Provides summary of verifying homoskedasticity

Provides summary of the Savage-Dickey density ratios for verification of structural shocks homoskedasticity. The outcomes can be used to make probabilistic statements about identification through heteroskedasticity closely following ideas by Lütkepohl& Woźniak (2020).

Usage

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

Arguments

object

an object of class SDDRidMSH obtained using the verify_identification.PosteriorBSVARMSH function.

...

additional arguments affecting the summary produced.

Value

A table reporting the logarithm of Bayes factors of homoskedastic to heteroskedastic posterior odds "log(SDDR)" for each structural shock, their numerical standard errors "NSE", and the implied posterior probability of the homoskedasticity and heteroskedasticity hypothesis, "Pr[homoskedasticity|data]" and "Pr[heteroskedasticity|data]" respectively.

References

Lütkepohl, H., and Woźniak, T., (2020) Bayesian Inference for Structural Vector Autoregressions Identified by Markov-Switching Heteroskedasticity. Journal of Economic Dynamics and Control 113, 103862, doi:10.1016/j.jedc.2020.103862 .

See also

verify_identification.PosteriorBSVARMSH

Author

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, M = 2)
#> The identification is set to the default option of lower-triangular structural matrix.
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)
#> **************************************************|
#> bsvars: Bayesian Structural Vector Autoregressions|
#> **************************************************|
#>  Gibbs sampler for the SVAR-stationaryMSH model             |
#> **************************************************|
#>  Progress of the MCMC simulation for 10 draws
#>     Every draw is saved via MCMC thinning
#>  Press Esc to interrupt the computations
#> **************************************************|

# verify heteroskedasticity
sddr           = verify_identification(posterior)
summary(sddr)
#>  **************************************************|
#>  bsvars: Bayesian Structural Vector Autoregressions|
#>  **************************************************|
#>    Summary of identification verification          |
#>    H0: s^2_nm  = 1 for all m  [homoskedasticity]   |
#>    H1: s^2_nm != 1 for some m [heteroskedasticity] |
#>  **************************************************|
#>          log(SDDR) NSE Pr[H0|data] Pr[H1|data]
#> shock 1  0.3743467   0 0.592508869   0.4074911
#> shock 2  0.9286965   0 0.716810759   0.2831892
#> shock 3 -5.3795903   0 0.004588558   0.9954114

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new(M = 2) |>
  estimate(S = 10) |> 
  verify_identification() |> 
  summary() -> sddr_summary
#> The identification is set to the default option of lower-triangular structural matrix.
#> **************************************************|
#> bsvars: Bayesian Structural Vector Autoregressions|
#> **************************************************|
#>  Gibbs sampler for the SVAR-stationaryMSH model             |
#> **************************************************|
#>  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|
#>  **************************************************|
#>    Summary of identification verification          |
#>    H0: s^2_nm  = 1 for all m  [homoskedasticity]   |
#>    H1: s^2_nm != 1 for some m [heteroskedasticity] |
#>  **************************************************|