scoringfunctions (version 1.1)

maesd_sf: MAE-SD scoring function

Description

The function maesd_sf computes the MAE-SD scoring function when \(y\) materialises and \(x\) is the predictive median functional.

The MAE-SD scoring function is defined by eq. (12) in Patton (2011).

Usage

maesd_sf(x, y)

Value

Vector of MAE-SD losses.

Arguments

x

Predictive median functional (prediction). It can be a vector of length \(n\) (must have the same length as \(y\)).

y

Realisation (true value) of process. It can be a vector of length \(n\) (must have the same length as \(x\)).

Details

The MAE-SD scoring function is defined by:

$$S(x, y) := |x^{1/2} - y^{1/2}|$$

Domain of function:

$$x > 0$$

$$y > 0$$

Range of function:

$$S(x, y) \geq 0, \forall x, y > 0$$

References

Gneiting T (2011) Making and evaluating point forecasts. Journal of the American Statistical Association 106(494):746--762. tools:::Rd_expr_doi("10.1198/jasa.2011.r10138").

Patton AJ (2011) Volatility forecast comparison using imperfect volatility proxies. Journal of Econometrics 160(1):246--256. tools:::Rd_expr_doi("10.1016/j.jeconom.2010.03.034").

Saerens M (2000) Building cost functions minimizing to some summary statistics. IEEE Transactions on Neural Networks 11(6):1263--1271. tools:::Rd_expr_doi("10.1109/72.883416").

Thomson W (1979) Eliciting production possibilities from a well-informed manager. Journal of Economic Theory 20(3):360--380. tools:::Rd_expr_doi("10.1016/0022-0531(79)90042-5").

Examples

# Compute the MAE-SD scoring function.

df <- data.frame(
    y = rep(x = 2, times = 3),
    x = 1:3
)

df$mae_sd_penalty <- maesd_sf(x = df$x, y = df$y)

print(df)