Source of apparent nonlinearity in empirical differences versus dependence components

Ascertain whether the nonlinear trend observed via LOWESS smoothing in scatter plots of cross-sectional performance differences (between IID-resampled and standard backtests) against dependence components reflects genuine underlying nonlinearity or is instead an artifact of noisy estimates, especially near the edges of the plots, for the JKP factor data analyzed with rolling-window mean-variance portfolios.

Background

In the empirical analysis on JKP factors, the authors compare standard backtests to IID-resampled backtests and relate their differences to estimated train–test and within-train dependence. Although linear relationships are weak but statistically significant, a LOWESS fit suggests possible nonlinear patterns.

The authors explicitly state uncertainty about whether the apparent nonlinearity is real or driven by noisy estimates at the boundaries, motivating a focused paper to disambiguate signal from noise in this context.