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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] 10.58596 0.6289418    9.873576     11.78743
#> 
#> $B$equation2
#>             mean       sd 5% quantile 95% quantile
#> B[2,1] -54.34818 3.144151   -59.31959    -49.79796
#> B[2,2]  37.39258 2.538504    33.58825     40.82855
#> 
#> $B$equation3
#>             mean       sd 5% quantile 95% quantile
#> B[3,1] -44.14697 4.834732   -52.68184    -38.53157
#> B[3,2] -47.45051 3.326023   -52.86897    -42.07421
#> B[3,3] 101.44064 7.433715    93.17360    113.06358
#> 
#> 
#> $A
#> $A$equation1
#>                 mean          sd 5% quantile 95% quantile
#> lag1_var1  1.2309016 0.015719105   1.2143158    1.2495828
#> lag1_var2  0.1988503 0.009902403   0.1852218    0.2121462
#> lag1_var3 -0.4657044 0.019144286  -0.4883770   -0.4397205
#> const      0.5491578 0.102823389   0.4214100    0.7096505
#> 
#> $A$equation2
#>                 mean         sd 5% quantile 95% quantile
#> lag1_var1  0.3984051 0.02743969   0.3598004    0.4442702
#> lag1_var2  1.2793203 0.02269762   1.2479364    1.3172526
#> lag1_var3 -0.7620605 0.03699388  -0.8240471   -0.7118160
#> const      0.6406510 0.19055423   0.3874277    0.9697347
#> 
#> $A$equation3
#>                mean         sd 5% quantile 95% quantile
#> lag1_var1 0.3065699 0.02502751   0.2724296    0.3425950
#> lag1_var2 0.2320335 0.02203158   0.2047520    0.2628622
#> lag1_var3 0.4113975 0.04072096   0.3550634    0.4735537
#> const     0.6508130 0.14295926   0.4983664    0.8668387
#> 
#> 
#> $hyper
#> $hyper$B
#>                            mean        sd 5% quantile 95% quantile
#> B[1,]_shrinkage        279.4535  177.8205    93.96507     532.1565
#> B[2,]_shrinkage        726.0074  275.7413   388.10410    1077.3320
#> B[3,]_shrinkage       1488.5063  600.3217   735.60690    2463.1713
#> B[1,]_shrinkage_scale 2197.4204 1255.6743  1053.30693    4997.9378
#> B[2,]_shrinkage_scale 3137.8909 1386.5789  1327.73168    5112.2093
#> B[3,]_shrinkage_scale 3453.1740 1760.1083  1313.26728    6761.4796
#> B_global_scale         261.1104  110.4119   102.11854     451.4488
#> 
#> $hyper$A
#>                            mean        sd 5% quantile 95% quantile
#> A[1,]_shrinkage       0.5560610 0.2340779   0.2831975    0.9530555
#> A[2,]_shrinkage       0.9025103 0.3682937   0.4620614    1.3447011
#> A[3,]_shrinkage       0.5707678 0.2784821   0.1623766    1.0455047
#> A[1,]_shrinkage_scale 6.8189620 2.0194534   3.6744493    9.5144057
#> A[2,]_shrinkage_scale 8.6539825 2.2308077   5.6838486   12.1113087
#> A[3,]_shrinkage_scale 5.5054275 1.7003552   2.9999186    7.6995466
#> A_global_scale        0.7290078 0.1489147   0.4375521    0.9071557
#> 
#> 
#> $df
#>         mean           sd  5% quantile 95% quantile 
#>    5.0017311    0.4894042    4.4651058    5.8071892 
#> 

# 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] 10.58596 0.6289418    9.873576     11.78743
#> 
#> $B$equation2
#>             mean       sd 5% quantile 95% quantile
#> B[2,1] -54.34818 3.144151   -59.31959    -49.79796
#> B[2,2]  37.39258 2.538504    33.58825     40.82855
#> 
#> $B$equation3
#>             mean       sd 5% quantile 95% quantile
#> B[3,1] -44.14697 4.834732   -52.68184    -38.53157
#> B[3,2] -47.45051 3.326023   -52.86897    -42.07421
#> B[3,3] 101.44064 7.433715    93.17360    113.06358
#> 
#> 
#> $A
#> $A$equation1
#>                 mean          sd 5% quantile 95% quantile
#> lag1_var1  1.2309016 0.015719105   1.2143158    1.2495828
#> lag1_var2  0.1988503 0.009902403   0.1852218    0.2121462
#> lag1_var3 -0.4657044 0.019144286  -0.4883770   -0.4397205
#> const      0.5491578 0.102823389   0.4214100    0.7096505
#> 
#> $A$equation2
#>                 mean         sd 5% quantile 95% quantile
#> lag1_var1  0.3984051 0.02743969   0.3598004    0.4442702
#> lag1_var2  1.2793203 0.02269762   1.2479364    1.3172526
#> lag1_var3 -0.7620605 0.03699388  -0.8240471   -0.7118160
#> const      0.6406510 0.19055423   0.3874277    0.9697347
#> 
#> $A$equation3
#>                mean         sd 5% quantile 95% quantile
#> lag1_var1 0.3065699 0.02502751   0.2724296    0.3425950
#> lag1_var2 0.2320335 0.02203158   0.2047520    0.2628622
#> lag1_var3 0.4113975 0.04072096   0.3550634    0.4735537
#> const     0.6508130 0.14295926   0.4983664    0.8668387
#> 
#> 
#> $hyper
#> $hyper$B
#>                            mean        sd 5% quantile 95% quantile
#> B[1,]_shrinkage        279.4535  177.8205    93.96507     532.1565
#> B[2,]_shrinkage        726.0074  275.7413   388.10410    1077.3320
#> B[3,]_shrinkage       1488.5063  600.3217   735.60690    2463.1713
#> B[1,]_shrinkage_scale 2197.4204 1255.6743  1053.30693    4997.9378
#> B[2,]_shrinkage_scale 3137.8909 1386.5789  1327.73168    5112.2093
#> B[3,]_shrinkage_scale 3453.1740 1760.1083  1313.26728    6761.4796
#> B_global_scale         261.1104  110.4119   102.11854     451.4488
#> 
#> $hyper$A
#>                            mean        sd 5% quantile 95% quantile
#> A[1,]_shrinkage       0.5560610 0.2340779   0.2831975    0.9530555
#> A[2,]_shrinkage       0.9025103 0.3682937   0.4620614    1.3447011
#> A[3,]_shrinkage       0.5707678 0.2784821   0.1623766    1.0455047
#> A[1,]_shrinkage_scale 6.8189620 2.0194534   3.6744493    9.5144057
#> A[2,]_shrinkage_scale 8.6539825 2.2308077   5.6838486   12.1113087
#> A[3,]_shrinkage_scale 5.5054275 1.7003552   2.9999186    7.6995466
#> A_global_scale        0.7290078 0.1489147   0.4375521    0.9071557
#> 
#> 
#> $df
#>         mean           sd  5% quantile 95% quantile 
#>    5.0017311    0.4894042    4.4651058    5.8071892 
#>