R: Fitting Bayesian VAR(p) of Flat Prior

bvar_flat {bvhar}

R Documentation

Fitting Bayesian VAR(p) of Flat Prior

Description

This function fits BVAR(p) with flat prior.

Usage

bvar_flat(y, p, bayes_spec = set_bvar_flat(), include_mean = TRUE)

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

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

Arguments

`y`	Time series data of which columns indicate the variables
`p`	VAR lag
`bayes_spec`	A BVAR model specification by `set_bvar_flat()`.
`include_mean`	Add constant term (Default: `TRUE`) or not (`FALSE`)
`x`	`bvarflat` object
`digits`	digit option to print
`...`	not used

Details

Ghosh et al. (2018) gives flat prior for residual matrix in BVAR.

Under this setting, there are many models such as hierarchical or non-hierarchical. This function chooses the most simple non-hierarchical matrix normal prior in Section 3.1.

A \mid \Sigma_e \sim MN(0, U^{-1}, \Sigma_e)

where U: precision matrix (MN: matrix normal).

p (\Sigma_e) \propto 1

Value

bvar_flat() returns an object bvarflat 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
df: Numer of Coefficients: mp + 1 or mp
p: Lag of VAR
m: Dimension of the time series
obs: Sample size used when training = totobs - p
totobs: Total number of the observation
process: Process string in the bayes_spec: "BVAR_Flat"
spec: Model specification (bvharspec)
type: include constant term ("const") or not ("none")
call: Matched call
prior_mean: Prior mean matrix of Matrix Normal distribution: zero matrix
prior_precision: Prior precision matrix of Matrix Normal distribution: U^{-1}
y0: Y_0
design: X_0
y: Raw input (matrix)

References

Ghosh, S., Khare, K., & Michailidis, G. (2018). High-Dimensional Posterior Consistency in Bayesian Vector Autoregressive Models. Journal of the American Statistical Association, 114(526).

Litterman, R. B. (1986). Forecasting with Bayesian Vector Autoregressions: Five Years of Experience. Journal of Business & Economic Statistics, 4(1), 25.