add_priors.gvecsubmodels: Add Priors to Country-Specific VECX Models of a GVAR Model
In franzmohr/bgvars: Bayesian Inference of Global Vector Autoregressive and Gloal Vector Error Correction Models
View source: R/add_priors.gvecsubmodels.R
add_priors.gvecsubmodels R Documentation
Add Priors to Country-Specific VECX Models of a GVAR Model
Description
Adds prior specifications to a list of country models, which was produced by
the function create_models.
Usage
## S3 method for class 'gvecsubmodels'
add_priors(
object,
...,
coef = list(v_i = 1, v_i_det = 0.1, shape = 3, rate = 1e-04, rate_det = 0.01),
coint = list(v_i = 0, p_tau_i = 1, shape = 3, rate = 1e-04, rho = 0.999),
sigma = list(df = "k", scale = 1, mu = 0, v_i = 0.01, sigma_h = 0.05),
ssvs = NULL,
bvs = NULL
)
Arguments
object
a named list, usually, the output of a call to create_models.
...
further arguments passed to or from other methods.
coef
a named list of prior specifications for the coefficients of the country-specific
models. For the default specification all prior means are set to zero and the diagonal elements of
the inverse prior variance-covariance matrix are set to 1 for coefficients corresponding to non-deterministic
terms. For deterministic coefficients the prior variances are set to 10 via v_i_det = 0.1.
The variances need to be specified as precisions, i.e. as inverses of the variances.
For further specifications see 'Details'.
coint
a named list of prior specifications for cointegration coefficients of
country-specific VEC models. See 'Details'.
sigma
a named list of prior specifications for the error variance-covariance matrix
of the country models. For the default specification of an inverse Wishart distribution
the prior degrees of freedom are set to the number of endogenous variables and
the prior variances to 1. See 'Details'.
ssvs
a named list of prior specifications for the SSVS algorithm. See 'Details'.
bvs
a named list of prior specifications for the BVS algorithm. See 'Details'.
Details
The argument coef can contain the following elements
v_ia numeric specifying the prior precision of the coefficients. Default is 1.
v_i_deta numeric specifying the prior precision of coefficients corresponding to deterministic terms. Default is 0.1.
coint_vara logical specifying whether the prior mean of the first own lag of an
endogenous variable in a VAR model should be set to 1. Default is FALSE.
consta numeric or character specifying the prior mean of coefficients, which correspond
to the intercept. If a numeric is provided, all prior means are set to this value.
If const = "mean", the means of the series of endogenous variables are used as prior means.
If const = "first", the first values of the series of endogenous variables are used as prior means.
minnesotaa list of length 4 containing parameters for the calculation of
the Minnesota prior, where the element names are kappa0, kappa1, kappa2 and kappa3.
For the endogenous variable i the prior variance of the lth
lag of regressor j is obtained as
\frac{\kappa_{0}}{l^2} \textrm{ for own lags of endogenous variables,}
\frac{\kappa_{0} \kappa_{1}}{l^2} \frac{\sigma_{i}^2}{\sigma_{j}^2} \textrm{ for endogenous variables other than own lags,}
\frac{\kappa_{0} \kappa_{2}}{(1 + l)^2} \frac{\sigma_{i}^2}{\sigma_{j}^2} \textrm{ for foreign and global exogenous variables,}
\kappa_{0} \kappa_{3} \sigma_{i}^2 \textrm{ for deterministic terms,}
where \sigma_{i} is the residual standard deviation of variable i of an unrestricted
LS estimate. For exogenous variables \sigma_{i} is the sample standard deviation.
If kappa2 = NULL, \kappa_{0} \kappa_{3} \sigma_{i}^2 will be used for foreign
and global exogenous variables instead.
For VEC models the function only provides priors for the non-cointegration part of the model. The
residual standard errors \sigma_i are based on an unrestricted LS regression of the
endogenous variables on the error correction term and the non-cointegration regressors.
max_vara numeric specifying the maximum prior variance that is allowed for
non-deterministic coefficients.
shapean integer specifying the prior degrees of freedom of the error term of the state equation. Default is 3.
ratea numeric specifying the prior error variance of the state equation. Default is 0.0001.
rate_deta numeric specifying the prior error variance of the state equation corresponding to deterministic terms. Default is 0.0001.
If minnesota is specified, v_i and v_i_det are ignored.
The argument coint can contain the following elements
coint_v_inumeric between 0 and 1 specifying the shrinkage of the cointegration space prior. Default is 0.
coint_p_tau_inumeric of the diagonal elements of the inverse prior matrix of
the central location of the cointegration space sp(\beta). Default is 1.
