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pith:WK2TILT5

pith:2026:WK2TILT5PE4I3XUPCJE2NSPKWP

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Adaptive Long-Run Variance Thresholding for Sparse Covariance Estimation in High-Dimensional Time Series

Wenhao Zhang, Zhaoxing Gao

Incorporating long-run variance into entrywise thresholds produces consistent sparse covariance estimates for high-dimensional time series under weak dependence.

arxiv:2605.14491 v1 · 2026-05-14 · stat.ME · math.ST · stat.TH

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Claims

C1strongest claim

Under suitable regularity conditions, the proposed estimator is consistent under the spectral norm and attains the optimal convergence rate over a class of sparse covariance matrices. We further establish support recovery consistency for identifying the nonzero entries of the covariance matrix.

C2weakest assumption

The data satisfy weak dependence conditions that allow the long-run variance to be estimated consistently and that the temporal dependence does not alter the stochastic behavior of the sample covariance beyond what the long-run variance adjustment corrects.

C3one line summary

An adaptive long-run variance thresholding method yields consistent sparse covariance estimates and support recovery for weakly dependent high-dimensional time series.

References

32 extracted · 32 resolved · 0 Pith anchors

[1] Andrews, D. W. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation.Econometrica: Journal of the Econometric Society, 817–858 1991

[2] J., and Levina, E 2008

[3] Cai, T., and Liu, W. (2011). Adaptive thresholding for sparse covariance matrix estima- tion.Journal of the American Statistical Association, 106(494), 672–684 2011

[4] T., and Zhou, H 2012

[5] T., and Zhou, H 2013

Formal links

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Receipt and verification

First computed	2026-05-17T23:39:06.429020Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2b5342e7d79388dde8f1249a6c9eab3d11a520542d1519dae44d0c456dac15e

Aliases

arxiv: 2605.14491 · arxiv_version: 2605.14491v1 · doi: 10.48550/arxiv.2605.14491 · pith_short_12: WK2TILT5PE4I · pith_short_16: WK2TILT5PE4I3XUP · pith_short_8: WK2TILT5

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/WK2TILT5PE4I3XUPCJE2NSPKWP \
  | 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: b2b5342e7d79388dde8f1249a6c9eab3d11a520542d1519dae44d0c456dac15e

Canonical record JSON

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    "abstract_canon_sha256": "835402c1cf48fd24855a8b651f388b31b88ac7b748700a2feab36161b8487312",
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    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-14T07:30:38Z",
    "title_canon_sha256": "3793bd08ee171fd1c145edc5d2d90c770782745cf7adbaa6a34c64a6b95d896c"
  },
  "schema_version": "1.0",
  "source": {
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    "kind": "arxiv",
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