BVAR (version 0.2.2)

bv_minnesota: Minnesota prior settings

Description

Provide settings for the Minnesota prior to bv_priors. See the Details section for further information.

Usage

bv_minnesota(
  lambda = bv_lambda(mode = 0.2, sd = 0.4, min = 0.0001, max = 5),
  alpha = bv_alpha(2, 0.25, 1, 3),
  psi = bv_psi(0.004, 0.004, "auto"),
  var = 10000000,
  b = "auto"
)
bv_mn(
  lambda = bv_lambda(mode = 0.2, sd = 0.4, min = 0.0001, max = 5),
  alpha = bv_alpha(2, 0.25, 1, 3),
  psi = bv_psi(0.004, 0.004, "auto"),
  var = 10000000,
  b = "auto"
)
bv_lambda(mode = 0.2, sd = 0.4, min = 0.0001, max = 5)
bv_alpha(mode = 2, sd = 0.25, min = 1, max = 3)
bv_psi(scale = 0.004, shape = 0.004, mode = "auto", min = "auto", max = "auto")

Arguments

lambda

List constructed via bv_lambda. Arguments are mode, sd, min and max. May also be provided as a mumeric vector of length 4. See the Details section for further information.

alpha

List constructed via bv_alpha. Arguments are mode, min and max. High values for mode may affect invertibility of the augmented data matrix. May also be provided as a mumeric vector of length 4. See the Details section for further information.

psi

List with elements scale, shape of the prior as well as mode and optionally min and max. The length of these needs to match the number of variables (i.e. columns) in the data. By default mode is set automatically to the squareroot of the innovations variance after fitting an \(AR(p)\) model to the data. By default min / max are set to mode divided / multiplied by \(100\). See the Details section for further information.

var

Numeric scalar with the prior variance on the model's constant.

b

Numeric matrix with the prior mean.

mode

Numeric scalar (/vector). Mode (or the like) of the parameter.

sd

Numeric scalar with the standard deviation.

min

Numeric scalar (/vector). Minimum allowed value.

max

Numeric scalar (/vector). Maximum allowed value.

scale, shape

Numeric scalar. Scale and shape parameters of a Gamma distribution.

Value

Returns a list of class bv_minnesota with options for bvar.

Details

Essentially this prior imposes the hypothesis, that the individual variables all follow random walk processes. This parsimonious specification typically performs well in forecasts of macroeconomic time series and is often used as a benchmark for evaluating accuracy (Kilian and L<U+00FC>tkepohl, 2017). The key parameter is \(\lambda\) (lambda), which controls the tightness of the prior. The parameter \(\alpha\) (alpha) governs variance decay with increasing lag order, while \(\psi\) (psi controls the prior's standard deviation on lags of variables other than the dependent. The Minnesota prior is often refined with additional priors, trying to minimise the importance of conditioning on initial observations. See bv_dummy for more information on such priors.

References

Kilian L, L<U+00FC>tkepohl H (2017). Structural Vector Autoregressive Analysis. Cambridge University Press.

See Also

bv_priors; bv_dummy

Examples

# NOT RUN {
# Adjust alpha and the Minnesota prior variance.
bv_mn(
  alpha = bv_alpha(mode = 0.5, sd = 1, min = 1e-12, max = 10),
  var = 1e6
)
# Optionally use a vector as shorthand
bv_mn(alpha = c(0.5, 1, 1e-12, 10), var = 1e6)

# Only adjust lambda's standard deviation
bv_mn(lambda = bv_lambda(sd = 2))
# }