minnesota_prior {bvartools}R Documentation

Minnesota Prior

Description

Calculates the Minnesota prior for a VAR model.

Usage

minnesota_prior(object, kappa0 = 2, kappa1 = 0.5, kappa2 = 0.5,
  kappa3 = 5, max_var = NULL, coint_var = FALSE)

Arguments

object

an object of class "bvarmodel", usually, a result of a call to gen_var or gen_vec.

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 kappa0.

kappa2

a numeric specifying the size of the prior standard deviations of exogenous variables relative to argument kappa0.

kappa3

a numeric specifying the size of the prior standard deviations of deterministic terms relative to argument kappa0.

max_var

a positive numeric specifying the maximum prior variance that is allowed for coefficients of non-deterministic variables. If NULL (default), the prior variances are not limited.

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.

Details

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.

Value

A list containing a matrix of prior means and the precision matrix.

References

Lütkepohl, H. (2007). New introduction to multiple time series analysis (2nd ed.). Berlin: Springer.

Examples


# Prepare data
data("e1")
data <- diff(log(e1))

# Generate model input
object <- gen_var(data)

# Obtain Minnesota prior
prior <- minnesota_prior(object)


[Package bvartools version 0.0.2 Index]