2) -0.101013 0.063478 0.0058762 -0.211806 -0.1474738 -0.104159
#> CCR:dVIX.lag(3) 0.035563 0.036672 0.0039854 -0.028744 0.0089679 0.035870
#> 75% 97.5%
#> CCR:(Intercept) 0.259265 0.433060
#> CCR:CCR.lag(1) -0.158367 -0.086786
#> CCR:CCR.lag(2) 0.110519 0.219632
#> CCR:CCR.lag(3) -0.017213 0.100438
#> CCR:dVIX.lag(1) 0.038467 0.083659
#> CCR:dVIX.lag(2) -0.058531 0.018828
#> CCR:dVIX.lag(3) 0.060342 0.100188
#>
#>
#> Scale parameter:
#> Mean Sd Sd(Mean) 2.5% 25% 50% 75% 97.5%
#> CCR.CCR 1.3045 0.13191 0.018168 1.0816 1.2064 1.2969 1.3931 1.5853
#>
#>
#> Extra parameter:
#> Mean Sd Sd(Mean) 2.5% 25% 50% 75% 97.5%
#> nu 2.495 0.11704 0.024628 2.2597 2.4165 2.4949 2.5733 2.712
#plot(fit4.mcmc)
# }