Bayesian VAR and VHAR
var_bayes() andvhar_bayes() fit BVAR andBVHAR each with various priors.
y: Multivariate time series data. It should be dataframe or matrix, which means that every column is numeric. Each columnindicates variable, i.e. it sould be wide format.porhar: VAR lag, or order of VHARnum_chains: Number of chains- If OpenMP is enabled, parallel loop will be run.
num_iter: Total number of iterationsnum_burn: Number of burn-inthinning: Thinningcoef_spec: Coefficient prior specification.- Minneosta prior
- BVAR:
set_bvar() - BVHAR:
set_bvhar()andset_weight_bvhar() - Can induce prior on\(\lambda\)using
lambda = set_lambda()
- BVAR:
- SSVS prior:
set_ssvs() - Horseshoe prior:
set_horseshoe() - NG prior:
set_ng() - DL prior:
set_dl()
- Minneosta prior
contem_spec: Contemporaneous prior specification.cov_spec: Covariance prior specification. Useset_ldlt()for homoskedastic model.include_mean = TRUE: By default, you include theconstant term in the model.minnesota = c("no", "short", "longrun"): Minnesota-typeshrinkage.verbose = FALSE: Progress barnum_thread: Number of thread for OpenMP- Used in parallel multi-chain loop
- This option is valid only when OpenMP in user’s machine.
Stochastic Search Variable Selection (SSVS) Prior
(fit_ssvs<-vhar_bayes(etf_train,num_chains =1,num_iter =20,coef_spec =set_ssvs(),contem_spec =set_ssvs(),cov_spec =set_ldlt(),include_mean =FALSE,minnesota ="longrun"))#> Call:#> vhar_bayes(y = etf_train, num_chains = 1, num_iter = 20, coef_spec = set_ssvs(),#> contem_spec = set_ssvs(), cov_spec = set_ldlt(), include_mean = FALSE,#> minnesota = "longrun")#>#> BVHAR with SSVS prior + SSVS prior#> Fitted by Gibbs sampling#> Total number of iteration: 20#> Number of burn-in: 10#> ====================================================#>#> Parameter Record:#> # A draws_df: 10 iterations, 1 chains, and 90 variables#> phi[1] phi[2] phi[3] phi[4] phi[5] phi[6] phi[7] phi[8]#> 1 -0.0876 -0.0175 -0.2211 0.048667 0.2732 0.0339 0.755 0.355#> 2 0.1705 -0.0185 -0.1899 0.198807 -0.0889 -0.0591 -0.169 0.201#> 3 -0.1823 -0.3229 -0.1574 -0.000812 0.3271 -0.2168 0.614 0.154#> 4 -0.0456 0.4376 -0.2301 0.105966 -0.7925 -0.1346 -0.401 0.235#> 5 0.1391 0.5049 -0.3111 -0.383728 -0.7563 -0.1516 0.386 0.835#> 6 0.1806 -0.1231 0.0320 -0.500005 0.1669 -0.4150 0.738 0.131#> 7 -0.0620 -0.3463 0.1281 -0.177550 0.5410 -0.4273 1.408 0.466#> 8 0.1520 0.3084 -0.0333 -0.851727 -0.5724 -0.4793 0.781 1.111#> 9 0.2625 -0.0168 -0.0794 -0.864491 0.2769 -0.0485 0.494 0.621#> 10 0.3484 0.5000 -0.2022 -0.970879 -0.5480 -0.1629 0.801 0.874#> # ... with 82 more variables#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}autoplot() for the fit (bvharsp object)provides coefficients heatmap. There istype argument, andthe defaulttype = "coef" draws the heatmap.
Horseshoe Prior
coef_spec is the initial specification byset_horseshoe(). Others are the same.
