R3 — multi-seed comparison with error bars

[brianmmaina]

30 seeds, and the result is sharper and considerably more negative than the single run suggested.

Nothing is reproduced

Statistic	Real	ZI mean ± sd	rel	z
cancels / new	95.8%	87.8 ± 0.5	8%	+17.3
executions / new	6.8%	14.3 ± 0.1	111%	−50.3
effective spread	300	693 ± 9	131%	−44.1
sign ACF lag 1	0.720	0.468 ± 0.006	35%	+42.5
sign ACF lag 5	0.340	0.015 ± 0.008	96%	+40.7
sign ACF lag 50	0.085	−0.001 ± 0.009	101%	+9.4

This corrects my R2 writeup

R2 called the structural properties "broadly reproduced" from one seed, on the strength of an 88% cancel ratio against a real 96%.

With error bars that gap is 17 standard deviations. The model lands on 87.8% ± 0.5% every single time — internally consistent, and consistently in the wrong place. Being precise is not the same as being right, and one draw could not tell the difference. That is the argument for the multi-seed step existing at all.

Both columns are necessary

My first verdict logic used z alone and called trade-level kurtosis "reproduced" — ZI 175 against a real 11.8, which is 1,389% wrong with |z| = 1.4, purely because the model's variance is enormous.

So the table reports relative error too, and either column alone misleads in opposite directions:

• large z, small rel — precise model, captures the phenomenon, misses the value
• small z, large rel — noisy model, captures nothing, merely cannot be excluded

Verdicts now distinguish NOT reproduced, inconclusive (model too variable), and both ~0 (two numbers agreeing only because neither is far from zero).

The finding that survives

Sign autocorrelation fails in a specific, interpretable shape: 35% low at lag 1, 96% low by lag 5, nothing beyond. The lag-1 value is mechanical — one market order walking several levels prints several same-signed executions in the same instant — not memory.

Real flow decays over a hundred trades. The question is not whether correlation exists but how far it reaches, and deleting strategic behaviour deletes the reach while leaving the artifact.

Method note

compare.py imports stylized_facts.analyse rather than reimplementing it, so a difference in the analysis cannot masquerade as a difference in the market. The real side remains a single session with no error bar, which the doc states as a limit rather than glossing.