Argument sigma can contain the following elements:
dfan integer or character specifying the prior degrees of freedom of the error term. Only
used, if the prior is inverse Wishart.
Default is "k", which indicates the amount of endogenous variables in the respective model.
"k + 3" can be used to set the prior to the amount of endogenous variables plus 3. If an integer
is provided, the degrees of freedom are set to this value in all models.
In all cases the rank r of the cointegration matrix is automatically added.
scalea numeric specifying the prior error variance of endogenous variables.
Default is 1.
shapea numeric or character specifying the prior shape parameter of the error term. Only
used, if the prior is inverse gamma or if time varying volatilities are estimated.
For models with constant volatility the default is "k", which indicates the amount of endogenous
variables in the respective country model. "k + 3" can be used to set the prior to the amount of
endogenous variables plus 3. If a numeric is provided, the shape parameters are set to this value in all
models. For models with stochastic volatility this prior refers to the error variance of the state
equation.
ratea numeric specifying the prior rate parameter of the error term. Only used, if the
prior is inverse gamma or if time varying volatilities are estimated. For models with stochastic
volatility this prior refers to the error variance of the state equation.
munumeric of the prior mean of the initial state of the log-volatilities.
Only used for models with time varying volatility.
v_inumeric of the prior precision of the initial state of the log-volatilities.
Only used for models with time varying volatility.
sigma_hnumeric of the initial draw for the variance of the log-volatilities.
Only used for models with time varying volatility.
constantnumeric of the constant, which is added before taking the log of the squared errors.
Only used for models with time varying volatility.
covarlogical indicating whether error covariances should be estimated. Only used
in combination with an inverse gamma prior or stochastic volatility, for which shape and
rate must be specified.
df and scale must be specified for an inverse Wishart prior. shape and rate
are required for an inverse gamma prior. For structural models or models with stochastic volatility
only a gamma prior specification is allowed.
Argument ssvs can contain the following elements:
inpriora numeric between 0 and 1 specifying the prior probability
of a variable to be included in the model.
taua numeric vector of two elements containing the prior standard errors
of restricted variables (\tau_0) as its first element and unrestricted variables (\tau_1)
as its second.
semiautomatican numeric vector of two elements containing the
factors by which the standard errors associated with an unconstrained least squares
estimate of the model are multiplied to obtain the prior standard errors
of restricted (\tau_0) and unrestricted (\tau_1) variables, respectively.
This is the semiautomatic approach described in George et al. (2008).
covarlogical indicating if SSVS should also be applied to the error covariance matrix
as in George et al. (2008).
exclude_detlogical indicating if deterministic terms should be excluded from the SSVS algorithm.
minnesotaa numeric vector of length 4 containing parameters for the calculation of
the Minnesota-like inclusion priors. See below.
Either tau or semiautomatic must be specified.
The argument bvs can contain the following elements
inpriora numeric between 0 and 1 specifying the prior probability
of a variable to be included in the model.
covarlogical indicating if BVS should also be applied to the error covariance matrix.
exclude_detlogical indicating if deterministic terms should be excluded from the BVS algorithm.
minnesotaa numeric vector of length 4 containing parameters for the calculation of
the Minnesota-like inclusion priors. See below.
If either ssvs$minnesota or bvs$minnesota is specified, prior inclusion probabilities
are calculated in a Minnesota-like fashion as
\frac{\kappa_1}{l} for own lags of endogenous variables,
\frac{\kappa_2}{l} for other endogenous variables,
\frac{\kappa_3}{1 + l} for exogenous variables,
\kappa_{4} for deterministic variables,
for lag l with \kappa_1, \kappa_2, \kappa_3, \kappa_4 as the first, second,
third and forth element in ssvs$minnesota or bvs$minnesota, respectively.
Value
A list of country models.
References
Chan, J., Koop, G., Poirier, D. J., & Tobias J. L. (2019). Bayesian econometric methods
(2nd ed.). Cambridge: Cambridge University Press.
George, E. I., Sun, D., & Ni, S. (2008). Bayesian stochastic search for VAR model
restrictions. Journal of Econometrics, 142(1), 553–580.
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.jeconom.2007.08.017")}
Koop, G., León-González, R., & Strachan R. W. (2010). Efficient posterior
simulation for cointegrated models with priors on the cointegration space.
Econometric Reviews, 29(2), 224–242.
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/07474930903382208")}
Koop, G., León-González, R., & Strachan R. W. (2011). Bayesian inference in
a time varying cointegration model. Journal of Econometrics, 165(2), 210–220.
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.jeconom.2011.07.007")}
Korobilis, D. (2013). VAR forecasting using Bayesian variable selection.
