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Provides posterior summary of heteroskedastic Structural VAR estimation

Source: R/summary.R
summary.PosteriorBSVARSV.Rd

Provides posterior mean, standard deviations, as well as 5 and 95 percentiles of the parameters: the structural matrix \(B\), autoregressive parameters \(A\), and hyper parameters.

Usage

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

Arguments

object

an object of class PosteriorBSVARSV obtained using the estimate() function applied to heteroskedastic Bayesian Structural VAR model specification set by function specify_bsvar_sv$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 \(A\), and hyper-parameters.

See also

estimate, specify_bsvar_sv

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_sv$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-SV model              |
#>    Non-centred SV model is estimated              |
#> **************************************************|
#>  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-SV model              |
#>    Non-centred SV model is estimated              |
#> **************************************************|
#>  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] 0.1462879 0.005193802   0.1378043    0.1529531
#> 
#> $B$equation2
#>             mean        sd 5% quantile 95% quantile
#> B[2,1] -12.99891 0.5447578   -13.75642    -12.18619
#> B[2,2]  41.61610 1.7240106    39.01878     43.90748
#> 
#> $B$equation3
#>              mean       sd 5% quantile 95% quantile
#> B[3,1] -39.409086 1.733700   -41.93632   -37.111713
#> B[3,2]  -8.419286 2.475866   -11.45846    -4.755063
#> B[3,3]  63.435376 2.668723    59.18161    66.867710
#> 
#> 
#> $A
#> $A$equation1
#>                   mean         sd 5% quantile 95% quantile
#> lag1_var1  0.739471768 0.07573504  0.66773681   0.88867386
#> lag1_var2 -0.009422047 0.02490824 -0.04758496   0.03048698
#> lag1_var3 -0.566930179 0.09036175 -0.74771986  -0.48472762
#> const     -0.109364180 0.21652074 -0.45144078   0.22948613
#> 
#> $A$equation2
#>                  mean         sd 5% quantile 95% quantile
#> lag1_var1 -0.08172641 0.02292961  -0.1170348  -0.04894066
#> lag1_var2  0.96173285 0.01593118   0.9332478   0.98101415
#> lag1_var3 -0.17296565 0.02854321  -0.2200927  -0.13299316
#> const     -0.35813686 0.12662532  -0.5946356  -0.19082468
#> 
#> $A$equation3
#>                   mean         sd 5% quantile 95% quantile
#> lag1_var1 -0.141881261 0.05055956 -0.18948464  -0.04496017
#> lag1_var2 -0.007132563 0.01777753 -0.04031295   0.02292552
#> lag1_var3  0.584834523 0.05978226  0.47219672   0.64592374
#> const     -0.087751979 0.15452236 -0.36588482   0.18737394
#> 
#> 
#> $hyper
#> $hyper$B
#>                             mean        sd 5% quantile 95% quantile
#> B[1,]_shrinkage         49.38860  36.20630    5.362346     117.6062
#> B[2,]_shrinkage        284.71505 177.36035  153.252593     473.8493
#> B[3,]_shrinkage        647.27030 436.39225  315.660079    1125.1985
#> B[1,]_shrinkage_scale  527.79917 319.31093   80.976747    1019.8120
#> B[2,]_shrinkage_scale 1004.33834 411.10772  510.010966    1678.4275
#> B[3,]_shrinkage_scale 1097.74281 491.79290  379.410666    1776.2121
#> B_global_scale          81.32742  36.40308   37.295484     127.1522
#> 
#> $hyper$A
#>                            mean        sd 5% quantile 95% quantile
#> A[1,]_shrinkage       0.9480643 0.6260121   0.2335475     2.464578
#> A[2,]_shrinkage       0.8596221 0.7745331   0.2327505     2.002212
#> A[3,]_shrinkage       0.9979775 0.8097213   0.4380638     2.404830
#> A[1,]_shrinkage_scale 9.3727336 3.6041905   3.7617984    14.858119
#> A[2,]_shrinkage_scale 9.2838609 6.6911294   2.8715596    20.962737
#> A[3,]_shrinkage_scale 9.3164700 5.1038341   5.0925410    21.082174
#> A_global_scale        1.0331385 0.4364563   0.4845417     1.755186
#> 
#> 

