verify_volatility | R Documentation |
This function will be deprecated starting from version 4.0.
It is replaced by verify_identification
function.
Computes the logarithm of Bayes factor for the homoskedasticity hypothesis
for each of the structural shocks via Savage-Dickey Density Ration (SDDR).
The hypothesis of homoskedasticity, H_0
, is represented by model-specific restrictions.
Consult help files for individual classes of models for details.
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 homoskedasticity of the structural shock. The estimation of both elements of the difference requires numerical integration.
verify_volatility(posterior)
posterior |
the |
An object of class SDDRvolatility
that is a list of three components:
logSDDR
an N
-vector with values of the logarithm of the Bayes factors for
the homoskedasticity 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.
components
a list of three components for the computation of the Bayes factor
an N
-vector with values of the logarithm of the Bayes factor denominators
an N
-vector with values of the logarithm of the Bayes factor numerators
an NxS
matrix of the log-full conditional posterior density ordinates computed to estimate the numerator
an Nx30
matrix containing the log-Bayes factors on the basis of which the standard errors are computed
Tomasz Woźniak wozniak.tom@pm.me
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")}.
# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)
# specify the model and set seed
specification = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)
set.seed(123)
# estimate the model
posterior = estimate(specification, 10)
# verify heteroskedasticity
sddr = verify_volatility(posterior)
# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
specify_bsvar_sv$new(p = 1) |>
estimate(S = 10) |>
verify_volatility() -> sddr
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