Upper Partial Moment — UPM • NNS

This function generates a univariate upper partial moment for any degree or target.

Usage

UPM(degree, target, variable, excess_ret = FALSE)

degree: numeric; (degree = 0) is frequency, (degree = 1) is area.
target: numeric; Set to target = mean(variable) for classical equivalences, but does not have to be. When excess_ret = FALSE, this can be a scalar or a vectorized target for the standard partial moment calculation. When excess_ret = TRUE, it is interpreted element-wise as the benchmark/threshold relative to variable.
variable: a numeric vector. data.frame or list type objects are not permissible.
excess_ret: logical; FALSE (default). If TRUE, switches from the standard vectorized-target partial moment to an element-wise excess-deviation calculation. For UPM, this computes pmax(variable - target, 0) raised to degree and averaged. In this mode, target must have length 1 or the same length as variable.

UPM of variable

Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" (ISBN: 1490523995)

Fred Viole, OVVO Financial Systems

set.seed(123)
x <- rnorm(100)
UPM(0, mean(x), x)
#> [1] 0.49