bvhar_minnesota: Fitting Bayesian VHAR of Minnesota Prior

In bvhar: Bayesian Vector Heterogeneous Autoregressive Modeling

Fitting Bayesian VHAR of Minnesota Prior

Description

This function fits BVHAR with Minnesota prior.

Usage

bvhar_minnesota(
  y,
  har = c(5, 22),
  num_chains = 1,
  num_iter = 1000,
  num_burn = floor(num_iter/2),
  thinning = 1,
  bayes_spec = set_bvhar(),
  scale_variance = 0.05,
  include_mean = TRUE,
  parallel = list(),
  verbose = FALSE,
  num_thread = 1
)

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

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

## S3 method for class 'bvharmn'
logLik(object, ...)

## S3 method for class 'bvharmn'
AIC(object, ...)

## S3 method for class 'bvharmn'
BIC(object, ...)

is.bvharmn(x)

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

## S3 method for class 'bvharhm'
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) or set_weight_bvhar().
scale_variance	Proposal distribution scaling constant to adjust an acceptance rate
include_mean	Add constant term (Default: TRUE) or not (FALSE)
parallel	List the same argument of optimParallel::optimParallel(). By default, this is empty, and the function does not execute parallel computation.
verbose	Print the progress bar in the console. By default, FALSE.
num_thread	Number of threads
x	Any object
digits	digit option to print
...	not used
object	A bvharmn object

Details

Apply Minnesota prior to Vector HAR: \Phi (VHAR matrices) and \Sigma_e (residual covariance).

\Phi \mid \Sigma_e \sim MN(M_0, \Omega_0, \Sigma_e)

\Sigma_e \sim IW(\Psi_0, \nu_0)

(MN: matrix normal, IW: inverse-wishart)

There are two types of Minnesota priors for BVHAR:

• VAR-type Minnesota prior specified by set_bvhar(), so-called BVHAR-S model.

• VHAR-type Minnesota prior specified by set_weight_bvhar(), so-called BVHAR-L model.

Value

bvhar_minnesota() returns an object bvharmn class. It is a list with the following components:

coefficients

Posterior Mean

fitted.values

Fitted values

residuals

Residuals

mn_mean

Posterior mean matrix of Matrix Normal distribution

mn_prec

Posterior precision matrix of Matrix Normal distribution

iw_scale

Posterior scale matrix of posterior inverse-wishart distribution

iw_shape

Posterior shape of inverse-Wishart distribution (\nu_0 - obs + 2). \nu_0: nrow(Dummy observation) - k

df

Numer of Coefficients: 3m + 1 or 3m

m

Dimension of the time series

obs

Sample size used when training = totobs - 22

prior_mean

Prior mean matrix of Matrix Normal distribution: M_0

prior_precision

Prior precision matrix of Matrix Normal distribution: \Omega_0^{-1}

prior_scale

Prior scale matrix of inverse-Wishart distribution: \Psi_0

prior_shape

Prior shape of inverse-Wishart distribution: \nu_0

y0

Y_0

design

X_0

p

3, this element exists to run the other functions

week

Order for weekly term

month

Order for monthly term

totobs

Total number of the observation

type

include constant term (const) or not (none)

HARtrans

VHAR linear transformation matrix: C_{HAR}

y

Raw input (matrix)

call

Matched call

process

Process string in the bayes_spec: BVHAR_MN_VAR (BVHAR-S) or BVHAR_MN_VHAR (BVHAR-L)

spec

Model specification (bvharspec)

It is also normaliw and bvharmod class.

References

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

See Also

• set_bvhar() to specify the hyperparameters of BVHAR-S

• set_weight_bvhar() to specify the hyperparameters of BVHAR-L

• summary.normaliw() to summarize BVHAR model

Examples

# Perform the function using etf_vix dataset
fit <- bvhar_minnesota(y = etf_vix[,1:3])
class(fit)

# Extract coef, fitted values, and residuals
coef(fit)
head(residuals(fit))
head(fitted(fit))

bvhar documentation built on June 25, 2025, 9:07 a.m.