Fitting Bayesian VHAR with Coefficient and Covariance Prior

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"),
  save_init = FALSE,
  convergence = NULL,
  verbose = FALSE,
  num_thread = 1
)

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

# 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.
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

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.

Details

Cholesky stochastic volatility modeling for VHAR based on $$\Sigma_t^{-1} = L^T D_t^{-1} L$$

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.