{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ET2XJHUP3FVMSY7AOLGXQSOFP6","short_pith_number":"pith:ET2XJHUP","canonical_record":{"source":{"id":"1312.2780","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-12-10T12:27:15Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"610f690790618f76566aada90fafff484f2186584cf0d2c796ede42aa15d8b1a","abstract_canon_sha256":"abc9909297eb0e6c8682e9c862a1a8cbf05196abcbc817f468558c19ebe3f4f0"},"schema_version":"1.0"},"canonical_sha256":"24f5749e8fd96ac963e072cd7849c57f8d062eda68994853c57812fa7a363e30","source":{"kind":"arxiv","id":"1312.2780","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2780","created_at":"2026-05-18T03:05:08Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2780v1","created_at":"2026-05-18T03:05:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2780","created_at":"2026-05-18T03:05:08Z"},{"alias_kind":"pith_short_12","alias_value":"ET2XJHUP3FVM","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"ET2XJHUP3FVMSY7A","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"ET2XJHUP","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ET2XJHUP3FVMSY7AOLGXQSOFP6","target":"record","payload":{"canonical_record":{"source":{"id":"1312.2780","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-12-10T12:27:15Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"610f690790618f76566aada90fafff484f2186584cf0d2c796ede42aa15d8b1a","abstract_canon_sha256":"abc9909297eb0e6c8682e9c862a1a8cbf05196abcbc817f468558c19ebe3f4f0"},"schema_version":"1.0"},"canonical_sha256":"24f5749e8fd96ac963e072cd7849c57f8d062eda68994853c57812fa7a363e30","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:08.849648Z","signature_b64":"d/PeABAcBX/e7eoApimSPNeFLanmomnRNpmEvTK7hitP2BQDUy5/Fd/VkvhsN4LLLJDx4kgnW0j6WEeRDTB6AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24f5749e8fd96ac963e072cd7849c57f8d062eda68994853c57812fa7a363e30","last_reissued_at":"2026-05-18T03:05:08.848947Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:08.848947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.2780","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":"2026-05-18T03:05:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HZvwLUniyNsODFYlxg4um7VPN+QOsSS3jOKc3Mcc76kHGNcMsMk6qeTtZxTG3GKlTT8omb7LioKrvh5XOdoUCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:54:02.418932Z"},"content_sha256":"7a99f2af53ff0797513d6d07daeff440b7cc2c0bf900ec05c8807a88e1e5b9ad","schema_version":"1.0","event_id":"sha256:7a99f2af53ff0797513d6d07daeff440b7cc2c0bf900ec05c8807a88e1e5b9ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ET2XJHUP3FVMSY7AOLGXQSOFP6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic volatility models with possible extremal clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Mohsen Rezapour, Thomas Mikosch","submitted_at":"2013-12-10T12:27:15Z","abstract_excerpt":"In this paper we consider a heavy-tailed stochastic volatility model, $X_t=\\sigma_tZ_t$, $t\\in\\mathbb{Z}$, where the volatility sequence $(\\sigma_t)$ and the i.i.d. noise sequence $(Z_t)$ are assumed independent, $(\\sigma_t)$ is regularly varying with index $\\alpha>0$, and the $Z_t$'s have moments of order larger than $\\alpha$. In the literature (see Ann. Appl. Probab. 8 (1998) 664-675, J. Appl. Probab. 38A (2001) 93-104, In Handbook of Financial Time Series (2009) 355-364 Springer), it is typically assumed that $(\\log\\sigma_t)$ is a Gaussian stationary sequence and the $Z_t$'s are regularly v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2780","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":"2026-05-18T03:05:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fKIVpADiqiKlqU4VyDdoQJgT/bJYYo74O9EhqHZeFWgc3oFSfQ5i9s4BWV0hC4roJn0ijcozeIhi9FAbJbeZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:54:02.419269Z"},"content_sha256":"e97dac8318edccb8157eac3606e8881b20aca02b74eec5afba40122b4e6d0436","schema_version":"1.0","event_id":"sha256:e97dac8318edccb8157eac3606e8881b20aca02b74eec5afba40122b4e6d0436"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ET2XJHUP3FVMSY7AOLGXQSOFP6/bundle.json","state_url":"https://pith.