minnesota_prior {bvartools} | R Documentation |
Calculates the Minnesota prior for a VAR model.
minnesota_prior(object, kappa0 = 2, kappa1 = 0.5, kappa2 = 0.5, kappa3 = 5, max_var = NULL, coint_var = FALSE)
object |
an object of class |
kappa0 |
a numeric specifying the prior standard deviation of coefficients that correspond to own lags of endogenous variables. |
kappa1 |
a numeric specifying the size of the prior standard deviations of endogenous
variables, which do not correspond to own lags, relative to argument |
kappa2 |
a numeric specifying the size of the prior standard deviations of exogenous
variables relative to argument |
kappa3 |
a numeric specifying the size of the prior standard deviations 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. |
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
≤ft( \frac{κ_{0}}{l} \right)^2 \textrm{ for own lags of endogenous variables,}
≤ft( \frac{κ_{0} κ_{1}}{l} \frac{σ_{i}}{σ_{j}} \right)^2 \textrm{ for endogenous variables other than own lags,}
≤ft( \frac{κ_{0} κ_{2}}{l} \frac{σ_{i}}{σ_{j}} \right)^2 \textrm{ for exogenous variables,}
(κ_{0} κ_{3})^2 \textrm{ for deterministic terms,}
where σ_{i} is the residual standard deviation of variable i of an unrestricted OLS estimate of the model. For exogenous variables σ_{i} corresponds to the standard deviation of the original series.
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 OLS 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.
Lütkepohl, H. (2007). New introduction to multiple time series analysis (2nd ed.). Berlin: Springer.
# Prepare data data("e1") data <- diff(log(e1)) # Generate model input object <- gen_var(data) # Obtain Minnesota prior prior <- minnesota_prior(object)