Bayesian VAR and VHAR

var_bayes() and vhar_bayes() fit BVAR and BVHAR each with various priors.

y: Multivariate time series data. It should be data frame or matrix, which means that every column is numeric. Each column indicates variable, i.e. it sould be wide format.
p or har: VAR lag, or order of VHAR
num_chains: Number of chains
- If OpenMP is enabled, parallel loop will be run.
num_iter: Total number of iterations
num_burn: Number of burn-in
thinning: Thinning
bayes_spec: Output of set_ssvs()
- Minneosta prior
  - BVAR: set_bvar()
  - BVHAR: set_bvhar() and set_weight_bvhar()
  - Can induce prior on \(\lambda\) using lambda = set_lambda()
- SSVS prior: set_ssvs()
- Horseshoe prior: set_horseshoe()
- NG prior: set_ng()
- DL prior: set_dl()
cov_spec: Covariance prior specification. Use set_ldlt() for homoskedastic model.
include_mean = TRUE: By default, you include the constant term in the model.
minnesota = c("no", "short", "longrun"): Minnesota-type shrinkage.
verbose = FALSE: Progress bar
num_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, bayes_spec = set_ssvs(), cov_spec = set_ldlt(), include_mean = FALSE, minnesota = "longrun"))
#> Call:
#> vhar_bayes(y = etf_train, num_chains = 1, num_iter = 20, bayes_spec = set_ssvs(), 
#>     cov_spec = set_ldlt(), include_mean = FALSE, minnesota = "longrun")
#> 
#> BVHAR with 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    0.302337  0.4543  -0.0375  -0.49548  -0.73538  -0.3439   0.162   0.567
#> 2    0.104371  0.1934  -0.2732  -0.00798  -0.19941   0.0301   0.213   0.492
#> 3    0.373726  0.8019  -0.3833  -0.64653  -1.14892   0.0196  -0.296   1.299
#> 4    0.096895  0.0861  -0.2299  -0.96209  -0.36561  -0.1900   0.754   0.902
#> 5   -0.000544  0.3906  -0.2333   0.03740  -0.38600   0.0149   0.450   0.855
#> 6    0.013843  0.2744  -0.2938   0.10003  -0.17177  -0.0979   0.702   0.922
#> 7   -0.243176  0.0134   0.0297  -0.46767  -0.38944  -0.2737   0.715   0.988
#> 8    0.119136  0.2333  -0.1710  -1.07673  -0.27910  -0.2497   1.797   0.858
#> 9   -0.123032  0.0541  -0.3807  -0.52832   0.03043   0.1313   0.684   1.394
#> 10  -0.007328  0.0410   0.0137  -0.98017   0.00218  -0.1690   1.298   1.312
#> # ... with 82 more variables
#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}

autoplot() for the fit (bvharsp object) provides coefficients heatmap. There is type argument, and the default type = "coef" draws the heatmap.

autoplot(fit_ssvs)

Horseshoe Prior

bayes_spec is the initial specification by set_horseshoe(). Others are the same.

(fit_hs <- vhar_bayes(etf_train, num_chains = 2, num_iter = 20, bayes_spec = set_horseshoe(), cov_spec = set_ldlt(), include_mean = FALSE, minnesota = "longrun"))
#> Call:
#> vhar_bayes(y = etf_train, num_chains = 2, num_iter = 20, bayes_spec = set_horseshoe(), 
#>     cov_spec = set_ldlt(), include_mean = FALSE, minnesota = "longrun")
#> 
#> BVHAR with 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    0.1855  -0.0384   0.0917   0.00753   0.1832   1.044   0.174144  -0.1117
#> 2    0.1331  -0.0762   0.0435  -0.00436   0.2640   0.817   0.229029  -0.0391
#> 3    0.1611  -0.1832   0.0624  -0.01279  -0.1236   0.688   0.195939  -0.0598
#> 4    0.2314  -0.0794   0.0186  -0.08791  -0.0304   1.010  -0.123500  -0.0472
#> 5    0.0946  -0.0219   0.0344   0.12698   0.0809   1.038  -0.002482   0.0370
#> 6    0.1352  -0.0795   0.0804  -0.07565   0.2018   0.910   0.001557  -0.0110
#> 7    0.0155  -0.1789  -0.0395   0.16233   0.5132   0.930  -0.000694  -0.0216
#> 8   -0.0507  -0.1769   0.0890  -0.03753   0.9218   0.768   0.003441  -0.1093
#> 9    0.2339   0.0354   0.0272   0.08280   0.5135   0.982  -0.009063   0.0401
#> 10   0.2393   0.0170   0.0167  -0.05259   0.6156   0.754  -0.010166  -0.0214
#> # ... with 10 more draws, and 116 more variables
#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}

autoplot(fit_hs)

