{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Q5P4VOS3WYE3OTODSKI3JCNGHQ","short_pith_number":"pith:Q5P4VOS3","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"},"canonical_sha256":"875fcaba5bb609b74dc39291b489a63c088f01e9c138a703368c2f2549214802","source":{"kind":"arxiv","id":"1505.05385","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05385","created_at":"2026-05-18T02:03:56Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05385v1","created_at":"2026-05-18T02:03:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05385","created_at":"2026-05-18T02:03:56Z"},{"alias_kind":"pith_short_12","alias_value":"Q5P4VOS3WYE3","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q5P4VOS3WYE3OTOD","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q5P4VOS3","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Q5P4VOS3WYE3OTODSKI3JCNGHQ","target":"record","payload":{"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"},"canonical_sha256":"875fcaba5bb609b74dc39291b489a63c088f01e9c138a703368c2f2549214802","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"},"source_kind":"arxiv","source_id":"1505.05385","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:03:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9bK/ZJPtxNvNEMa+wAFxEQeFKvjoj4XmKLhRqz6Wd8khpD6sDw7VgB224Z3ZiW2dBlX1kOIvLlo/YgQ1gUjADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:22:17.272111Z"},"content_sha256":"44e1f7774193498b53162e83d9ad01d79fc3025533bbbfac6df0393786064a3a","schema_version":"1.0","event_id":"sha256:44e1f7774193498b53162e83d9ad01d79fc3025533bbbfac6df0393786064a3a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Q5P4VOS3WYE3OTODSKI3JCNGHQ","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:03:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fz22zRJlCy/JacyMvdqdGi6aMAqX953SiUpXfPo1e2XM4qJudOvh5xjrBDFNc5XTwXP5J/hQ7lr8O7+dPHsCAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:22:17.272480Z"},"content_sha256":"bebd8665cfd7ab247be30bfd916ecc9c298ddf7f73621dc1de20c986e7b8fa1e","schema_version":"1.0","event_id":"sha256:bebd8665cfd7ab247be30bfd916ecc9c298ddf7f73621dc1de20c986e7b8fa1e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q5P4VOS3WYE3OTODSKI3JCNGHQ/bundle.json","state_url":"https://pith.science/pith/Q5P4VOS3WYE3OTODSKI3JCNGHQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q5P4VOS3WYE3OTODSKI3JCNGHQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T10:22:17Z","links":{"resolver":"https://pith.science/pith/Q5P4VOS3WYE3OTODSKI3JCNGHQ","bundle":"https://pith.science/pith/Q5P4VOS3WYE3OTODSKI3JCNGHQ/bundle.json","state":"https://pith.science/pith/Q5P4VOS3WYE3OTODSKI3JCNGHQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q5P4VOS3WYE3OTODSKI3JCNGHQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Q5P4VOS3WYE3OTODSKI3JCNGHQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a458e8aae25baebc42287180c9135e99e242bade780a121b6b99bf8de6a98e41","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-05-20T13:49:54Z","title_canon_sha256":"2b86c7ae0692e9556d4ab43b1b280b996dfab43005b34926b7041fdc6f8d6d77"},"schema_version":"1.0","source":{"id":"1505.05385","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05385","created_at":"2026-05-18T02:03:56Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05385v1","created_at":"2026-05-18T02:03:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05385","created_at":"2026-05-18T02:03:56Z"},{"alias_kind":"pith_short_12","alias_value":"Q5P4VOS3WYE3","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q5P4VOS3WYE3OTOD","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q5P4VOS3","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:bebd8665cfd7ab247be30bfd916ecc9c298ddf7f73621dc1de20c986e7b8fa1e","target":"graph","created_at":"2026-05-18T02:03:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Muneya Matsui, Thomas Mikosch","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-05-20T13:49:54Z","title":"The extremogram and the cross-extremogram for a bivariate GARCH(1,1) process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05385","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:44e1f7774193498b53162e83d9ad01d79fc3025533bbbfac6df0393786064a3a","target":"record","created_at":"2026-05-18T02:03:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a458e8aae25baebc42287180c9135e99e242bade780a121b6b99bf8de6a98e41","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-05-20T13:49:54Z","title_canon_sha256":"2b86c7ae0692e9556d4ab43b1b280b996dfab43005b34926b7041fdc6f8d6d77"},"schema_version":"1.0","source":{"id":"1505.05385","kind":"arxiv","version":1}},"canonical_sha256":"875fcaba5bb609b74dc39291b489a63c088f01e9c138a703368c2f2549214802","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"875fcaba5bb609b74dc39291b489a63c088f01e9c138a703368c2f2549214802","first_computed_at":"2026-05-18T02:03:56.524749Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:56.524749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c8pv6x5StJMTPIppmgRRp8O5nTKw+tLHKor4AX/7UH0opIuK4QkYNpRyfv+MAiFwv51Oi2V1ddWpTK/u+wehAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:56.525395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.05385","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44e1f7774193498b53162e83d9ad01d79fc3025533bbbfac6df0393786064a3a","sha256:bebd8665cfd7ab247be30bfd916ecc9c298ddf7f73621dc1de20c986e7b8fa1e"],"state_sha256":"f779db7e9f82d91b0ef0c253a65e2c1e45b563053bb488318d205e4872884956"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NbhtmqJxKCwXojq6iA0dXw/B4Nsl9J/QZAxGssvhWE0MA5EM8kUX/nqg6EN4/v1+Nrj7ma/o0QP4X3GzJywoAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T10:22:17.274389Z","bundle_sha256":"dc45901c0b077b3928184c7451c102c97fb20e43d770371eae253aa70570b6d3"}}