bv_dummy: Dummy prior settings

Description

Allows the creation of dummy observation priors for bv_priors. See the Details section for information on common dummy priors.

Usage

bv_dummy(mode = 1, sd = 1, min = 0.0001, max = 5, fun)
bv_soc(mode = 1, sd = 1, min = 0.0001, max = 50)
bv_sur(mode = 1, sd = 1, min = 0.0001, max = 50)

Arguments

mode

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

Numeric scalar with the standard deviation.

min

Numeric scalar (/vector). Minimum allowed value.

max

Numeric scalar (/vector). Maximum allowed value.

fun

Function taking Y, lags and the prior's parameter par to generate and return a named list with elements X and Y (numeric matrices).

Value

Returns a named list of class bv_dummy for bv_priors.

Details

Dummy priors are often used to "reduce the importance of the deterministic component implied by VARs estimated conditioning on the initial observations" (Giannone et al. 2015, p. 440). One such prior is the sum-of-coefficients (SOC) prior, which imposes the notion that a no-change forecast is optimal at the beginning of a time series. Its key parameter $μ$ controls the tightness - i.e. for low values the model is pulled towards a form with as many unit roots as variables and no cointegration. Another such prior is the single-unit-root (SUR) prior, that allows for cointegration relationships in the data. It pushes variables either towards their unconditional mean or towards the presence of at least one unit root. These priors are implemented via Theil mixed estimation, i.e. by adding dummy-observations on top of the data matrix. They are readily available via the shorthand functions bv_soc and bv_sur.

References

Giannone, D., Lenza, M., & Primiceri, G. E. (2015). Prior Selection for Vector Autoregressions. Review of Economics and Statistics, 97, 436-451. https://doi.org/10.1162/REST_a_00483.

Examples

Run this code

# NOT RUN {
# Create a sum-of-coefficients prior
add_soc <- function(Y, lags, par) {
  soc <- if(lags == 1) {diag(Y[1, ]) / par} else {
    diag(colMeans(Y[1:lags, ])) / par
  }
  Y_soc <- soc
  X_soc <- cbind(rep(0, ncol(Y)), matrix(rep(soc, lags), nrow = ncol(Y)))

  return(list("Y" = Y_soc, "X" = X_soc))
}
soc <- bv_dummy(mode = 1, sd = 1, min = 0.0001, max = 50, fun = add_soc)

# Create a single-unit-root prior
add_sur <- function(Y, lags, par) {
  sur <- if(lags == 1) {Y[1, ] / par} else {
    colMeans(Y[1:lags, ]) / par
  }
  Y_sur <- sur
  X_sur <- c(1 / par, rep(sur, lags))

  return(list("Y" = Y_sur, "X" = X_sur))
}

sur <- bv_dummy(mode = 1, sd = 1, min = 0.0001, max = 50, fun = add_sur)

# Adding them to the prior list with `bv_priors()`
priors_dum <- bv_priors(hyper = "auto", soc = soc, sur = sur)
# }

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