bv_dummy {BVAR} R Documentation

## 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. 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. `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` Numeric scalar. Minimum / maximum allowed value. Note that for psi these are set automatically or need to provided as vectors. `max` Numeric scalar. Minimum / maximum allowed value. Note that for psi these are set automatically or need to provided as vectors. `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).

### Details

Dummy priors are often used to "reduce the importance of the deterministic component implied by VARs estimated conditioning on the initial observations" (Giannone, Lenza and Primiceri, 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 mu 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 available via the functions `bv_soc` and `bv_sur`.

### Value

Returns a named list of class `bv_dummy` for `bv_priors`.

### Functions

• `bv_soc`: Sum-of-coefficients dummy prior

• `bv_sur`: Single-unit-root dummy prior

### References

Giannone, D. and Lenza, M. and Primiceri, G. E. (2015) Prior Selection for Vector Autoregressions. The Review of Economics and Statistics, 97:2, 436-451, doi: 10.1162/REST_a_00483.

`bv_priors`; `bv_minnesota`

### Examples

```# 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)

# Add the new custom dummy priors
bv_priors(hyper = "auto", soc = soc, sur = sur)
```

[Package BVAR version 1.0.2 Index]