{"paper":{"title":"Adaptive Long-Run Variance Thresholding for Sparse Covariance Estimation in High-Dimensional Time Series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Incorporating long-run variance into entrywise thresholds produces consistent sparse covariance estimates for high-dimensional time series under weak dependence.","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Wenhao Zhang, Zhaoxing Gao","submitted_at":"2026-05-14T07:30:38Z","abstract_excerpt":"Estimating a sparse covariance matrix is a fundamental problem in high-dimensional statistics. However, thresholding methods developed for independent data are generally not directly applicable to high-dimensional time series, where temporal dependence alters the stochastic behavior of sample covariance estimators. This paper studies sparse covariance matrix estimation for high-dimensional time series under weak dependence. We propose a thresholding procedure that incorporates long-run variance into the construction of entry-specific thresholds, thereby adapting to temporal dependence. Under s"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"An adaptive long-run variance thresholding method yields consistent sparse covariance estimates and support recovery for weakly dependent high-dimensional time series.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Incorporating long-run variance into entrywise thresholds produces consistent sparse covariance estimates for high-dimensional time series under weak dependence.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"090c553d62da6dde64dd30cf963d1d6da0b0418aadf873d7b42a747aa17b9442"},"source":{"id":"2605.14491","kind":"arxiv","version":1},"verdict":{"id":"d72c2664-0791-4d90-a321-9fc707aff565","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:44:10.250492Z","strongest_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.","one_line_summary":"An adaptive long-run variance thresholding method yields consistent sparse covariance estimates and support recovery for weakly dependent high-dimensional time series.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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.","pith_extraction_headline":"Incorporating long-run variance into entrywise thresholds produces consistent sparse covariance estimates for high-dimensional time series under weak dependence."},"references":{"count":32,"sample":[{"doi":"","year":1991,"title":"Andrews, D. W. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation.Econometrica: Journal of the Econometric Society, 817–858","work_id":"4726b82c-8fc7-4f3f-af33-5a1e0aabb744","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2008,"title":"J., and Levina, E","work_id":"e5935f4e-1a91-4ef0-902b-e910d869a1cf","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"Cai, T., and Liu, W. (2011). Adaptive thresholding for sparse covariance matrix estima- tion.Journal of the American Statistical Association, 106(494), 672–684","work_id":"05ae0c23-e97b-44d7-a0f0-c00476a04b6c","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2012,"title":"T., and Zhou, H","work_id":"479574a1-8ba9-47b2-829b-3b588147aaa4","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2013,"title":"T., and Zhou, H","work_id":"f35817ef-7335-46ff-b1ae-aee2009a487c","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":32,"snapshot_sha256":"d9562a6be8f2dd3b19be8dc81c9a4cf83c5f386c98e0e109ed23f741a454df0b","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"f7522f2f4a59c70e0c76e7142497846c4d5af2f3008c433aedbf6754f9454371"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}