bvhar_ssvs: Fitting Bayesian VHAR of SSVS Prior

Description

This function fits BVAR(p) with stochastic search variable selection (SSVS) prior.

Usage

bvhar_ssvs(
  y,
  har = c(5, 22),
  num_chains = 1,
  num_iter = 1000,
  num_burn = floor(num_iter/2),
  thinning = 1,
  bayes_spec = choose_ssvs(y = y, ord = har, type = "VHAR", param = c(0.1, 10),
    include_mean = include_mean, gamma_param = c(0.01, 0.01), mean_non = 0, sd_non = 0.1),
  init_spec = init_ssvs(type = "auto"),
  include_mean = TRUE,
  minnesota = c("no", "short", "longrun"),
  verbose = FALSE,
  num_thread = 1
)
# S3 method for bvharssvs
print(x, digits = max(3L, getOption("digits") - 3L), ...)
# S3 method for bvharssvs
knit_print(x, ...)

Value

bvhar_ssvs returns an object named bvharssvs

class. It is a list with the following components:

coefficients: Posterior mean of VAR coefficients.

chol_posterior

Posterior mean of cholesky factor matrix

covmat

Posterior mean of covariance matrix

omega_posterior

Posterior mean of omega

pip

Posterior inclusion probability

param

posterior::draws_df with every variable: alpha, eta, psi, omega, and gamma

param_names

Name of every parameter.

Numer of Coefficients: 3m + 1 or 3m

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

week

Order for weekly term

month

Order for monthly term

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

type

include constant term (const) or not (none)

spec

SSVS specification defined by set_ssvs()

init

Initial specification defined by init_ssvs()

chain

The numer of chains

iter

Total iterations

burn

Burn-in

thin

Thinning

group

Indicators for group.

num_group

Number of groups.

HARtrans

VHAR linear transformation matrix

$Y_0$

design

$X_0$

Raw input

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 warm-up (burn-in). Half of the iteration is the default choice.
thinning: Thinning every thinning-th iteration
bayes_spec: A SSVS model specification by set_ssvs(). By default, use a default semiautomatic approach choose_ssvs().
init_spec: SSVS initialization specification by init_ssvs(). By default, use OLS for coefficient and cholesky factor while 1 for dummies.
include_mean: Add constant term (Default: TRUE) or not (FALSE)
minnesota: Apply cross-variable shrinkage structure (Minnesota-way). Two type: short type and longrun type. By default, no.
verbose: Print the progress bar in the console. By default, FALSE.
num_thread: Number of threads
x: bvharssvs object
digits: digit option to print
...: not used

Details

SSVS prior gives prior to parameters $\alpha = vec(A)$ (VAR coefficient) and $\Sigma_e^{-1} = \Psi \Psi^T$ (residual covariance).

$$\alpha_j \mid \gamma_j \sim (1 - \gamma_j) N(0, \kappa_{0j}^2) + \gamma_j N(0, \kappa_{1j}^2)$$ $$\gamma_j \sim Bernoulli(q_j)$$

and for upper triangular matrix $\Psi$,

$$\psi_{jj}^2 \sim Gamma(shape = a_j, rate = b_j)$$ $$\psi_{ij} \mid w_{ij} \sim (1 - w_{ij}) N(0, \kappa_{0,ij}^2) + w_{ij} N(0, \kappa_{1,ij}^2)$$ $$w_{ij} \sim Bernoulli(q_{ij})$$

Gibbs sampler is used for the estimation.

References

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