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$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-SV model              |
#>    Non-centred SV model is estimated              |
#> **************************************************|
#>  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-SV model              |
#>    Non-centred SV model is estimated              |
#> **************************************************|
#>  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] 0.1462879 0.005193802   0.1378043    0.1529531
#> 
#> $B$equation2
#>             mean        sd 5% quantile 95% quantile
#> B[2,1] -12.99891 0.5447578   -13.75642    -12.18619
#> B[2,2]  41.61610 1.7240106    39.01878     43.90748
#> 
#> $B$equation3
#>              mean       sd 5% quantile 95% quantile
#> B[3,1] -39.409086 1.733700   -41.93632   -37.111713
#> B[3,2]  -8.419286 2.475866   -11.45846    -4.755063
#> B[3,3]  63.435376 2.668723    59.18161    66.867710
#> 
#> 
#> $A
#> $A$equation1
#>                   mean         sd 5% quantile 95% quantile
#> lag1_var1  0.739471768 0.07573504  0.66773681   0.88867386
#> lag1_var2 -0.009422047 0.02490824 -0.04758496   0.03048698
#> lag1_var3 -0.566930179 0.09036175 -0.74771986  -0.48472762
#> const     -0.109364180 0.21652074 -0.45144078   0.22948613
#> 
#> $A$equation2
#>                  mean         sd 5% quantile 95% quantile
#> lag1_var1 -0.08172641 0.02292961  -0.1170348  -0.04894066
#> lag1_var2  0.96173285 0.01593118   0.9332478   0.98101415
#> lag1_var3 -0.17296565 0.02854321  -0.2200927  -0.13299316
#> const     -0.35813686 0.12662532  -0.5946356  -0.19082468
#> 
#> $A$equation3
#>                   mean         sd 5% quantile 95% quantile
#> lag1_var1 -0.141881261 0.05055956 -0.18948464  -0.04496017
#> lag1_var2 -0.007132563 0.01777753 -0.04031295   0.02292552
#> lag1_var3  0.584834523 0.05978226  0.47219672   0.64592374
#> const     -0.087751979 0.15452236 -0.36588482   0.18737394
#> 
#> 
#> $hyper
#> $hyper$B
#>                             mean        sd 5% quantile 95% quantile
#> B[1,]_shrinkage         49.38860  36.20630    5.362346     117.6062
#> B[2,]_shrinkage        284.71505 177.36035  153.252593     473.8493
#> B[3,]_shrinkage        647.27030 436.39225  315.660079    1125.1985
#> B[1,]_shrinkage_scale  527.79917 319.31093   80.976747    1019.8120
#> B[2,]_shrinkage_scale 1004.33834 411.10772  510.010966    1678.4275
#> B[3,]_shrinkage_scale 1097.74281 491.79290  379.410666    1776.2121
#> B_global_scale          81.32742  36.40308   37.295484     127.1522
#> 
#> $hyper$A
#>                            mean        sd 5% quantile 95% quantile
#> A[1,]_shrinkage       0.9480643 0.6260121   0.2335475     2.464578
#> A[2,]_shrinkage       0.8596221 0.7745331   0.2327505     2.002212
#> A[3,]_shrinkage       0.9979775 0.8097213   0.4380638     2.404830
#> A[1,]_shrinkage_scale 9.3727336 3.6041905   3.7617984    14.858119
#> A[2,]_shrinkage_scale 9.2838609 6.6911294   2.8715596    20.962737
#> A[3,]_shrinkage_scale 9.3164700 5.1038341   5.0925410    21.082174
#> A_global_scale        1.0331385 0.4364563   0.4845417     1.755186
#> 
#>