maesd_sf {scoringfunctions}

MAE-SD scoring function

Description

The function maesd_sf computes the MAE-SD scoring function when y materializes 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)

Arguments

x

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

y

Realization (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

Value

Vector of MAE-SD losses.

Note

For details on the MAE-SD scoring function, see Gneiting (2011) and Patton (2011).

The median functional is the median of the probability distribution F of y (Gneiting 2011).

The MAE-SD scoring function is negatively oriented (i.e. the smaller, the better).

The MAE-SD scoring function is strictly consistent for the median functional relative to the family \mathbb{F} of potential probability distributions F for the future y for which E_F[Y^{1/2}] exists and is finite (Thomson 1979, Saerens 2000, Gneiting 2011).

References

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

Patton AJ (2011) Volatility forecast comparison using imperfect volatility proxies. Journal of Econometrics 160(1):246–256. 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. doi:10.1109/72.883416.

Thomson W (1979) Eliciting production possibilities from a well-informed manager. Journal of Economic Theory 20(3):360–380. 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)