R: Specify prior on PHI

specify_prior_phi {bayesianVARs}

R Documentation

Specify prior on PHI

Description

Configures prior on PHI, the matrix of reduced-form VAR coefficients.

Usage

specify_prior_phi(
  data = NULL,
  M = ncol(data),
  lags = 1L,
  prior = "HS",
  priormean = 0,
  PHI_tol = 1e-18,
  DL_a = "1/K",
  DL_tol = 0,
  R2D2_a = 0.1,
  R2D2_b = 0.5,
  R2D2_tol = 0,
  NG_a = 0.1,
  NG_b = 1,
  NG_c = 1,
  NG_tol = 0,
  SSVS_c0 = 0.01,
  SSVS_c1 = 100,
  SSVS_semiautomatic = TRUE,
  SSVS_p = 0.5,
  HMP_lambda1 = c(0.01, 0.01),
  HMP_lambda2 = c(0.01, 0.01),
  normal_sds = 10,
  global_grouping = "global",
  ...
)

Arguments

`data`	Optional. Data matrix (can be a time series object). Each of `M` columns is assumed to contain a single time-series of length `T`.
`M`	positive integer indicating the number of time-series of the VAR.
`lags`	positive integer indicating the order of the VAR, i.e. the number of lags of the dependent variables included as predictors.
`prior`	character, one of `"HS"`, `"R2D2"`, `"NG"`, `"DL"`, `"SSVS"`, `"HMP"` or `"normal"`.
`priormean`	real numbers indicating the prior means of the VAR coefficients. One single number means that the prior mean of all own-lag coefficients w.r.t. the first lag equals `priormean` and `0` else. A vector of length M means that the prior mean of the own-lag coefficients w.r.t. the first lag equals `priormean` and `0` else. If `priormean` is a matrix of dimension `c(lagsM,M)`, then each of the `M` columns is assumed to contain `lagsM` prior means for the VAR coefficients of the respective VAR equations.
`PHI_tol`	Minimum number that the absolute value of a VAR coefficient draw can take. Prevents numerical issues that can appear when strong shrinkage is enforced if chosen to be greater than zero.
`DL_a`	(Single) positive real number. The value is interpreted as the concentration parameter for the local scales. Smaller values enforce heavier shrinkage. If the argument `global_grouping` specifies e.g. `k` groups, then `DL_a` can be a numeric vector of length `k` and the elements indicate the shrinkage in each group. A matrix of dimension `c(s,2)` specifies a discrete hyperprior, where the first column contains `s` support points and the second column contains the associated prior probabilities. `DL_a` has only to be specified if `prior="DL"`.
`DL_tol`	Minimum number that a parameter draw of one of the shrinking parameters of the Dirichlet Laplace prior can take. Prevents numerical issues that can appear when strong shrinkage is enforced if chosen to be greater than zero. `DL_tol` has only to be specified if `prior="DL"`.
`R2D2_a`	(Single) positive real number. The value is interpreted as the concentration parameter for the local scales. Smaller values enforce heavier shrinkage. If the argument `global_grouping` specifies e.g. `k` groups, then `R2D2_a` can be a numeric vector of length `k` and the elements indicate the shrinkage in each group. A matrix of dimension `c(s,2)` specifies a discrete hyperprior, where the first column contains `s` support points and the second column contains the associated prior probabilities. `R2D2_a` has only to be specified if `prior="R2D2"`.
`R2D2_b`	(Single) positive real number. The value indicates the shape parameter of the inverse gamma prior on the (semi-)global scales. If the argument `global_grouping` specifies e.g. `k` groups, then `NG_b` can be a numeric vector of length `k` and the elements determine the shape parameter in each group. `R2D2_b` has only to be specified if `prior="R2D2"`.
`R2D2_tol`	Minimum number that a parameter draw of one of the shrinking parameters of the R2D2 prior can take. Prevents numerical issues that can appear when strong shrinkage is enforced if chosen to be greater than zero. `R2D2_tol` has only to be specified if `prior="R2D2"`.
`NG_a`	(Single) positive real number. The value is interpreted as the concentration parameter for the local scales. Smaller values enforce heavier shrinkage. If the argument `global_grouping` specifies e.g. `k` groups, then `NG_a` can be a numeric vector of length `k` and the elements indicate the shrinkage in each group. A matrix of dimension `c(s,2)` specifies a discrete hyperprior, where the first column contains `s` support points and the second column contains the associated prior probabilities. `NG_a` has only to be specified if `prior="NG"`.
`NG_b`	(Single) positive real number. The value indicates the shape parameter of the inverse gamma prior on the (semi-)global scales. If the argument `global_grouping` specifies e.g. `k` groups, then `NG_b` can be a numeric vector of length `k` and the elements determine the shape parameter in each group. `NG_b` has only to be specified if `prior="NG"`.
`NG_c`	(Single) positive real number. The value indicates the scale parameter of the inverse gamma prior on the (semi-)global scales. If the argument `global_grouping` specifies e.g. `k` groups, then `NG_c` can be a numeric vector of length `k` and the elements determine the scale parameter in each group. Expert option would be to set the scale parameter proportional to `NG_a`. E.g. in the case where a discrete hyperprior for `NG_a` is chosen, a desired proportion of let's say `0.2` is achieved by setting `NG_c="0.2a"` (character input!). `NG_c` has only to be specified if `prior="NG"`.
`NG_tol`	Minimum number that a parameter draw of one of the shrinking parameters of the normal-gamma prior can take. Prevents numerical issues that can appear when strong shrinkage is enforced if chosen to be greater than zero. `NG_tol` has only to be specified if `prior="NG"`.
`SSVS_c0`	single positive number indicating the (unscaled) standard deviation of the spike component. `SSVS_c0` has only to be specified if `prior="SSVS"`. It should be that `SSVS_{c0} \ll SSVS_{c1}`! `SSVS_c0` has only to be specified if `prior="SSVS"`.
`SSVS_c1`	single positive number indicating the (unscaled) standard deviation of the slab component. `SSVS_c0` has only to be specified if `prior="SSVS"`. It should be that `SSVS_{c0} \ll SSVS_{c1}`!
`SSVS_semiautomatic`	logical. If `SSVS_semiautomatic=TRUE` both `SSVS_c0` and `SSVS_c1` will be scaled by the variances of the posterior of PHI under a FLAT conjugate (dependent Normal-Wishart prior). `SSVS_semiautomatic` has only to be specified if `prior="SSVS"`.
`SSVS_p`	Either a single positive number in the range `(0,1)` indicating the (fixed) prior inclusion probability of each coefficient. Or numeric vector of length 2 with positive entries indicating the shape parameters of the Beta distribution. In that case a Beta hyperprior is placed on the prior inclusion probability. `SSVS_p` has only to be specified if `prior="SSVS"`.
`HMP_lambda1`	numeric vector of length 2. Both entries must be positive. The first indicates the shape and the second the rate of the Gamma hyperprior on own-lag coefficients. `HMP_lambda1` has only to be specified if `prior="HMP"`.
`HMP_lambda2`	numeric vector of length 2. Both entries must be positive. The first indicates the shape and the second the rate of the Gamma hyperprior on cross-lag coefficients. `HMP_lambda2` has only to be specified if `prior="HMP"`.
`normal_sds`	numeric vector of length `n`, where `n = lags M^2` is the number of all VAR coefficients (excluding the intercept), indicating the prior variances. A single number will be recycled accordingly! Must be positive. `normal_sds` has only to be specified if `prior="normal"`.
`global_grouping`	One of `"global"`, `"equation-wise"`, `"covariate-wise"`, `"olcl-lagwise"` `"fol"` indicating the sub-groups of the semi-global(-local) modifications to HS, R2D2, NG, DL and SSVS prior. Works also with user-specified indicator matrix of dimension `c(lags*M,M)`. Only relevant if `prior="HS"`, `prior="DL"`, `prior="R2D2"`, `prior="NG"` or `prior="SSVS"`.
`...`	Do not use!

