verify_autoregression.PosteriorBSVAR | R Documentation |
Computes the logarithm of Bayes factor for the joint hypothesis,
H_0
, possibly for many autoregressive parameters represented by argument
hypothesis
via Savage-Dickey Density Ration (SDDR).
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 hypothesis. The estimation of both elements of the difference requires numerical integration.
## S3 method for class 'PosteriorBSVAR'
verify_autoregression(posterior, hypothesis)
posterior |
the |
hypothesis |
an |
An object of class SDDRautoregression
that is a list of three components:
logSDDR
a scalar with values of the logarithm of the Bayes factors for
the autoregressive 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 NxS
matrix of the log-full conditional posterior density ordinates computed to estimate the denominator
a 30
-vector containing the log-Bayes factors on the basis of which the standard errors are computed
Tomasz Woźniak wozniak.tom@pm.me
Woźniak, T., and Droumaguet, M., (2024) Bayesian Assessment of Identifying Restrictions for Heteroskedastic Structural VARs
# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)
# specify the model and set seed
specification = specify_bsvar$new(us_fiscal_lsuw, p = 1)
set.seed(123)
# estimate the model
posterior = estimate(specification, 10)
# verify autoregression
H0 = matrix(NA, ncol(us_fiscal_lsuw), ncol(us_fiscal_lsuw) + 1)
H0[1,3] = 0 # a hypothesis of no Granger causality from gdp to ttr
sddr = verify_autoregression(posterior, H0)
# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
specify_bsvar$new(p = 1) |>
estimate(S = 10) |>
verify_autoregression(hypothesis = H0) -> sddr
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