{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:Q5P4VOS3WYE3OTODSKI3JCNGHQ","short_pith_number":"pith:Q5P4VOS3","schema_version":"1.0","canonical_sha256":"875fcaba5bb609b74dc39291b489a63c088f01e9c138a703368c2f2549214802","source":{"kind":"arxiv","id":"1505.05385","version":1},"attestation_state":"computed","paper":{"title":"The extremogram and the cross-extremogram for a bivariate GARCH(1,1) process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Muneya Matsui, Thomas Mikosch","submitted_at":"2015-05-20T13:49:54Z","abstract_excerpt":"In this paper, we derive some asymptotic theory for the extremogram and cross-extremogram of a bivariate GARCH(1,1) process. We show that the tails of the components of a bivariate GARCH(1,1) process may exhibit power law behavior but, depending on the choice of the parameters, the tail indices of the components may differ. We apply the theory to 5-minute return data of stock prices and foreign exchange rates. We judge the fit of a bivariate GARCH(1,1) model by considering the sample extremogram and cross-extremogram of the residuals. The results are in agreement with the iid hypothesis of the"},"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":"1505.05385","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-05-20T13:49:54Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"2b86c7ae0692e9556d4ab43b1b280b996dfab43005b34926b7041fdc6f8d6d77","abstract_canon_sha256":"a458e8aae25baebc42287180c9135e99e242bade780a121b6b99bf8de6a98e41"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:56.525395Z","signature_b64":"c8pv6x5StJMTPIppmgRRp8O5nTKw+tLHKor4AX/7UH0opIuK4QkYNpRyfv+MAiFwv51Oi2V1ddWpTK/u+wehAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"875fcaba5bb609b74dc39291b489a63c088f01e9c138a703368c2f2549214802","last_reissued_at":"2026-05-18T02:03:56.524749Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:56.524749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The extremogram and the cross-extremogram for a bivariate GARCH(1,1) process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Muneya Matsui, Thomas Mikosch","submitted_at":"2015-05-20T13:49:54Z","abstract_excerpt":"In this paper, we derive some asymptotic theory for the extremogram and cross-extremogram of a bivariate GARCH(1,1) process. We show that the tails of the components of a bivariate GARCH(1,1) process may exhibit power law behavior but, depending on the choice of the parameters, the tail indices of the components may differ. We apply the theory to 5-minute return data of stock prices and foreign exchange rates. We judge the fit of a bivariate GARCH(1,1) model by considering the sample extremogram and cross-extremogram of the residuals. The results are in agreement with the iid hypothesis of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05385","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":"1505.05385","created_at":"2026-05-18T02:03:56.524852+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.05385v1","created_at":"2026-05-18T02:03:56.524852+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05385","created_at":"2026-05-18T02:03:56.524852+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q5P4VOS3WYE3","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q5P4VOS3WYE3OTOD","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q5P4VOS3","created_at":"2026-05-18T12:29:37.295048+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/Q5P4VOS3WYE3OTODSKI3JCNGHQ","json":"https://pith.science/pith/Q5P4VOS3WYE3OTODSKI3JCNGHQ.json","graph_json":"https://pith.science/api/pith-number/Q5P4VOS3WYE3OTODSKI3JCNGHQ/graph.json","events_json":"https://pith.science/api/pith-number/Q5P4VOS3WYE3OTODSKI3JCNGHQ/events.json","paper":"https://pith.science/paper/Q5P4VOS3"},"agent_actions":{"view_html":"https://pith.science/pith/Q5P4VOS3WYE3OTODSKI3JCNGHQ","download_json":"https://pith.science/pith/Q5P4VOS3WYE3OTODSKI3JCNGHQ.json","view_paper":"https://pith.science/paper/Q5P4VOS3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.05385&json=true","fetch_graph":"https://pith.science/api/pith-number/Q5P4VOS3WYE3OTODSKI3JCNGHQ/graph.json","fetch_events":"https://pith.science/api/pith-number/Q5P4VOS3WYE3OTODSKI3JCNGHQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q5P4VOS3WYE3OTODSKI3JCNGHQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q5P4VOS3WYE3OTODSKI3JCNGHQ/action/storage_attestation","attest_author":"https://pith.science/pith/Q5P4VOS3WYE3OTODSKI3JCNGHQ/action/author_attestation","sign_citation":"https://pith.science/pith/Q5P4VOS3WYE3OTODSKI3JCNGHQ/action/citation_signature","submit_replication":"https://pith.science/pith/Q5P4VOS3WYE3OTODSKI3JCNGHQ/action/replication_record"}},"created_at":"2026-05-18T02:03:56.524852+00:00","updated_at":"2026-05-18T02:03:56.524852+00:00"}