science/pith/ET2XJHUP3FVMSY7AOLGXQSOFP6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ET2XJHUP3FVMSY7AOLGXQSOFP6/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":"2026-06-20T06:54:02Z","links":{"resolver":"https://pith.science/pith/ET2XJHUP3FVMSY7AOLGXQSOFP6","bundle":"https://pith.science/pith/ET2XJHUP3FVMSY7AOLGXQSOFP6/bundle.json","state":"https://pith.science/pith/ET2XJHUP3FVMSY7AOLGXQSOFP6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ET2XJHUP3FVMSY7AOLGXQSOFP6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ET2XJHUP3FVMSY7AOLGXQSOFP6","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":"abc9909297eb0e6c8682e9c862a1a8cbf05196abcbc817f468558c19ebe3f4f0","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-12-10T12:27:15Z","title_canon_sha256":"610f690790618f76566aada90fafff484f2186584cf0d2c796ede42aa15d8b1a"},"schema_version":"1.0","source":{"id":"1312.2780","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2780","created_at":"2026-05-18T03:05:08Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2780v1","created_at":"2026-05-18T03:05:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2780","created_at":"2026-05-18T03:05:08Z"},{"alias_kind":"pith_short_12","alias_value":"ET2XJHUP3FVM","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"ET2XJHUP3FVMSY7A","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"ET2XJHUP","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:e97dac8318edccb8157eac3606e8881b20aca02b74eec5afba40122b4e6d0436","target":"graph","created_at":"2026-05-18T03:05:08Z","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 consider a heavy-tailed stochastic volatility model, $X_t=\\sigma_tZ_t$, $t\\in\\mathbb{Z}$, where the volatility sequence $(\\sigma_t)$ and the i.i.d. noise sequence $(Z_t)$ are assumed independent, $(\\sigma_t)$ is regularly varying with index $\\alpha>0$, and the $Z_t$'s have moments of order larger than $\\alpha$. In the literature (see Ann. Appl. Probab. 8 (1998) 664-675, J. Appl. Probab. 38A (2001) 93-104, In Handbook of Financial Time Series (2009) 355-364 Springer), it is typically assumed that $(\\log\\sigma_t)$ is a Gaussian stationary sequence and the $Z_t$'s are regularly v","authors_text":"Mohsen Rezapour, Thomas Mikosch","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-12-10T12:27:15Z","title":"Stochastic volatility models with possible extremal clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2780","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":"sha256:7a99f2af53ff0797513d6d07daeff440b7cc2c0bf900ec05c8807a88e1e5b9ad","target":"record","created_at":"2026-05-18T03:05:08Z","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":"abc9909297eb0e6c8682e9c862a1a8cbf05196abcbc817f468558c19ebe3f4f0","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-12-10T12:27:15Z","title_canon_sha256":"610f690790618f76566aada90fafff484f2186584cf0d2c796ede42aa15d8b1a"},"schema_version":"1.0","source":{"id":"1312.2780","kind":"arxiv","version":1}},"canonical_sha256":"24f5749e8fd96ac963e072cd7849c57f8d062eda68994853c57812fa7a363e30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24f5749e8fd96ac963e072cd7849c57f8d062eda68994853c57812fa7a363e30","first_computed_at":"2026-05-18T03:05:08.848947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:08.848947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d/PeABAcBX/e7eoApimSPNeFLanmomnRNpmEvTK7hitP2BQDUy5/Fd/VkvhsN4LLLJDx4kgnW0j6WEeRDTB6AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:08.849648Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.2780","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a99f2af53ff0797513d6d07daeff440b7cc2c0bf900ec05c8807a88e1e5b9ad","sha256:e97dac8318edccb8157eac3606e8881b20aca02b74eec5afba40122b4e6d0436"],"state_sha256":"5bc32c0badf4f6d750c6f4385a142c8f3ab8f82ac59b20bd80b9e4cda8327af9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UeMuEL0iAtpfIUIrWQL3/Vd8WYq+v0Lfs+JscaQz14DmYmMwSjbCe9/j8Add4c254xGKtXFcNf05lALQZsaEBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:54:02.421110Z","bundle_sha256":"df407c7bd5c8d41c954815677b9da11a7f02279fcfaac26c91b0b93c9d4d80e8"}}