{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FX3ADLR7WK63O3QRHRBWRVS2RG","short_pith_number":"pith:FX3ADLR7","canonical_record":{"source":{"id":"1803.00739","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-03-02T07:22:33Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"a50d82fb7dc74612b5e9bbb9b83ff5e2810eff89cf58f54fd798803344cf8967","abstract_canon_sha256":"fd5aa01b565dd8405981f23fea1580c659d1c2f7d4b80daf73429e78d125af39"},"schema_version":"1.0"},"canonical_sha256":"2df601ae3fb2bdb76e113c4368d65a898343d22ab0cf1395d2bb0f7dac87990b","source":{"kind":"arxiv","id":"1803.00739","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00739","created_at":"2026-05-18T00:22:07Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00739v1","created_at":"2026-05-18T00:22:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00739","created_at":"2026-05-18T00:22:07Z"},{"alias_kind":"pith_short_12","alias_value":"FX3ADLR7WK63","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FX3ADLR7WK63O3QR","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FX3ADLR7","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FX3ADLR7WK63O3QRHRBWRVS2RG","target":"record","payload":{"canonical_record":{"source":{"id":"1803.00739","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-03-02T07:22:33Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"a50d82fb7dc74612b5e9bbb9b83ff5e2810eff89cf58f54fd798803344cf8967","abstract_canon_sha256":"fd5aa01b565dd8405981f23fea1580c659d1c2f7d4b80daf73429e78d125af39"},"schema_version":"1.0"},"canonical_sha256":"2df601ae3fb2bdb76e113c4368d65a898343d22ab0cf1395d2bb0f7dac87990b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:07.996928Z","signature_b64":"KAKX1gBoS/NmyLyR0xLakjtt7O129U9trgjkrV5VtxPbjPMJWhWANpnlVom41JA0nh5Ywdgx5qL0xrDbiVkpAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2df601ae3fb2bdb76e113c4368d65a898343d22ab0cf1395d2bb0f7dac87990b","last_reissued_at":"2026-05-18T00:22:07.996354Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:07.996354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.00739","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":"2026-05-18T00:22:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Bc5MpBIYc56d98oIja77TRyao2bgogF7Zn/o+2tEFuiih9d9EL5zRNyzxV697/Q/4OAWs/tVw6R4G7w4l+wCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:03:18.460537Z"},"content_sha256":"c0ea0df43982c1c03cef65ac408de45ae1a51b1b3a7fcf8c3d89d4d1f34d1d7d","schema_version":"1.0","event_id":"sha256:c0ea0df43982c1c03cef65ac408de45ae1a51b1b3a7fcf8c3d89d4d1f34d1d7d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FX3ADLR7WK63O3QRHRBWRVS2RG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Markov Switch Smooth Transition HYGARCH Model: Stability and Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Ferdous Mohammadi Basatini, Saeid Rezakhah","submitted_at":"2018-03-02T07:22:33Z","abstract_excerpt":"HYGARCH model is basically used to model long-range dependence in volatility. We propose Markov switch smooth-transition HYGARCH model, where the volatility in each state is a time-dependent convex combination of GARCH and FIGARCH. This model provides a flexible structure to capture different levels of volatilities and also short and long memory effects. The necessary and sufficient condition for the asymptotic stability is derived. Forecast of conditional variance is studied by using all past information through a parsimonious way. Bayesian estimations based on Gibbs sampling are provided. A "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00739","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":"2026-05-18T00:22:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q4hlCDGa23MSK4wCEjQpzFcz8bPlQCdHNKu/jCwGbkKDkzHwxVfxo0g8mcgGwAYqTGNTgsZsbwPhbM5RwnJBDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:03:18.460882Z"},"content_sha256":"1a5bfcca7536a18a8187b1640f90c46d4bb90a181ba0a450bacf28ec72c81425","schema_version":"1.0","event_id":"sha256:1a5bfcca7536a18a8187b1640f90c46d4bb90a181ba0a450bacf28ec72c81425"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FX3ADLR7WK63O3QRHRBWRVS2RG/bundle.