Pith Number

pith:HI75BB7V

pith:2025:HI75BB7VAGXK4D5DID6BU47ZAM

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A robust and scalable estimation for high-dimensional volatility models

Kejun Chen, Qianqian Zhu, Yuchang Lin

Data truncation and regularized least squares achieve non-asymptotic error bounds and minimax optimal rates for high-dimensional BEKK-ARCH models under heavy tails.

arxiv:2510.17578 v3 · 2025-10-20 · math.ST · stat.TH

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-26T02:03:58.369049Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a3fd087f501aeae0fa340fc1a73f90309673ed411cf9fa0dd4809327eae3e05

Aliases

arxiv: 2510.17578 · arxiv_version: 2510.17578v3 · doi: 10.48550/arxiv.2510.17578 · pith_short_12: HI75BB7VAGXK · pith_short_16: HI75BB7VAGXK4D5D · pith_short_8: HI75BB7V

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HI75BB7VAGXK4D5DID6BU47ZAM \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 3a3fd087f501aeae0fa340fc1a73f90309673ed411cf9fa0dd4809327eae3e05

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77b6e635f1c235d4bc5cfdb3bd4268c4ea3389f46591f384264295b0a6084b12",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2025-10-20T14:27:33Z",
    "title_canon_sha256": "1f0b005a8059853f66b80677c7e7a0b546cda73e6275caca4d125bcd3b4bbb38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.17578",
    "kind": "arxiv",
    "version": 3
  }
}