Phase 2: realised variance — estimators validated on simulated ground truth

[NavyBlueCheese]

What was built

• src/fxvrp/realized/estimators.py — RV, subsample-averaged RV, TSRV (Zhang-Mykland-Ait-Sahalia 2005 with the small-sample adjustment), realised kernel (Parzen weights, BNHLS plug-in bandwidth), realised semivariance.
• src/fxvrp/realized/jumps.py — bipower variation, tripower quarticity, jump variation, and the Huang-Tauchen ratio jump statistic.
• src/fxvrp/realized/sampling.py — previous-tick calendar-time sampling on log mid-quotes (Hansen-Lunde), DST-aware 17:00-ET FX day windows.
• src/fxvrp/realized/panel.py + scripts/build_rv_panel.py — the daily RV panel; thin days flagged on in-window quote updates (held quotes fill any grid, so grid-return counts cannot detect thinness).
• src/fxvrp/realized/signature.py + scripts/fig_signature.py — the volatility signature plot; paper/figures/signature_plot.pdf generated from real ticks.
• paper/notes/methodology_realized.md — methodology drafted while building, per the brief.

Ground-truth results (the section 3 table, realised rows)

• RV -> sigma^2 T under GBM (<1% bias at fine sampling; sampling-noise std matches sqrt(2/n)).
• RV tracks each Heston path's recorded integral of v dt: corr > 0.999, within 10%.
• Naive RV under noise equals IV + 2 n omega^2 within 5% and diverges in sampling frequency (demonstrated); TSRV and the realised kernel recover the truth.
• BPV recovers the continuous part only under Merton; RV - BPV tracks the true per-path sum of squared jumps (corr > 0.99).
• Jump test: empirical size within binomial tolerance of nominal 5% on 800 jump-free days; power > 60% on days with visible jumps.
• TQ/BPV^2 -> 1 under constant volatility (the studentisation the z-test relies on).

Full suite: 78 passed, coverage 92.1%, mypy --strict clean, ruff clean.

Real-data output (extends automatically as the backfill completes)

54 usable FX days on disk so far (March 2020 + early 2007): mean annualised vol 11.8%, max 26.5% (COVID), 4 jump days at the 0.1% level including 2020-03-03 - the Fed's emergency inter-meeting cut. The signature curve shows ~35% RV inflation at 5s sampling, flattening at the 5-minute baseline.

Known uncertainties

• TSRV and kernel-bandwidth equation numbers not verified against the papers; flagged TODO(verify) in docstrings, behaviour pinned by tests.
• Kernel end-point jittering (BNHLS practice paper) not implemented; documented simplification.
• The panel spans whatever ticks the backfill has ingested; rerun scripts/build_rv_panel.py to extend.