Journal of Applied Econometrics, 28(2), 204–230. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/jae.1271")}
Lütkepohl, H. (2006). New introduction to multiple time series analysis (2nd ed.). Berlin: Springer.
franzmohr/bgvars documentation built on Sept. 2, 2023, 12:45 p.m.
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View source: R/add_priors.gvecsubmodels.R
| add_priors.gvecsubmodels | R Documentation |
Add Priors to Country-Specific VECX Models of a GVAR Model
Description
Adds prior specifications to a list of country models, which was produced by
the function create_models.
Usage
## S3 method for class 'gvecsubmodels'
add_priors(
object,
...,
coef = list(v_i = 1, v_i_det = 0.1, shape = 3, rate = 1e-04, rate_det = 0.01),
coint = list(v_i = 0, p_tau_i = 1, shape = 3, rate = 1e-04, rho = 0.999),
sigma = list(df = "k", scale = 1, mu = 0, v_i = 0.01, sigma_h = 0.05),
ssvs = NULL,
bvs = NULL
)
Arguments
object |
a named list, usually, the output of a call to |
... |
further arguments passed to or from other methods. |
coef |
a named list of prior specifications for the coefficients of the country-specific
models. For the default specification all prior means are set to zero and the diagonal elements of
the inverse prior variance-covariance matrix are set to 1 for coefficients corresponding to non-deterministic
terms. For deterministic coefficients the prior variances are set to 10 via |
coint |
a named list of prior specifications for cointegration coefficients of country-specific VEC models. See 'Details'. |
sigma |
a named list of prior specifications for the error variance-covariance matrix of the country models. For the default specification of an inverse Wishart distribution the prior degrees of freedom are set to the number of endogenous variables and the prior variances to 1. See 'Details'. |
ssvs |
a named list of prior specifications for the SSVS algorithm. See 'Details'. |
bvs |
a named list of prior specifications for the BVS algorithm. See 'Details'. |
Details
The argument coef can contain the following elements
v_ia numeric specifying the prior precision of the coefficients. Default is 1.
v_i_deta numeric specifying the prior precision of coefficients corresponding to deterministic terms. Default is 0.1.
coint_vara logical specifying whether the prior mean of the first own lag of an endogenous variable in a VAR model should be set to 1. Default is
FALSE.consta numeric or character specifying the prior mean of coefficients, which correspond to the intercept. If a numeric is provided, all prior means are set to this value. If
const = "mean", the means of the series of endogenous variables are used as prior means. Ifconst = "first", the first values of the series of endogenous variables are used as prior means.minnesotaa list of length 4 containing parameters for the calculation of the Minnesota prior, where the element names are
kappa0,kappa1,kappa2andkappa3. For the endogenous variableithe prior variance of thelth lag of regressorjis obtained as\frac{\kappa_{0}}{l^2} \textrm{ for own lags of endogenous variables,}\frac{\kappa_{0} \kappa_{1}}{l^2} \frac{\sigma_{i}^2}{\sigma_{j}^2} \textrm{ for endogenous variables other than own lags,}\frac{\kappa_{0} \kappa_{2}}{(1 + l)^2} \frac{\sigma_{i}^2}{\sigma_{j}^2} \textrm{ for foreign and global exogenous variables,}\kappa_{0} \kappa_{3} \sigma_{i}^2 \textrm{ for deterministic terms,}where
\sigma_{i}is the residual standard deviation of variableiof an unrestricted LS estimate. For exogenous variables\sigma_{i}is the sample standard deviation. Ifkappa2 = NULL,\kappa_{0} \kappa_{3} \sigma_{i}^2will be used for foreign and global exogenous variables instead.For VEC models the function only provides priors for the non-cointegration part of the model. The residual standard errors
\sigma_iare based on an unrestricted LS regression of the endogenous variables on the error correction term and the non-cointegration regressors.max_vara numeric specifying the maximum prior variance that is allowed for non-deterministic coefficients.
shapean integer specifying the prior degrees of freedom of the error term of the state equation. Default is 3.
ratea numeric specifying the prior error variance of the state equation. Default is 0.0001.
rate_deta numeric specifying the prior error variance of the state equation corresponding to deterministic terms. Default is 0.0001.
If minnesota is specified, v_i and v_i_det are ignored.
The argument coint can contain the following elements
coint_v_inumeric between 0 and 1 specifying the shrinkage of the cointegration space prior. Default is 0.
coint_p_tau_inumeric of the diagonal elements of the inverse prior matrix of the central location of the cointegration space
sp(\beta). Default is 1.