(fit_hs<-vhar_bayes(etf_train,num_chains =2,num_iter =20,coef_spec =set_horseshoe(),contem_spec =set_horseshoe(),cov_spec =set_ldlt(),include_mean =FALSE,minnesota ="longrun"))#> Call:#> vhar_bayes(y = etf_train, num_chains = 2, num_iter = 20, coef_spec = set_horseshoe(),#> contem_spec = set_horseshoe(), cov_spec = set_ldlt(), include_mean = FALSE,#> minnesota = "longrun")#>#> BVHAR with Horseshoe prior + Horseshoe prior#> Fitted by Gibbs sampling#> Number of chains: 2#> Total number of iteration: 20#> Number of burn-in: 10#> ====================================================#>#> Parameter Record:#> # A draws_df: 10 iterations, 2 chains, and 124 variables#> phi[1] phi[2] phi[3] phi[4] phi[5] phi[6] phi[7] phi[8]#> 1 -0.04495 -0.2428 -0.408630 0.2169 1.363 0.663 -2.49e-02 -0.1709#> 2 0.08816 0.0361 0.000658 -0.2194 0.715 0.721 1.18e-02 -0.2143#> 3 0.00684 0.0276 -0.111765 0.0407 1.079 0.931 3.58e-04 -0.0892#> 4 0.00944 0.0530 0.168523 -0.0199 -0.477 0.959 -1.54e-03 0.0292#> 5 -0.00226 0.0121 -0.054365 0.2389 0.682 0.971 1.99e-03 0.0678#> 6 0.03164 -0.0434 -0.105660 -0.0190 0.203 0.898 2.89e-04 0.0595#> 7 -0.20536 -0.1265 -0.009287 0.4954 -0.123 0.608 1.29e-04 -0.1439#> 8 0.00274 -0.1432 -0.000363 -0.1834 0.194 0.679 -6.89e-05 -0.1870#> 9 0.16452 -0.0938 0.009767 -0.0540 0.255 0.573 -5.64e-04 -0.2881#> 10 0.18610 -0.3555 0.000239 0.4681 -0.181 0.686 1.01e-03 -0.2060#> # ... with 10 more draws, and 116 more variables#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}Minnesota Prior
(fit_mn<-vhar_bayes(etf_train,num_chains =2,num_iter =20,coef_spec =set_bvhar(lambda =set_lambda()),cov_spec =set_ldlt(),include_mean =FALSE,minnesota ="longrun"))#> Call:#> vhar_bayes(y = etf_train, num_chains = 2, num_iter = 20, coef_spec = set_bvhar(lambda = set_lambda()),#> cov_spec = set_ldlt(), include_mean = FALSE, minnesota = "longrun")#>#> BVHAR with MN_Hierarchical prior + MN_Hierarchical prior#> Fitted by Gibbs sampling#> Number of chains: 2#> Total number of iteration: 20#> Number of burn-in: 10#> ====================================================#>#> Parameter Record:#> # A draws_df: 10 iterations, 2 chains, and 63 variables#> phi[1] phi[2] phi[3] phi[4] phi[5] phi[6] phi[7] phi[8]#> 1 0.0772 -0.19792 -0.02059 0.02107 0.18810 0.653 0.6363 -0.1294#> 2 0.1971 0.03031 0.02267 -0.16524 0.16601 0.963 0.5907 0.1467#> 3 -0.0652 0.04858 0.13853 0.41502 0.21091 0.913 0.0569 -0.2873#> 4 0.0462 0.01200 0.24799 0.28023 0.05044 1.155 -0.0932 0.0422#> 5 0.3616 -0.13088 0.16699 0.00432 0.12119 0.705 -0.0217 0.1122#> 6 0.3236 -0.11465 0.01582 0.03471 0.00207 0.675 -0.1075 -0.0457#> 7 0.1022 -0.11147 -0.00271 -0.00526 0.11684 0.538 0.3197 0.0984#> 8 0.2079 0.00524 0.02906 -0.06189 -0.07685 0.781 0.1671 0.0594#> 9 0.4017 -0.11320 0.07950 -0.08998 0.05990 0.959 0.2355 -0.1646#> 10 0.2470 -0.29699 0.25608 -0.05925 -0.00420 0.736 0.2196 -0.2519#> # ... with 10 more draws, and 55 more variables#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}Normal-Gamma prior
