Minnesota Prior
Calculates the Minnesota prior for a VAR model.
minnesota_prior( object, kappa0 = 2, kappa1 = 0.5, kappa2 = NULL, kappa3 = 5, max_var = NULL, coint_var = FALSE, sigma = "AR" )
object |
an object of class |
kappa0 |
a numeric specifying the prior variance of coefficients that correspond to own lags of endogenous variables. |
kappa1 |
a numeric specifying the size of the prior variance of endogenous
variables, which do not correspond to own lags, relative to argument |
kappa2 |
a numeric specifying the size of the prior variance of non-deterministic exogenous
variables relative to argument |
kappa3 |
a numeric specifying the size of the prior variance of deterministic
terms relative to argument |
max_var |
a positive numeric specifying the maximum prior variance that is allowed for
coefficients of non-deterministic variables. If |
coint_var |
a logical specifying whether the model is a cointegrated VAR model, for which the prior means of first own lags should be set to one. |
sigma |
either |
The function calculates the Minnesota prior of a VAR model. For the endogenous variable i the prior variance of the lth lag of regressor j is obtained as
\frac{κ_{0}}{l^2} \textrm{ for own lags of endogenous variables,}
\frac{κ_{0} κ_{1}}{l^2} \frac{σ_{i}^2}{σ_{j}^2} \textrm{ for endogenous variables other than own lags,}
\frac{κ_{0} κ_{2}}{(l + 1)^2} \frac{σ_{i}^2}{σ_{j}^2} \textrm{ for exogenous variables,}
κ_{0} κ_{3} σ_{i}^2 \textrm{ for deterministic terms,}
where σ_{i} is the residual standard deviation of variable i of an unrestricted LS estimate. For exogenous variables σ_{i} is the sample standard deviation.
For VEC models the function only provides priors for the non-cointegration part of the model. The residual standard errors σ_i are based on an unrestricted LS regression of the endogenous variables on the error correction term and the non-cointegration regressors.
A list containing a matrix of prior means and the precision matrix of the cofficients and the inverse variance-covariance matrix of the error term, which was obtained by an LS estimation.
Chan, J., Koop, G., Poirier, D. J., & Tobias, J. L. (2020). Bayesian Econometric Methods (2nd ed.). Cambridge: University Press.
Lütkepohl, H. (2006). New introduction to multiple time series analysis (2nd ed.). Berlin: Springer.
# Load data
data("e1")
data <- diff(log(e1))
# Generate model input
object <- gen_var(data)
# Obtain Minnesota prior
prior <- minnesota_prior(object)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.