Fitting Bayesian VAR(p) of Flat Prior

This function fits BVAR(p) with flat prior.

Usage

bvar_flat(
  y,
  p,
  num_chains = 1,
  num_iter = 1000,
  num_burn = floor(num_iter/2),
  thinning = 1,
  bayes_spec = set_bvar_flat(),
  include_mean = TRUE,
  verbose = FALSE,
  num_thread = 1
)

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

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

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

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

is.bvarflat(x)

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

Arguments

y: Time series data of which columns indicate the variables
p: VAR lag
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 BVAR model specification by set_bvar_flat().
include_mean: Add constant term (Default: TRUE) or not (FALSE)
verbose: Print the progress bar in the console. By default, FALSE.
num_thread: Number of threads
x: bvarflat object
digits: digit option to print
...: not used
object: A bvarflat object

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)

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). $$p (\Sigma_e) \propto 1$$

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.