| bvar_minnesota {bvhar} | R Documentation |
Fitting Bayesian VAR(p) of Minnesota Prior
Description
This function fits BVAR(p) with Minnesota prior.
Usage
bvar_minnesota(y, p = 1, bayes_spec = set_bvar(), include_mean = TRUE)
## S3 method for class 'bvarmn'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
## S3 method for class 'bvarmn'
knit_print(x, ...)
Arguments
y |
Time series data of which columns indicate the variables |
p |
VAR lag (Default: 1) |
bayes_spec |
A BVAR model specification by |
include_mean |
Add constant term (Default: |
x |
|
digits |
digit option to print |
... |
not used |
Details
Minnesota prior gives prior to parameters A (VAR matrices) and \Sigma_e (residual covariance).
A \mid \Sigma_e \sim MN(A_0, \Omega_0, \Sigma_e)
\Sigma_e \sim IW(S_0, \alpha_0)
(MN: matrix normal, IW: inverse-wishart)
Value
bvar_minnesota() returns an object bvarmn 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 (
alpha_0- obs + 2).\alpha_0: nrow(Dummy observation) - k- 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
- call
Matched call
- process
Process string in the
bayes_spec:"BVAR_Minnesota"- spec
Model specification (
bvharspec)- type
include constant term (
"const") or not ("none")- prior_mean
Prior mean matrix of Matrix Normal distribution:
A_0- prior_precision
Prior precision matrix of Matrix Normal distribution:
\Omega_0^{-1}- prior_scale
Prior scale matrix of inverse-Wishart distribution:
S_0- prior_shape
Prior shape of inverse-Wishart distribution:
\alpha_0- y0
Y_0- design
X_0- y
Raw input (
matrix)
It is also normaliw and bvharmod class.
References
Bańbura, M., Giannone, D., & Reichlin, L. (2010). Large Bayesian vector auto regressions. Journal of Applied Econometrics, 25(1).
Giannone, D., Lenza, M., & Primiceri, G. E. (2015). Prior Selection for Vector Autoregressions. Review of Economics and Statistics, 97(2).
Litterman, R. B. (1986). Forecasting with Bayesian Vector Autoregressions: Five Years of Experience. Journal of Business & Economic Statistics, 4(1), 25.
KADIYALA, K.R. and KARLSSON, S. (1997), NUMERICAL METHODS FOR ESTIMATION AND INFERENCE IN BAYESIAN VAR-MODELS. J. Appl. Econ., 12: 99-132.
Karlsson, S. (2013). Chapter 15 Forecasting with Bayesian Vector Autoregression. Handbook of Economic Forecasting, 2, 791–897.
Sims, C. A., & Zha, T. (1998). Bayesian Methods for Dynamic Multivariate Models. International Economic Review, 39(4), 949–968.
See Also
-
set_bvar()to specify the hyperparameters of Minnesota prior. -
summary.normaliw()to summarize BVAR model -
predict.bvarmn()to forecast the BVAR process
Examples
# Perform the function using etf_vix dataset
fit <- bvar_minnesota(y = etf_vix[,1:3], p = 2)
class(fit)
# Extract coef, fitted values, and residuals
coef(fit)
head(residuals(fit))
head(fitted(fit))