Details

For details concerning prior-elicitation for VARs please see Gruber & Kastner (2023).

Currently one can choose between six hierarchical shrinkage priors and a normal prior: prior="HS" stands for the Horseshoe-prior, ⁠prior="R2D2⁠ for the R^2-induced-Dirichlet-decompostion-prior, prior="NG" for the normal-gamma-prior, prior="DL" for the Dirichlet-Laplace-prior, prior="SSVS" for the stochastic-search-variable-selection-prior, prior="HMP" for the semi-hierarchical Minnesota prior and prior=normal for the normal-prior.

Semi-global shrinkage, i.e. group-specific shrinkage for pre-specified subgroups of the coefficients, can be achieved through the argument global_grouping.

Value

A baysianVARs_prior_phi-object.

References

Gruber, L. and Kastner, G. (2023). Forecasting macroeconomic data with Bayesian VARs: Sparse or dense? It depends! arXiv:2206.04902.

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Horseshoe prior for a VAR(2)
phi_hs <- specify_prior_phi(data = data, lags = 2L ,prior = "HS")

# Semi-global-local Horseshoe prior for a VAR(2) with semi-global shrinkage parameters for
# cross-lag and own-lag coefficients in each lag
phi_hs_sg <- specify_prior_phi(data = data, lags = 2L, prior = "HS",
global_grouping = "olcl-lagwise")

# Semi-global-local Horseshoe prior for a VAR(2) with equation-wise shrinkage
# construct indicator matrix for equation-wise shrinkage
semi_global_mat <- matrix(1:ncol(data), 2*ncol(data), ncol(data),
byrow = TRUE)
phi_hs_ew <- specify_prior_phi(data = data, lags = 2L, prior = "HS",
global_grouping = semi_global_mat)
# (for equation-wise shrinkage one can also use 'global_grouping = "equation-wise"')


# Estimate model with your prior configuration of choice
mod <- bvar(data, lags = 2L, prior_phi = phi_hs_sg, quiet = TRUE)

[Package bayesianVARs version 0.1.3 Index]