(fit_ng<-vhar_bayes(etf_train,num_chains =2,num_iter =20,coef_spec =set_ng(),cov_spec =set_ldlt(),include_mean =FALSE,minnesota ="longrun"))#> Call:#> vhar_bayes(y = etf_train, num_chains = 2, num_iter = 20, coef_spec = set_ng(),#> cov_spec = set_ldlt(), include_mean = FALSE, minnesota = "longrun")#>#> BVHAR with NG prior + NG prior#> Fitted by Metropolis-within-Gibbs#> Number of chains: 2#> Total number of iteration: 20#> Number of burn-in: 10#> ====================================================#>#> Parameter Record:#> # A draws_df: 10 iterations, 2 chains, and 97 variables#> phi[1] phi[2] phi[3] phi[4] phi[5] phi[6] phi[7] phi[8]#> 1 0.29085 0.01876 0.00254 0.53359 0.7936 1.001 -0.00506 -0.1146#> 2 0.27410 -0.00536 -0.00289 -0.08364 0.3323 0.916 0.00200 0.0479#> 3 0.14191 0.00524 -0.00385 0.04266 0.5909 1.105 0.24897 -0.0465#> 4 0.14230 -0.00688 -0.00775 -0.08325 0.2356 1.178 -0.06971 -0.0873#> 5 0.06147 -0.08083 -0.01876 -0.01126 0.3633 0.905 0.01817 -0.0240#> 6 0.01886 0.10961 -0.01871 -0.01531 0.0815 1.002 0.01369 0.0155#> 7 0.06842 -0.01518 -0.04223 0.03511 -0.0854 1.007 -0.05042 0.0542#> 8 0.10784 -0.00400 -0.02816 -0.00807 -0.1218 0.967 -0.04223 -0.0218#> 9 -0.00779 -0.04138 0.03443 -0.00719 -0.0669 0.914 -0.02592 0.0282#> 10 -0.05957 -0.04837 0.03679 -0.05329 -0.4538 0.989 0.49214 0.0819#> # ... with 10 more draws, and 89 more variables#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}Dirichlet-Laplace prior
(fit_dl<-vhar_bayes(etf_train,num_chains =2,num_iter =20,coef_spec =set_dl(),cov_spec =set_ldlt(),include_mean =FALSE,minnesota ="longrun"))#> Call:#> vhar_bayes(y = etf_train, num_chains = 2, num_iter = 20, coef_spec = set_dl(),#> cov_spec = set_ldlt(), include_mean = FALSE, minnesota = "longrun")#>#> BVHAR with DL prior + DL prior#> Fitted by Gibbs sampling#> Number of chains: 2#> Total number of iteration: 20#> Number of burn-in: 10#> ====================================================#>#> Parameter Record:#> # A draws_df: 10 iterations, 2 chains, and 91 variables#> phi[1] phi[2] phi[3] phi[4] phi[5] phi[6] phi[7]#> 1 0.475 0.054925 0.05211 0.295807 8.65e-03 1.040 -0.00754#> 2 0.286 -0.011270 0.17011 0.472838 1.45e-02 1.052 0.11047#> 3 0.485 0.020806 -0.00340 0.334332 2.32e-02 1.070 0.01431#> 4 0.225 -0.021273 0.00787 0.252865 -1.52e-03 1.027 -0.09594#> 5 0.410 -0.002813 0.04916 -0.049722 -5.29e-04 0.848 0.01767#> 6 0.284 0.000958 0.32848 -0.000480 -2.06e-03 0.746 0.34579#> 7 0.307 -0.000115 0.29406 0.001189 9.94e-04 1.205 -0.00690#> 8 0.195 -0.003034 0.60744 0.000355 -6.74e-04 0.881 0.16946#> 9 0.410 -0.059060 0.32520 -0.000557 -7.36e-05 1.019 -0.00190#> 10 0.226 -0.043607 0.68878 0.152129 -7.01e-05 1.085 0.00128#> phi[8]#> 1 -5.57e-04#> 2 2.48e-05#> 3 1.35e-03#> 4 -9.89e-03#> 5 1.34e-01#> 6 1.58e-02#> 7 4.67e-02#> 8 1.10e-02#> 9 -1.41e-03#> 10 1.43e-03#> # ... with 10 more draws, and 83 more variables#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}