Fitting Bayesian VAR(p) of Horseshoe Prior — bvar

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 class 'bvarhs'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

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

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

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.
df: Numer of Coefficients: mp + 1 or mp
p: Lag of VAR
m: 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.
y0: \(Y_0\)
design: \(X_0\)
y: Raw input

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.