verify_normality: Verifies normality of structural shocks equation by equation

In bsvars: Bayesian Estimation of Structural Vector Autoregressive Models

Verifies normality of structural shocks equation by equation

Description

Computes the logarithm of Bayes factor for the normality hypothesis for each of the structural shocks via Savage-Dickey Density Ration (SDDR). The hypothesis of normality, H_0, is represented by restriction that the equation-specific degrees of freedom parameter is equal to infinity, \nu_n\rightarrow\infty. The logarithm of Bayes factor for this hypothesis can be computed using the SDDR as the difference of logarithms of the marginal posterior distribution ordinate at the restriction less the marginal prior distribution ordinate at the same point:

log p(H_0 | data) - log p(H_0)

Therefore, a negative value of the difference is the evidence against normality of the structural shock. The estimation of th first element relies on kernel density estimation of the marginal posterior density, whereas the second element is equal to the log of value 1.

Usage

verify_normality(posterior)

Arguments

posterior

the posterior element of the list from the estimation outcome

Value

An object of class SDDRnormality that is a list of three components:

logSDDR an N-vector with values of the logarithm of the Bayes factors for the normality hypothesis for each of the shocks

log_SDDR_se an N-vector with estimation standard errors of the logarithm of the Bayes factors reported in output element logSDDR that are computed based on 30 random sub-samples of the log-ordinates of the marginal posterior and prior distributions.

Author(s)

Tomasz Woźniak [e-mail]

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, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.jedc.2020.103862")}.

Lütkepohl, H., Shang, F., Uzeda, L., and Woźniak, T. (2024) Partial Identification of Heteroskedastic Structural VARs: Theory and Bayesian Inference. University of Melbourne Working Paper, 1–57, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.48550/arXiv.2404.11057")}.

Examples

# simple workflow
############################################################
# specify the model
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, distribution = "t")

# estimate the model
posterior      = estimate(specification, 10)

# verify heteroskedasticity
sddr           = verify_normality(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_sv$new(distribution = "t") |>
  estimate(S = 10) |> 
  verify_normality() -> sddr

bsvars documentation built on Aug. 22, 2026, 5:09 p.m.