bv_minnesota {BVAR} | R Documentation |
Provide settings for the Minnesota prior to bv_priors
. See the
Details section for further information.
bv_minnesota( lambda = bv_lambda(), alpha = bv_alpha(), psi = bv_psi(), var = 10000000, b = 1 ) bv_mn( lambda = bv_lambda(), alpha = bv_alpha(), psi = bv_psi(), var = 10000000, b = 1 ) 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")
lambda |
List constructed via |
alpha |
List constructed via |
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 square-root of the
innovations variance after fitting an AR(p) model to the data.
If |
var |
Numeric scalar with the prior variance on the model's constant. |
b |
Numeric scalar, vector or matrix with the prior mean. A scalar is applied to all variables, with a default value of 1. Consider setting it to 0 for growth rates. A vector needs to match the number of variables (i.e. columns) in the data, with a prior mean per variable. If provided, a matrix needs to have a column per variable (M), and M * p + 1 rows, where p is the number of lags applied. |
mode, sd |
Numeric scalar. Mode / standard deviation of the parameter. Note that the mode of psi is set automatically by default, and would need to be provided as vector. |
min, max |
Numeric scalar. Minimum / maximum allowed value. Note that for psi these are set automatically or need to provided as vectors. |
scale, shape |
Numeric scalar. Scale and shape parameters of a Gamma distribution. |
Essentially this prior imposes the hypothesis, that 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 Lütkepohl, 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.
Returns a list of class bv_minnesota
with options for
bvar
.
bv_lambda
: Tightness of the Minnesota prior
bv_alpha
: Variance decay with increasing lag order
bv_psi
: Prior standard deviation on other lags
Kilian, L. and Lütkepohl, H. (2017). Structural Vector Autoregressive Analysis. Cambridge University Press, https://doi.org/10.1017/9781108164818
# 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)) # Provide prior modes for psi (for a VAR with three variables) bv_mn(psi = bv_psi(mode = c(0.7, 0.3, 0.9)))