Fitting Bayesian VHAR-SV — bvhar

This function fits VHAR-SV. It can have Minnesota, SSVS, and Horseshoe prior. This function is deprecated. Use vhar_bayes() with cov_spec = set_sv() option.

Usage

bvhar_sv(
  y,
  har = c(5, 22),
  num_chains = 1,
  num_iter = 1000,
  num_burn = floor(num_iter/2),
  thinning = 1,
  bayes_spec = set_bvhar(),
  sv_spec = set_sv(),
  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 'bvharsv'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

# S3 method for class 'bvharsv'
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().
sv_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: bvarsv object
digits: digit option to print
...: not used

Value

bvhar_sv() 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 $$\Sigma_t = L^T D_t^{-1} L$$

References

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