bvhar_minnesota {bvhar}

Fitting Bayesian VHAR of Minnesota Prior

Description

This function fits BVHAR with Minnesota prior.

Usage

bvhar_minnesota(
  y,
  har = c(5, 22),
  bayes_spec = set_bvhar(),
  include_mean = TRUE
)

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

## S3 method for class 'bvharmn'
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).

bayes_spec

A BVHAR model specification by set_bvhar() (default) or set_weight_bvhar().

include_mean

Add constant term (Default: TRUE) or not (FALSE)

x

bvarmn object

digits

digit option to print

...

not used

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.

Two types of Minnesota priors builds different dummy variables for Y0. See var_design_formulation.

Value

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

coefficients

Posterior Mean matrix of Matrix Normal distribution

fitted.values

Fitted values

residuals

Residuals

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

p

3, this element exists to run the other functions

week

Order for weekly term

month

Order for monthly term

m

Dimension of the time series

obs

Sample size used when training = totobs - 22

totobs

Total number of the observation

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)

type

include constant term ("const") or not ("none")

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

HARtrans

VHAR linear transformation matrix: C_{HAR}

y0

Y_0

design

X_0

y

Raw input (matrix)

It is also normaliw and bvharmod class.

References

Kim, Y. G., and Baek, C. (2023). Bayesian vector heterogeneous autoregressive modeling. Journal of Statistical Computation and Simulation.

See Also

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

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

• coef.bvharmn(), residuals.bvharmn(), and fitted.bvharmn()

• summary.normaliw() to summarize BVHAR model

• predict.bvharmn() to forecast the BVHAR process

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))