Key points are not available for this paper at this time.
Background and gap: Regime models underpin capital, risk-limit, and hedging decisions, yet existing literature evaluates one fitted specification at a time. Basel IV and SR 11-7 require structural stability across admissible specifications. Contribution: We provide the first systematic audit of representation invariance for discrete-state regime models, measuring partition agreement by ARI and coarse risk-ordering agreement by a matching-free rank-aligned metric calibrated against a 1 / K null. Method: We test four single-asset case studies under four model classes (HMM, GMM, k-means, spectral) at K ∈ 2, 3, 4, 5. Eight representations (seven for all assets, one VIX-based for S disagreement persists under k-means and at non-overlapping windows. Top-1 ordering Jaccard at K = 3 is 0. 47 against a 1 / K = 0. 20 null, a 2. 4 × excess comparable to the partition signal. Significance: Representation-conditional CVaR diverges by 39–73% of the unconditional CVaR on average and approaches 300% in COVID-19 stress (BTC-USD HMM peak 299%). We recommend a cross-representation envelope as a diagnostic complement to temporal backtesting; the registered admissible class (Supplementary Section? ? ) is narrow, so the reported ARI is a conservative upper bound.
Zheng et al. (Wed,) studied this question.