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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] 5.683473 0.270597    5.305968      6.00139
#> 
#> $B$equation2
#>            mean       sd 5% quantile 95% quantile
#> B[2,1] 16.60781 2.285398    13.97238     20.53425
#> B[2,2] 51.58255 3.553366    46.76183     56.95305
#> 
#> $B$equation3
#>             mean       sd 5% quantile 95% quantile
#> B[3,1] -56.11701 2.584825  -59.857149    -53.06085
#> B[3,2]  11.36434 2.821094    6.887335     15.62287
#> B[3,3]  69.24383 3.266620   64.327254     73.23511
#> 
#> 
#> $A
#> $A$equation1
#>                  mean         sd 5% quantile 95% quantile
#> lag1_var1  1.44333116 0.01763852  1.42279587    1.4759796
#> lag1_var2 -0.14176708 0.02522578 -0.17551781   -0.1049694
#> lag1_var3 -0.33758180 0.03316838 -0.39636935   -0.3003929
#> const      0.09625648 0.13516819 -0.06067087    0.3223017
#> 
#> $A$equation2
#>                 mean         sd 5% quantile 95% quantile
#> lag1_var1 -0.1723648 0.01500039  -0.1950080   -0.1468958
#> lag1_var2  1.0179641 0.01374906   0.9968141    1.0373253
#> lag1_var3  0.1485959 0.01362534   0.1335286    0.1701090
#> const     -0.2823277 0.08249560  -0.3949441   -0.1641334
#> 
#> $A$equation3
#>                 mean         sd 5% quantile 95% quantile
#> lag1_var1  0.4175438 0.02066918   0.3956690   0.44983763
#> lag1_var2 -0.1188649 0.02833001  -0.1645518  -0.07965057
#> lag1_var3  0.6660893 0.01374631   0.6432788   0.68828124
#> const      0.1245590 0.11228241  -0.0352645   0.29256423
#> 
#> 
#> $hyper
#> $hyper$B
#>                            mean        sd 5% quantile 95% quantile
#> B[1,]_shrinkage        404.9914  293.2989    107.4329     867.1980
#> B[2,]_shrinkage        706.7319  427.1349    250.1326    1353.5998
#> B[3,]_shrinkage       1036.5466  461.9636    502.3239    1888.6574
#> B[1,]_shrinkage_scale 3752.2937 2151.0982   1091.0831    7311.8121
#> B[2,]_shrinkage_scale 4732.4588 2442.1000   1437.0846    9323.6021
#> B[3,]_shrinkage_scale 5079.5538 2332.7047   1628.8525    8703.0604
#> B_global_scale         405.0931  179.0249    101.0425     634.0845
#> 
#> $hyper$A
#>                            mean        sd 5% quantile 95% quantile
#> A[1,]_shrinkage       0.5096583 0.3625476   0.2665960    1.0096442
#> A[2,]_shrinkage       0.3470133 0.1480129   0.1518203    0.5869494
#> A[3,]_shrinkage       0.4128128 0.2162187   0.1967992    0.8327323
#> A[1,]_shrinkage_scale 4.9415393 1.5862675   3.0978850    7.1957609
#> A[2,]_shrinkage_scale 4.5707284 1.2301488   2.9930029    6.4187707
#> A[3,]_shrinkage_scale 5.0105320 1.5121636   3.1038318    6.8492489
#> A_global_scale        0.5721111 0.1192033   0.4231608    0.7478832
#> 
#> 
#> $df
#>         mean           sd  5% quantile 95% quantile 
#>    4.6373010    0.8939566    3.2099088    5.7832688 
#> 

# 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] 5.683473 0.270597    5.305968      6.00139
#> 
#> $B$equation2
#>            mean       sd 5% quantile 95% quantile
#> B[2,1] 16.60781 2.285398    13.97238     20.53425
#> B[2,2] 51.58255 3.553366    46.76183     56.95305
#> 
#> $B$equation3
#>             mean       sd 5% quantile 95% quantile
#> B[3,1] -56.11701 2.584825  -59.857149    -53.06085
#> B[3,2]  11.36434 2.821094    6.887335     15.62287
#> B[3,3]  69.24383 3.266620   64.327254     73.23511
#> 
#> 
#> $A
#> $A$equation1
#>                  mean         sd 5% quantile 95% quantile
#> lag1_var1  1.44333116 0.01763852  1.42279587    1.4759796
#> lag1_var2 -0.14176708 0.02522578 -0.17551781   -0.1049694
#> lag1_var3 -0.33758180 0.03316838 -0.39636935   -0.3003929
#> const      0.09625648 0.13516819 -0.06067087    0.3223017
#> 
#> $A$equation2
#>                 mean         sd 5% quantile 95% quantile
#> lag1_var1 -0.1723648 0.01500039  -0.1950080   -0.1468958
#> lag1_var2  1.0179641 0.01374906   0.9968141    1.0373253
#> lag1_var3  0.1485959 0.01362534   0.1335286    0.1701090
#> const     -0.2823277 0.08249560  -0.3949441   -0.1641334
#> 
#> $A$equation3
#>                 mean         sd 5% quantile 95% quantile
#> lag1_var1  0.4175438 0.02066918   0.3956690   0.44983763
#> lag1_var2 -0.1188649 0.02833001  -0.1645518  -0.07965057
#> lag1_var3  0.6660893 0.01374631   0.6432788   0.68828124
#> const      0.1245590 0.11228241  -0.0352645   0.29256423
#> 
#> 
#> $hyper
#> $hyper$B
#>                            mean        sd 5% quantile 95% quantile
#> B[1,]_shrinkage        404.9914  293.2989    107.4329     867.1980
#> B[2,]_shrinkage        706.7319  427.1349    250.1326    1353.5998
#> B[3,]_shrinkage       1036.5466  461.9636    502.3239    1888.6574
#> B[1,]_shrinkage_scale 3752.2937 2151.0982   1091.0831    7311.8121
#> B[2,]_shrinkage_scale 4732.4588 2442.1000   1437.0846    9323.6021
#> B[3,]_shrinkage_scale 5079.5538 2332.7047   1628.8525    8703.0604
#> B_global_scale         405.0931  179.0249    101.0425     634.0845
#> 
#> $hyper$A
#>                            mean        sd 5% quantile 95% quantile
#> A[1,]_shrinkage       0.5096583 0.3625476   0.2665960    1.0096442
#> A[2,]_shrinkage       0.3470133 0.1480129   0.1518203    0.5869494
#> A[3,]_shrinkage       0.4128128 0.2162187   0.1967992    0.8327323
#> A[1,]_shrinkage_scale 4.9415393 1.5862675   3.0978850    7.1957609
#> A[2,]_shrinkage_scale 4.5707284 1.2301488   2.9930029    6.4187707
#> A[3,]_shrinkage_scale 5.0105320 1.5121636   3.1038318    6.8492489
#> A_global_scale        0.5721111 0.1192033   0.4231608    0.7478832
#> 
#> 
#> $df
#>         mean           sd  5% quantile 95% quantile 
#>    4.6373010    0.8939566    3.2099088    5.7832688 
#>