{"paper":{"title":"A robust and scalable estimation for high-dimensional volatility models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Data truncation and regularized least squares achieve non-asymptotic error bounds and minimax optimal rates for high-dimensional BEKK-ARCH models under heavy tails.","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Kejun Chen, Qianqian Zhu, Yuchang Lin","submitted_at":"2025-10-20T14:27:33Z","abstract_excerpt":"This paper introduces a robust and computationally efficient estimation framework for high-dimensional volatility models in the BEKK-ARCH class. The proposed approach employs data truncation to ensure robustness against heavy-tailed distributions and utilizes a regularized least squares method for efficient optimization in high-dimensional settings. Non-asymptotic error bounds are established for the resulting estimators under heavy-tailed regimes, and the minimax optimal convergence rate is derived. Moreover, a robust BIC and a Ridge-type estimator are introduced for selecting the model order"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Non-asymptotic error bounds are established for the resulting estimators under heavy-tailed regime, and the minimax optimal convergence rate is derived. Moreover, a robust BIC and a Ridge-type estimator are introduced for selecting the model order and the number of BEKK components, respectively, with their selection consistency established under heavy-tailed settings.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The BEKK-ARCH model admits an equivalent VAR representation that preserves the volatility structure sufficiently for regularized least squares to recover the parameters, and that data truncation at a fixed or data-driven level removes heavy-tail effects without biasing the central moments needed for the bounds.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A data-truncated regularized least squares estimator for high-dimensional BEKK-ARCH volatility models achieves non-asymptotic error bounds and minimax optimal rates under heavy tails, with consistent selection via robust BIC and ridge estimators.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Data truncation and regularized least squares achieve non-asymptotic error bounds and minimax optimal rates for high-dimensional BEKK-ARCH models under heavy tails.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b6fe29a53707e19b51d53f074bff8299daf531a9f4d3e0841418c94a359c8036"},"source":{"id":"2510.17578","kind":"arxiv","version":3},"verdict":{"id":"15edb0b3-87a2-4c50-a0ce-cd05bf3884c7","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-18T06:10:49.355905Z","strongest_claim":"Non-asymptotic error bounds are established for the resulting estimators under heavy-tailed regime, and the minimax optimal convergence rate is derived. Moreover, a robust BIC and a Ridge-type estimator are introduced for selecting the model order and the number of BEKK components, respectively, with their selection consistency established under heavy-tailed settings.","one_line_summary":"A data-truncated regularized least squares estimator for high-dimensional BEKK-ARCH volatility models achieves non-asymptotic error bounds and minimax optimal rates under heavy tails, with consistent selection via robust BIC and ridge estimators.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The BEKK-ARCH model admits an equivalent VAR representation that preserves the volatility structure sufficiently for regularized least squares to recover the parameters, and that data truncation at a fixed or data-driven level removes heavy-tail effects without biasing the central moments needed for the bounds.","pith_extraction_headline":"Data truncation and regularized least squares achieve non-asymptotic error bounds and minimax optimal rates for high-dimensional BEKK-ARCH models under heavy tails."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.17578/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"e6fabd2b98e5c250579fc52eb86618fc1e5c6f6e3e01171f893cb0fbc384cb49"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}