{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BQABMIYRBTYZKFKNYUDSU3IHCD","short_pith_number":"pith:BQABMIYR","schema_version":"1.0","canonical_sha256":"0c001623110cf195154dc5072a6d0710e7f64162fc319471beba8058565bf533","source":{"kind":"arxiv","id":"1212.1997","version":1},"attestation_state":"computed","paper":{"title":"Estimation of volatility functionals: the case of a square root n window","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean Jacod (IMJ), Mathieu Rosenbaum (LPMA)","submitted_at":"2012-12-10T09:01:26Z","abstract_excerpt":"We consider a multidimensional Ito semimartingale regularly sampled on [0,t] at high frequency 1/\\Delta_n, with \\Delta_n going to zero. The goal of this paper is to provide an estimator for the integral over [0,t] of a given function of the volatility matrix, with the optimal rate 1/\\sqrt{\\Delta_n} and minimal asymptotic variance. To achieve this we use spot volatility estimators based on observations within time intervals of length k_n\\Delta_n. In [5] this was done with k_n tending to infinity and k_n\\sqrt{\\Delta_n} tending to 0, and a central limit theorem was given after suitable de-biasing"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1212.1997","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-12-10T09:01:26Z","cross_cats_sorted":[],"title_canon_sha256":"a2896e2ff2e932ebfa6a32bfd76593e270b959492be647d70721abd4bce3d879","abstract_canon_sha256":"95a8d9b724cc5176a48dc11438f602b0fbbfadd6280af9b5c182f01bae7d6944"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:54.556937Z","signature_b64":"7R4tmdvt/VGOFoi1VfW5DVyP7rqMZ3mUoBP9Tb1qsaXjimsvf2IV1MOCkzZAtjV1gg4ZNGafaEul3bIPfto9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c001623110cf195154dc5072a6d0710e7f64162fc319471beba8058565bf533","last_reissued_at":"2026-05-18T03:38:54.556564Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:54.556564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Estimation of volatility functionals: the case of a square root n window","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean Jacod (IMJ), Mathieu Rosenbaum (LPMA)","submitted_at":"2012-12-10T09:01:26Z","abstract_excerpt":"We consider a multidimensional Ito semimartingale regularly sampled on [0,t] at high frequency 1/\\Delta_n, with \\Delta_n going to zero. The goal of this paper is to provide an estimator for the integral over [0,t] of a given function of the volatility matrix, with the optimal rate 1/\\sqrt{\\Delta_n} and minimal asymptotic variance. To achieve this we use spot volatility estimators based on observations within time intervals of length k_n\\Delta_n. In [5] this was done with k_n tending to infinity and k_n\\sqrt{\\Delta_n} tending to 0, and a central limit theorem was given after suitable de-biasing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1997","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1212.1997","created_at":"2026-05-18T03:38:54.556631+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.1997v1","created_at":"2026-05-18T03:38:54.556631+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1997","created_at":"2026-05-18T03:38:54.556631+00:00"},{"alias_kind":"pith_short_12","alias_value":"BQABMIYRBTYZ","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"BQABMIYRBTYZKFKN","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"BQABMIYR","created_at":"2026-05-18T12:27:01.376967+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BQABMIYRBTYZKFKNYUDSU3IHCD","json":"https://pith.science/pith/BQABMIYRBTYZKFKNYUDSU3IHCD.json","graph_json":"https://pith.science/api/pith-number/BQABMIYRBTYZKFKNYUDSU3IHCD/graph.json","events_json":"https://pith.science/api/pith-number/BQABMIYRBTYZKFKNYUDSU3IHCD/events.json","paper":"https://pith.science/paper/BQABMIYR"},"agent_actions":{"view_html":"https://pith.science/pith/BQABMIYRBTYZKFKNYUDSU3IHCD","download_json":"https://pith.science/pith/BQABMIYRBTYZKFKNYUDSU3IHCD.json","view_paper":"https://pith.science/paper/BQABMIYR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.1997&json=true","fetch_graph":"https://pith.science/api/pith-number/BQABMIYRBTYZKFKNYUDSU3IHCD/graph.json","fetch_events":"https://pith.science/api/pith-number/BQABMIYRBTYZKFKNYUDSU3IHCD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BQABMIYRBTYZKFKNYUDSU3IHCD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BQABMIYRBTYZKFKNYUDSU3IHCD/action/storage_attestation","attest_author":"https://pith.science/pith/BQABMIYRBTYZKFKNYUDSU3IHCD/action/author_attestation","sign_citation":"https://pith.science/pith/BQABMIYRBTYZKFKNYUDSU3IHCD/action/citation_signature","submit_replication":"https://pith.science/pith/BQABMIYRBTYZKFKNYUDSU3IHCD/action/replication_record"}},"created_at":"2026-05-18T03:38:54.556631+00:00","updated_at":"2026-05-18T03:38:54.556631+00:00"}