bvar_horseshoe: Fitting Bayesian VAR(p) of Horseshoe Prior

Description

This function fits BVAR(p) with horseshoe prior.

Usage

bvar_horseshoe(
  y,
  p,
  num_chains = 1,
  num_iter = 1000,
  num_burn = floor(num_iter/2),
  thinning = 1,
  bayes_spec = set_horseshoe(),
  include_mean = TRUE,
  minnesota = FALSE,
  algo = c("block", "gibbs"),
  verbose = FALSE,
  num_thread = 1
)
# S3 method for bvarhs
print(x, digits = max(3L, getOption("digits") - 3L), ...)
# S3 method for bvarhs
knit_print(x, ...)

Value

bvar_horseshoe returns an object named bvarhs

class. It is a list with the following components:

coefficients: Posterior mean of VAR coefficients.

covmat

Posterior mean of covariance matrix

psi_posterior

Posterior mean of precision matrix \(\Psi\)

pip

Posterior inclusion probabilities.

param

posterior::draws_df with every variable: alpha, lambda, tau, omega, and eta

param_names

Name of every parameter.

Numer of Coefficients: mp + 1 or mp

Lag of VAR

Dimension of the data

obs

Sample size used when training = totobs - p

totobs

Total number of the observation

call

Matched call

process

Description of the model, e.g. VAR_Horseshoe

type

include constant term (const) or not (none)

algo

Usual Gibbs sampling (gibbs) or fast sampling (fast)

spec

Horseshoe specification defined by set_horseshoe()

chain

The numer of chains

iter

Total iterations

burn

Burn-in

thin

Thinning

group

Indicators for group.

num_group

Number of groups.

\(Y_0\)

design

\(X_0\)

Raw input

Arguments

y: Time series data of which columns indicate the variables
p: VAR lag
num_chains: Number of MCMC chains
num_iter: MCMC iteration number
num_burn: Number of burn-in (warm-up). Half of the iteration is the default choice.
thinning: Thinning every thinning-th iteration
bayes_spec: Horseshoe initialization specification by set_horseshoe().
include_mean: Add constant term (Default: TRUE) or not (FALSE)
minnesota: Minnesota type
algo: Ordinary gibbs sampling (gibbs) or blocked gibbs (Default: block).
verbose: Print the progress bar in the console. By default, FALSE.
num_thread: Number of threads
x: bvarhs object
digits: digit option to print
...: not used

References

Carvalho, C. M., Polson, N. G., & Scott, J. G. (2010). The horseshoe estimator for sparse signals. Biometrika, 97(2), 465-480.

Makalic, E., & Schmidt, D. F. (2016). A Simple Sampler for the Horseshoe Estimator. IEEE Signal Processing Letters, 23(1), 179-182.