Objective
Test whether an adaptive state-dependent splice horizon H*(theta, x), chosen by rolling log-linear diagnostics on the mean strip sequence, can beat fixed-horizon baselines for MC cap-rate pricing error.
Setup
- Model: 54 free parameters, geometric tail operator eta_H * r/(1-r) with global r
- Evaluator: 3-arm bakeoff (B0=Fixed-100, B1=Fixed-150, A0=adaptive) with CRN within each cell
- Comparators: B0, B1 at R in {50, 100, 250, 500}; deep benchmark Q_deep at R=10000, H=1500
- Acceptance: 6 pre-registered criteria (A1-A6)
Procedure
- Pilot bakeoff to calibrate thresholds (eps_rho=0.001863, eps_fit=0.001759, eps_hold=0.006110)
- Phase B: 327-cell panel x R in {50,100,250,500} x S=10 seeds per cell, CRN-controlled
- Smoothness probes: 11,016 perturbations (6 dims x 3 epsilons x 2 regimes x 3 assets)
- R-stability and summary-sensitivity analysis
- Audit: independent re-implementation + oracle grid search + monotonicity census
Results
- A0/B0 at R_prod=250: 0.775 (22.5% improvement; auditor 0.74); A1 threshold <0.70: FAIL by 7.5pp
- A0/B1 at R_prod=250: 0.886 (A2 threshold <1.10: PASS)
- H* bimodal: 49% H=80, 36% H=150 (A3 PASS); sd(H*) < 1 grid step in 98.4% of cells (A6 PASS)
- Smoothness: 98.5% below 3x baseline; 7/11016 edge-case violations at one theta (A4 FAIL, 0.06%)
- R-robustness: A0/B0 = 1.04 (R=50), 1.06 (R=100), 0.78 (R=250), 0.68 (R=500). Advantage only at R>=250 (A5 FAIL)
- Panel contamination (audit): 3/6 theta CSVs identical MD5 — only 4 unique theta, dgp_truth weighted 3x
- Non-monotonicity (audit): only 12.3% of cells show error decreasing monotonically with H at R=250
- Audit verdict: PARTIAL PASS with caveats
Analysis
The adaptive rule is real but R-conditional: at R>=250 it beats both fixed baselines, but at R⇐100 diagnostic noise swamps the signal. The bimodality is correct (fast-decay vs slow-propagation cells), but the deeper finding is the 87.7% non-monotonicity — the geometric tail operator with a single global decay rate r introduces state-dependent bias that no splice-timing rule can eliminate. The locked thresholds are mean-specific and do not transfer to median or E[log] strip summaries. CRN is essential (non-CRN gives A0/B0 ~ 1.38 vs 0.74).
Claim updates
- principal-eigenvalue-determines-long-run-asset: Bimodal H* distribution (49% H=80, 36% H=150) is consistent with state-dependent approach to the principal eigenvalue’s asymptotic regime, but the 87.7% non-monotonicity in error vs H reveals that the geometric tail operator’s single global decay rate is an imperfect proxy for the true state-dependent spectral radius.
- bond-dividend-strip-prices-regime-switching: Adaptive splice timing validates the Riccati strip structure at short horizons but exposes the geometric tail operator as a misspecification for state-dependent pricing at intermediate horizons.
Follow-up
- Tail operator replacement (state-dependent r(x), local rho refit, non-geometric operators)
- Panel decontamination (replace 3 duplicate thetas with stress cases)
- User decision: accept 22%, raise R_prod to 500, or replace tail operator first