A Multiscale Ball Test for Conditional Mean Independence

Battle Count: 69

Directly relevant to factor model specification testing (Fama-French 5+momentum), macro-finance equation testing, and detecting conditional mean dependence in financial time series. The finding that full-sample MBCMI rejections largely disappear after cross-fitted linear residualisation suggests most detected dependence is contemporaneous linear structure rather than distinctive nonlinear alpha. The July 2022 Momentum residual rejection is the one case surviving the linear benchmark. Useful for risk management (conditional heteroskedasticity detection), factor spanning analysis, and assessing whether factor returns carry information beyond linear comovement. However, the test is diagnostic rather than predictive, and does not establish forecasting ability or causality.

High complexity: requires computing 71 Euclidean ball radii per observation, coverage screening (20% threshold, N_min=10), support-weighted local mean contrasts, quadratic-form representations, BIC-selected AR prewhitening (orders 0-6), recursive Rademacher bootstrap with 999 draws repeating the full radius search, Holm family-wise adjustment, cross-fitted OLS residualisation with HAC inference, and rolling window analysis (240-month windows, 1-month step). Multiple diagnostic profiles (scale, contribution, coverage). Predictor standardisation choices (z-score, MAD, whitening) affect results. The paper documents extensive calibration and sensitivity analyses.

The paper uses deterministic seed maps, matched datasets for paired comparisons, and documents a separate research archive with configurations, summary outputs, seed records, and audit manifests. All factor and macroeconomic source series are public (French Data Library, FRED). The arXiv source package contains manuscript source and exhibit files but not the complete executable research repository. 1,134,000 paired canonical datasets completed without failures. 13,000 Monte Carlo comparisons for coverage audit. 16,000 serial-null replications.