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Provides posterior summary of Structural VAR with t-distributed shocks estimation

Source: R/summary.R
summary.PosteriorBSVART.Rd

Provides posterior mean, standard deviations, as well as 5 and 95 percentiles of the parameters: the structural matrix \(B\), autoregressive parameters \(A\), hyper-parameters, and Student-t degrees-of-freedom parameter \(\nu\).

Usage

# S3 method for class 'PosteriorBSVART'
summary(object, ...)

Arguments

object

an object of class PosteriorBSVART obtained using the estimate() function applied to homoskedastic Bayesian Structural VAR model specification set by function specify_bsvar$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: the structural matrix \(B\), autoregressive parameters \(A\), hyper-parameters, and Student-t degrees-of-freedom parameter \(\nu\).

See also

estimate, specify_bsvar_t

Author

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_t$new(us_fiscal_lsuw)
#> The identification is set to the default option of lower-triangular structural matrix.

# run the burn-in
burn_in        = estimate(specification, 10)
#> **************************************************|
#> bsvars: Bayesian Structural Vector Autoregressions|
#> **************************************************|
#>  Gibbs sampler for the SVAR model                 |
#>     with t-distributed structural skocks          |
#> **************************************************|
#>  Progress of the MCMC simulation for 10 draws
#>     Every draw is saved via MCMC thinning
#>  Press Esc to interrupt the computations
#> **************************************************|

# estimate the model
posterior      = estimate(burn_in, 20)
#> **************************************************|
#> bsvars: Bayesian Structural Vector Autoregressions|
#> **************************************************|
#>  Gibbs sampler for the SVAR model                 |
#>     with t-distributed structural skocks          |
#> **************************************************|
#>  Progress of the MCMC simulation for 20 draws
#>     Every draw is saved via MCMC thinning
#>  Press Esc to interrupt the computations
#> **************************************************|
summary(posterior)
#>  **************************************************|
#>  bsvars: Bayesian Structural Vector Autoregressions|
#>  **************************************************|
#>    Posterior summary of the parameters             |
#>  **************************************************|
#> $B
#> $B$equation1
#>            mean       sd 5% quantile 95% quantile
#> B[1,1] 83.08816 7.432982    72.19555     91.92885
#> 
#> $B$equation2
#>              mean       sd 5% quantile 95% quantile
#> B[2,1] -0.5959876 5.426337   -7.852271     8.569945
#> B[2,2] 79.4563110 5.040195   71.187514    84.532685
#> 
#> $B$equation3
#>             mean        sd 5% quantile 95% quantile
#> B[3,1] -33.97542  5.291424   -43.49804    -26.56615
#> B[3,2] -17.43226  3.853681   -23.34845    -11.97249
#> B[3,3] 200.09898 15.868333   179.13264    230.84429
#> 
#> 
#> $A
#> $A$equation1
#>                  mean         sd 5% quantile 95% quantile
#> lag1_var1  0.95515898 0.01082254  0.94364018  0.973210217
#> lag1_var2 -0.01658253 0.00937834 -0.03029286 -0.002966908
#> lag1_var3  0.05472966 0.01300958  0.03499293  0.071770452
#> const     -0.17058367 0.07472968 -0.28676693 -0.082284728
#> 
#> $A$equation2
#>                  mean         sd  5% quantile  95% quantile
#> lag1_var1 -0.02539492 0.01407778 -0.040142424 -0.0009308137
#> lag1_var2  0.97163967 0.01153201  0.960738367  0.9885101394
#> lag1_var3  0.03526041 0.01762726  0.003969758  0.0554698741
#> const     -0.25601299 0.09970515 -0.344046641 -0.1184152479
#> 
#> $A$equation3
#>                   mean          sd 5% quantile  95% quantile
#> lag1_var1 -0.012351306 0.007580670 -0.02239774  0.0003360014
#> lag1_var2 -0.006622576 0.003430107 -0.01225370 -0.0021860068
#> lag1_var3  1.014068782 0.009189047  0.99921105  1.0268460661
#> const     -0.072239571 0.030080708 -0.12406986 -0.0362163961
#> 
#> 
#> $hyper
#> $hyper$B
#>                            mean        sd 5% quantile 95% quantile
#> B[1,]_shrinkage       1538.4521 1086.7148   522.63568     3787.957
#> B[2,]_shrinkage       1344.5971  773.6346   556.55965     2283.403
#> B[3,]_shrinkage       4378.9388 1998.8022  2513.58917     8288.018
#> B[1,]_shrinkage_scale 7242.0050 4524.1381   958.83915    15363.983
#> B[2,]_shrinkage_scale 6799.8176 3659.0235  1430.41042    10309.693
#> B[3,]_shrinkage_scale 8397.8055 5035.6770  2062.87791    16054.700
#> B_global_scale         712.8364  454.3309    94.91977     1397.221
#> 
#> $hyper$A
#>                            mean         sd 5% quantile 95% quantile
#> A[1,]_shrinkage       0.2924931 0.11731013   0.1237939    0.4852739
#> A[2,]_shrinkage       0.3176801 0.17044913   0.1235787    0.5810493
#> A[3,]_shrinkage       0.3032528 0.14587096   0.1556416    0.6575046
#> A[1,]_shrinkage_scale 3.9883278 1.59082284   2.3625417    7.3505790
#> A[2,]_shrinkage_scale 4.0441837 1.60295292   2.1928113    7.2486669
#> A[3,]_shrinkage_scale 3.6247049 1.25573437   1.9689292    5.7684156
#> A_global_scale        0.4975190 0.09776025   0.3563678    0.6273223
#> 
#> 
#> $df
#>         mean           sd  5% quantile 95% quantile 
#>    3.3085244    0.5851244    2.6646985    4.1772968 
#> 

