The Bid & Ask

Quotations, Dispatches, and the Daily Tape

Saturday, August 15, 2026

Rejected thesis

2026-08-15 — every t-stat in this file below horizon 1 was inflated

The result

Not a rejected thesis: a defect in the instrument that judged them.

research/experiments/framework.t_stat computed the textbook IID statistic, mean / (sd / sqrt(n)), and evaluate_signal handed it IC and decile-spread series built from horizon-day forward returns sampled every day. Neighbouring observations of a 21-day forward return share 20 of their 21 days. They are not independent draws, and dividing by a standard error that assumes they are understates it by roughly sqrt(horizon).

Measured on pure zero-mean noise — no information present by construction — 500 trials per horizon, 1,200 observations each:

Horizon mean |t| naive mean |t| Newey-West cleared |t|>2 naive cleared |t|>2 NW
1 0.77 0.77 4 % 4 %
5 1.78 0.97 39 % 8 %
21 3.60 0.97 68 % 9 %
63 6.82 1.10 81 % 14 %

At the 21-day horizon the old statistic cleared the usual significance bar on noise two times in three. Horizon 1 is unaffected, which is the control: with no overlap the correction is a no-op and the 4 % false positive rate is the nominal one.

Fixed by Newey-West (Bartlett kernel) standard errors, with the lag count derived from the sampling interval rather than assumed daily, so a weekly-resampled panel at horizon 21 gets 3 lags rather than 20. The residual 9–14 % is the known finite-sample conservatism of the estimator, not a further bug.

What this does not do is re-run anything. Every report in this file at horizon 5 or longer was scored with the inflated statistic, so its t-stats read high — including the ones used to reject theses, where an inflated t made the rejection look better-evidenced than it was. The verdicts themselves mostly rest on effect sizes and Sharpe rather than t alone, and no verdict has been revised on this basis yet. Re-running the validators is a deliberate act; until it happens, read every t-stat above dated before 2026-08-15 as an upper bound.

At a glance
VerdictRejected

Every result here is reproducible from the script named above. Reports are in the repository.

Other rejected theses