Argument sigma can contain the following elements:
dfan integer or character specifying the prior degrees of freedom of the error term. Only used, if the prior is inverse Wishart. Default is
"k", which indicates the amount of endogenous variables in the respective model."k + 3"can be used to set the prior to the amount of endogenous variables plus 3. If an integer is provided, the degrees of freedom are set to this value in all models. In all cases the rankrof the cointegration matrix is automatically added.scalea numeric specifying the prior error variance of endogenous variables. Default is 1.
shapea numeric or character specifying the prior shape parameter of the error term. Only used, if the prior is inverse gamma or if time varying volatilities are estimated. For models with constant volatility the default is
"k", which indicates the amount of endogenous variables in the respective country model."k + 3"can be used to set the prior to the amount of endogenous variables plus 3. If a numeric is provided, the shape parameters are set to this value in all models. For models with stochastic volatility this prior refers to the error variance of the state equation.ratea numeric specifying the prior rate parameter of the error term. Only used, if the prior is inverse gamma or if time varying volatilities are estimated. For models with stochastic volatility this prior refers to the error variance of the state equation.
munumeric of the prior mean of the initial state of the log-volatilities. Only used for models with time varying volatility.
v_inumeric of the prior precision of the initial state of the log-volatilities. Only used for models with time varying volatility.
sigma_hnumeric of the initial draw for the variance of the log-volatilities. Only used for models with time varying volatility.
constantnumeric of the constant, which is added before taking the log of the squared errors. Only used for models with time varying volatility.
covarlogical indicating whether error covariances should be estimated. Only used in combination with an inverse gamma prior or stochastic volatility, for which
shapeandratemust be specified.
df and scale must be specified for an inverse Wishart prior. shape and rate
are required for an inverse gamma prior. For structural models or models with stochastic volatility
only a gamma prior specification is allowed.
Argument ssvs can contain the following elements:
inpriora numeric between 0 and 1 specifying the prior probability of a variable to be included in the model.
taua numeric vector of two elements containing the prior standard errors of restricted variables (
\tau_0) as its first element and unrestricted variables (\tau_1) as its second.semiautomatican numeric vector of two elements containing the factors by which the standard errors associated with an unconstrained least squares estimate of the model are multiplied to obtain the prior standard errors of restricted (
\tau_0) and unrestricted (\tau_1) variables, respectively. This is the semiautomatic approach described in George et al. (2008).covarlogical indicating if SSVS should also be applied to the error covariance matrix as in George et al. (2008).
exclude_detlogical indicating if deterministic terms should be excluded from the SSVS algorithm.
minnesotaa numeric vector of length 4 containing parameters for the calculation of the Minnesota-like inclusion priors. See below.
Either tau or semiautomatic must be specified.
The argument bvs can contain the following elements
inpriora numeric between 0 and 1 specifying the prior probability of a variable to be included in the model.
covarlogical indicating if BVS should also be applied to the error covariance matrix.
exclude_detlogical indicating if deterministic terms should be excluded from the BVS algorithm.
minnesotaa numeric vector of length 4 containing parameters for the calculation of the Minnesota-like inclusion priors. See below.
If either ssvs$minnesota or bvs$minnesota is specified, prior inclusion probabilities
are calculated in a Minnesota-like fashion as
\frac{\kappa_1}{l} | for own lags of endogenous variables, |
\frac{\kappa_2}{l} | for other endogenous variables, |
\frac{\kappa_3}{1 + l} | for exogenous variables, |
\kappa_{4} | for deterministic variables, |
for lag l with \kappa_1, \kappa_2, \kappa_3, \kappa_4 as the first, second,
third and forth element in ssvs$minnesota or bvs$minnesota, respectively.
Value
A list of country models.
References
Chan, J., Koop, G., Poirier, D. J., & Tobias J. L. (2019). Bayesian econometric methods (2nd ed.). Cambridge: Cambridge University Press.
George, E. I., Sun, D., & Ni, S. (2008). Bayesian stochastic search for VAR model restrictions. Journal of Econometrics, 142(1), 553–580. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.jeconom.2007.08.017")}
Koop, G., León-González, R., & Strachan R. W. (2010). Efficient posterior simulation for cointegrated models with priors on the cointegration space. Econometric Reviews, 29(2), 224–242. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/07474930903382208")}
Koop, G., León-González, R., & Strachan R. W. (2011). Bayesian inference in a time varying cointegration model. Journal of Econometrics, 165(2), 210–220. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.jeconom.2011.07.007")}
Korobilis, D. (2013). VAR forecasting using Bayesian variable selection. Journal of Applied Econometrics, 28(2), 204–230. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/jae.1271")}
Lütkepohl, H. (2006). New introduction to multiple time series analysis (2nd ed.). Berlin: Springer.
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