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_t$new() |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  summary()
#> The identification is set to the default option of lower-triangular structural matrix.
#> **************************************************|
#> bsvars: Bayesian Structural Vector Autoregressions|
#> **************************************************|
#>  Gibbs sampler for the SVAR model                 |
#>     with t-distributed structural skocks          |
#> **************************************************|
#>  Progress of the MCMC simulation for 10 draws
#>     Every draw is saved via MCMC thinning
#>  Press Esc to interrupt the computations
#> **************************************************|
#> **************************************************|
#> bsvars: Bayesian Structural Vector Autoregressions|
#> **************************************************|
#>  Gibbs sampler for the SVAR model                 |
#>     with t-distributed structural skocks          |
#> **************************************************|
#>  Progress of the MCMC simulation for 20 draws
#>     Every draw is saved via MCMC thinning
#>  Press Esc to interrupt the computations
#> **************************************************|
#>  **************************************************|
#>  bsvars: Bayesian Structural Vector Autoregressions|
#>  **************************************************|
#>    Posterior summary of the parameters             |
#>  **************************************************|
#> $B
#> $B$equation1
#>            mean       sd 5% quantile 95% quantile
#> B[1,1] 83.08816 7.432982    72.19555     91.92885
#> 
#> $B$equation2
#>              mean       sd 5% quantile 95% quantile
#> B[2,1] -0.5959876 5.426337   -7.852271     8.569945
#> B[2,2] 79.4563110 5.040195   71.187514    84.532685
#> 
#> $B$equation3
#>             mean        sd 5% quantile 95% quantile
#> B[3,1] -33.97542  5.291424   -43.49804    -26.56615
#> B[3,2] -17.43226  3.853681   -23.34845    -11.97249
#> B[3,3] 200.09898 15.868333   179.13264    230.84429
#> 
#> 
#> $A
#> $A$equation1
#>                  mean         sd 5% quantile 95% quantile
#> lag1_var1  0.95515898 0.01082254  0.94364018  0.973210217
#> lag1_var2 -0.01658253 0.00937834 -0.03029286 -0.002966908
#> lag1_var3  0.05472966 0.01300958  0.03499293  0.071770452
#> const     -0.17058367 0.07472968 -0.28676693 -0.082284728
#> 
#> $A$equation2
#>                  mean         sd  5% quantile  95% quantile
#> lag1_var1 -0.02539492 0.01407778 -0.040142424 -0.0009308137
#> lag1_var2  0.97163967 0.01153201  0.960738367  0.9885101394
#> lag1_var3  0.03526041 0.01762726  0.003969758  0.0554698741
#> const     -0.25601299 0.09970515 -0.344046641 -0.1184152479
#> 
#> $A$equation3
#>                   mean          sd 5% quantile  95% quantile
#> lag1_var1 -0.012351306 0.007580670 -0.02239774  0.0003360014
#> lag1_var2 -0.006622576 0.003430107 -0.01225370 -0.0021860068
#> lag1_var3  1.014068782 0.009189047  0.99921105  1.0268460661
#> const     -0.072239571 0.030080708 -0.12406986 -0.0362163961
#> 
#> 
#> $hyper
#> $hyper$B
#>                            mean        sd 5% quantile 95% quantile
#> B[1,]_shrinkage       1538.4521 1086.7148   522.63568     3787.957
#> B[2,]_shrinkage       1344.5971  773.6346   556.55965     2283.403
#> B[3,]_shrinkage       4378.9388 1998.8022  2513.58917     8288.018
#> B[1,]_shrinkage_scale 7242.0050 4524.1381   958.83915    15363.983
#> B[2,]_shrinkage_scale 6799.8176 3659.0235  1430.41042    10309.693
#> B[3,]_shrinkage_scale 8397.8055 5035.6770  2062.87791    16054.700
#> B_global_scale         712.8364  454.3309    94.91977     1397.221
#> 
#> $hyper$A
#>                            mean         sd 5% quantile 95% quantile
#> A[1,]_shrinkage       0.2924931 0.11731013   0.1237939    0.4852739
#> A[2,]_shrinkage       0.3176801 0.17044913   0.1235787    0.5810493
#> A[3,]_shrinkage       0.3032528 0.14587096   0.1556416    0.6575046
#> A[1,]_shrinkage_scale 3.9883278 1.59082284   2.3625417    7.3505790
#> A[2,]_shrinkage_scale 4.0441837 1.60295292   2.1928113    7.2486669
#> A[3,]_shrinkage_scale 3.6247049 1.25573437   1.9689292    5.7684156
#> A_global_scale        0.4975190 0.09776025   0.3563678    0.6273223
#> 
#> 
#> $df
#>         mean           sd  5% quantile 95% quantile 
#>    3.3085244    0.5851244    2.6646985    4.1772968 
#>