PBO: Probability of Backtest Overfitting

In NMOF: Numerical Methods and Optimization in Finance

Probability of Backtest Overfitting

Description

Estimate probability of backtest overfitting, as described in Bailey et al. 2017

Usage

PBO(M, s = 12, fun = colMeans,
    threshold = 0, ..., loop.fun = TRUE)

Arguments

M	a numeric matrix
s	number of submatrices
fun	a function
threshold	a scalar
...	additional arguments passed to fun
loop.fun	logical: if TRUE, fun is called separately for every column of M; if FALSE, fun will be passed the whole matrix M

Details

fun is called with M as its first argument.

Value

A list:

pbo	probability
lambda	vector of logits
in.sample	numeric
out.of.sample	numeric

Author(s)

Enrico Schumann

References

Bailey, D. H. et al. (2017). The probability of backtest overfitting. Journal of Computational Finance 20 (4), 39–69. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.21314/JCF.2016.322")}

Examples

## might run a few seconds
N <- 5000
T <- 480
M <- array(rnorm(N*T, sd = 0.01), dim = c(T, N))
p <- PBO(M, s = 12, fun = colMeans, loop.fun = FALSE)
str(p)

NMOF documentation built on Nov. 5, 2025, 6:38 p.m.