Hyperpriors for Bayesian Models — set

Set hyperpriors of Bayesian VAR and VHAR models.

Usage

set_lambda(mode = 0.2, sd = 0.4, param = NULL, lower = 1e-05, upper = 3)

set_psi(shape = 4e-04, scale = 4e-04, lower = 1e-05, upper = 3)

# S3 method for class 'bvharpriorspec'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

is.bvharpriorspec(x)

# S3 method for class 'bvharpriorspec'
knit_print(x, ...)

Arguments

mode: Mode of Gamma distribution. By default, .2.
sd: Standard deviation of Gamma distribution. By default, .4.
param: Shape and rate of Gamma distribution, in the form of c(shape, rate). If specified, ignore mode and sd.
lower: Lower bound for stats::optim(). By default, 1e-5.
upper: Upper bound for stats::optim(). By default, 3.
shape: Shape of Inverse Gamma distribution. By default, (.02)^2.
scale: Scale of Inverse Gamma distribution. By default, (.02)^2.
x: bvharpriorspec object
digits: digit option to print
...: not used

Value

bvharpriorspec object

Details

In addition to Normal-IW priors set_bvar(), set_bvhar(), and set_weight_bvhar(), these functions give hierarchical structure to the model.

set_lambda() specifies hyperprior for \(\lambda\) (lambda), which is Gamma distribution.
set_psi() specifies hyperprior for \(\psi / (\nu_0 - k - 1) = \sigma^2\) (sigma), which is Inverse gamma distribution.

The following set of (mode, sd) are recommended by Sims and Zha (1998) for set_lambda().

(mode = .2, sd = .4): default
(mode = 1, sd = 1)

Giannone et al. (2015) suggested data-based selection for set_psi(). It chooses (0.02)^2 based on its empirical data set.

References

Giannone, D., Lenza, M., & Primiceri, G. E. (2015). Prior Selection for Vector Autoregressions. Review of Economics and Statistics, 97(2).

Examples

# Hirearchical BVAR specification------------------------
set_bvar(
  sigma = set_psi(shape = 4e-4, scale = 4e-4),
  lambda = set_lambda(mode = .2, sd = .4),
  delta = rep(1, 3),
  eps = 1e-04 # eps = 1e-04
)
#> Model Specification for BVAR
#> 
#> Parameters: Coefficent matrice and Covariance matrix
#> Prior: MN_Hierarchical
#> ========================================================
#> 
#> Setting for 'sigma':
#> Hyperprior specification for psi
#> 
#> [1]  psi ~ Inv-Gamma(shape = 4e-04, scale =4e-04)
#> 
#> Setting for 'lambda':
#> Hyperprior specification for lambda
#> 
#> [1]  lambda ~ Gamma(shape = 1.64038820320221, rate =3.20194101601104)
#> 
#> Setting for 'delta':
#> [1]  1  1  1
#> 
#> Setting for 'eps':
#> [1]  1e-04
#> 
#> Setting for 'hierarchical':
#> [1]  TRUE
#>