Minnesota Prior

(fit_mn <- vhar_bayes(etf_train, num_chains = 2, num_iter = 20, bayes_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, bayes_spec = set_bvhar(lambda = set_lambda()), 
#>     cov_spec = set_ldlt(), include_mean = FALSE, minnesota = "longrun")
#> 
#> BVHAR with 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   0.1686  -0.143   0.13034  -0.0657  -0.11305   0.661   0.5624   0.10648
#> 2   0.1005  -0.269  -0.14573   0.0930   0.16561   0.735   0.3021  -0.00244
#> 3   0.1220  -0.170   0.41477  -0.0598   0.04038   0.895   0.2439   0.12261
#> 4   0.4330  -0.288  -0.06231   0.3149   0.09932   0.676   0.3609  -0.12742
#> 5   0.2204  -0.340   0.24797   0.1936  -0.00245   0.770   0.3964   0.51818
#> 6   0.0512  -0.149   0.06390   0.1700   0.09526   0.941  -0.0637   0.19208
#> 7   0.2391  -0.141  -0.08897   0.1985   0.06612   0.805   0.6443   0.02353
#> 8   0.0730  -0.134   0.28012  -0.0270   0.02806   1.214   0.0161   0.34295
#> 9   0.1150  -0.153  -0.00198  -0.0903   0.21183   0.788   0.2147   0.05751
#> 10  0.3004  -0.121   0.09600   0.1277   0.08608   0.994  -0.1748   0.07166
#> # ... 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, bayes_spec = set_ng(), cov_spec = set_ldlt(), include_mean = FALSE, minnesota = "longrun"))
#> Call:
#> vhar_bayes(y = etf_train, num_chains = 2, num_iter = 20, bayes_spec = set_ng(), 
#>     cov_spec = set_ldlt(), include_mean = FALSE, minnesota = "longrun")
#> 
#> BVHAR with 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   0.0286  -0.2591  -0.03628   0.01683  -0.0793   0.850  -2.62e-03  -0.0234
#> 2   0.1764  -0.1495   0.10561   0.46727  -0.3730   0.884  -8.19e-04  -0.0641
#> 3   0.1770  -0.0700  -0.07599   0.47825  -0.2118   0.837  -7.99e-05  -0.1851
#> 4   0.1387  -0.0920  -0.10209  -0.23041   0.7426   0.785   1.66e-04  -0.3194
#> 5   0.1595  -0.0768   0.10225  -0.19119   0.5377   0.862   6.83e-03  -0.1070
#> 6   0.1898  -0.0122   0.06377  -0.07537   0.2501   0.916  -7.20e-03  -0.0866
#> 7   0.1076  -0.1012  -0.01462  -0.02458  -0.2058   0.848   1.96e-03  -0.1484
#> 8   0.0518  -0.1187  -0.00787   0.01360   0.2845   0.884  -2.93e-03  -0.1846
#> 9   0.0324   0.0248   0.00776   0.00518  -0.2800   0.915  -6.40e-04  -0.0946
#> 10  0.0355  -0.0192  -0.00332   0.17294   0.1699   0.907   1.21e-03  -0.0072
#> # ... 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, bayes_spec = set_dl(), cov_spec = set_ldlt(), include_mean = FALSE, minnesota = "longrun"))
#> Call:
#> vhar_bayes(y = etf_train, num_chains = 2, num_iter = 20, bayes_spec = set_dl(), 
#>     cov_spec = set_ldlt(), include_mean = FALSE, minnesota = "longrun")
#> 
#> BVHAR with 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]   phi[8]
#> 1    0.0250  -8.83e-06   0.2545   0.48021  -0.3337   0.924   0.005993   0.0256
#> 2   -0.0387  -2.08e-05   0.1024  -0.57919   0.6413   1.019  -0.003358  -0.0174
#> 3    0.0382   2.79e-05  -0.0122  -0.32929   0.6744   0.862  -0.003425  -0.0885
#> 4    0.0521   4.13e-04   0.0102   0.42088   0.1243   0.862   0.000224  -0.2401
#> 5    0.0489  -4.61e-04   0.0170   0.25111  -0.0435   0.858   0.048764  -0.0781
#> 6    0.1106  -1.04e-03   0.1506   1.09276   0.0783   0.796  -0.030539   0.0473
#> 7    0.3234  -2.68e-03   0.0985  -0.00342   0.0960   0.898  -0.008409  -0.0741
#> 8    0.6329  -9.72e-03   0.1035   0.01004   0.1997   0.995   0.079793  -0.0200
#> 9    0.1595   1.42e-02   0.1221  -0.00888   0.4695   0.925   0.023668   0.0208
#> 10   0.4132  -2.37e-02   0.0884   0.01846   0.1896   1.115  -0.067019  -0.0254
#> # ... with 10 more draws, and 83 more variables
#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}