vhar_bayes: Fitting Bayesian VHAR with Coefficient and Covariance Prior

In bvhar: Bayesian Vector Heterogeneous Autoregressive Modeling

Fitting Bayesian VHAR with Coefficient and Covariance Prior

Description

This function fits BVHAR. Covariance term can be homoskedastic or heteroskedastic (stochastic volatility). It can have Minnesota, SSVS, and Horseshoe prior.

Usage

vhar_bayes(
  y,
  har = c(5, 22),
  num_chains = 1,
  num_iter = 1000,
  num_burn = floor(num_iter/2),
  thinning = 1,
  bayes_spec = set_bvhar(),
  cov_spec = set_ldlt(),
  intercept = set_intercept(),
  include_mean = TRUE,
  minnesota = c("longrun", "short", "no"),
  ggl = TRUE,
  save_init = FALSE,
  convergence = NULL,
  verbose = FALSE,
  num_thread = 1
)

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

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

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

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

Arguments

y	Time series data of which columns indicate the variables
har	Numeric vector for weekly and monthly order. By default, c(5, 22).
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	A BVHAR model specification by set_bvhar() (default) set_weight_bvhar(), set_ssvs(), or set_horseshoe().
cov_spec	SV specification by set_sv().
intercept	Prior for the constant term by set_intercept().
include_mean	Add constant term (Default: TRUE) or not (FALSE)
minnesota	Apply cross-variable shrinkage structure (Minnesota-way). Two type: short type and longrun (default) type. You can also set no.
ggl	If TRUE (default), use additional group shrinkage parameter for group structure. Otherwise, use group shrinkage parameter instead of global shirnkage parameter. Applies to HS, NG, and DL priors.
save_init	Save every record starting from the initial values (TRUE). By default, exclude the initial values in the record (FALSE), even when num_burn = 0 and thinning = 1. If num_burn > 0 or thinning != 1, this option is ignored.
convergence	Convergence threshold for rhat < convergence. By default, NULL which means no warning.
verbose	Print the progress bar in the console. By default, FALSE.
num_thread	Number of threads
x	bvharldlt object
digits	digit option to print
...	not used

Details

Cholesky stochastic volatility modeling for VHAR based on

\Sigma_t^{-1} = L^T D_t^{-1} L

Value

vhar_bayes() returns an object named bvharsv class. It is a list with the following components:

coefficients

Posterior mean of coefficients.

chol_posterior

Posterior mean of contemporaneous effects.

param

Every set of MCMC trace.

param_names

Name of every parameter.

group

Indicators for group.

num_group

Number of groups.

df

Numer of Coefficients: ⁠3m + 1⁠ or ⁠3m⁠

p

3 (The number of terms. It contains this element for usage in other functions.)

week

Order for weekly term

month

Order for monthly term

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. VHAR_SSVS_SV, VHAR_Horseshoe_SV, or VHAR_minnesota-part_SV

type

include constant term (const) or not (none)

spec

Coefficients prior specification

sv

log volatility prior specification

init

Initial values

intercept

Intercept prior specification

chain

The numer of chains

iter

Total iterations

burn

Burn-in

thin

Thinning

HARtrans

VHAR linear transformation matrix

y0

Y_0

design

X_0

y

Raw input

If it is SSVS or Horseshoe:

pip

Posterior inclusion probabilities.

References

Kim, Y. G., and Baek, C. (2024). Bayesian vector heterogeneous autoregressive modeling. Journal of Statistical Computation and Simulation, 94(6), 1139-1157.

Kim, Y. G., and Baek, C. (n.d.). Working paper.

bvhar documentation built on April 4, 2025, 5:22 a.m.