json","state_url":"https://pith.science/pith/FX3ADLR7WK63O3QRHRBWRVS2RG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FX3ADLR7WK63O3QRHRBWRVS2RG/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":"2026-06-24T22:03:18Z","links":{"resolver":"https://pith.science/pith/FX3ADLR7WK63O3QRHRBWRVS2RG","bundle":"https://pith.science/pith/FX3ADLR7WK63O3QRHRBWRVS2RG/bundle.json","state":"https://pith.science/pith/FX3ADLR7WK63O3QRHRBWRVS2RG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FX3ADLR7WK63O3QRHRBWRVS2RG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FX3ADLR7WK63O3QRHRBWRVS2RG","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":"fd5aa01b565dd8405981f23fea1580c659d1c2f7d4b80daf73429e78d125af39","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-03-02T07:22:33Z","title_canon_sha256":"a50d82fb7dc74612b5e9bbb9b83ff5e2810eff89cf58f54fd798803344cf8967"},"schema_version":"1.0","source":{"id":"1803.00739","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00739","created_at":"2026-05-18T00:22:07Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00739v1","created_at":"2026-05-18T00:22:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00739","created_at":"2026-05-18T00:22:07Z"},{"alias_kind":"pith_short_12","alias_value":"FX3ADLR7WK63","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FX3ADLR7WK63O3QR","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FX3ADLR7","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:1a5bfcca7536a18a8187b1640f90c46d4bb90a181ba0a450bacf28ec72c81425","target":"graph","created_at":"2026-05-18T00:22:07Z","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":"HYGARCH model is basically used to model long-range dependence in volatility. We propose Markov switch smooth-transition HYGARCH model, where the volatility in each state is a time-dependent convex combination of GARCH and FIGARCH. This model provides a flexible structure to capture different levels of volatilities and also short and long memory effects. The necessary and sufficient condition for the asymptotic stability is derived. Forecast of conditional variance is studied by using all past information through a parsimonious way. Bayesian estimations based on Gibbs sampling are provided. A ","authors_text":"Ferdous Mohammadi Basatini, Saeid Rezakhah","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-03-02T07:22:33Z","title":"Markov Switch Smooth Transition HYGARCH Model: Stability and Estimation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00739","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:c0ea0df43982c1c03cef65ac408de45ae1a51b1b3a7fcf8c3d89d4d1f34d1d7d","target":"record","created_at":"2026-05-18T00:22:07Z","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":"fd5aa01b565dd8405981f23fea1580c659d1c2f7d4b80daf73429e78d125af39","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-03-02T07:22:33Z","title_canon_sha256":"a50d82fb7dc74612b5e9bbb9b83ff5e2810eff89cf58f54fd798803344cf8967"},"schema_version":"1.0","source":{"id":"1803.00739","kind":"arxiv","version":1}},"canonical_sha256":"2df601ae3fb2bdb76e113c4368d65a898343d22ab0cf1395d2bb0f7dac87990b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2df601ae3fb2bdb76e113c4368d65a898343d22ab0cf1395d2bb0f7dac87990b","first_computed_at":"2026-05-18T00:22:07.996354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:07.996354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KAKX1gBoS/NmyLyR0xLakjtt7O129U9trgjkrV5VtxPbjPMJWhWANpnlVom41JA0nh5Ywdgx5qL0xrDbiVkpAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:07.996928Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.00739","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0ea0df43982c1c03cef65ac408de45ae1a51b1b3a7fcf8c3d89d4d1f34d1d7d","sha256:1a5bfcca7536a18a8187b1640f90c46d4bb90a181ba0a450bacf28ec72c81425"],"state_sha256":"f3ccd4be2408d4ab32e20412d4739dc172683519cb410362a9cefd0aa4dea82e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r/q9ZKhMPkdaW2PJ94pfVLlxLMDnr2ociwBNG2lT5Y0V0wzlA6poFXHHUFaMBr2FhWVtWuO9IqhCScAVA/oeAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:03:18.462987Z","bundle_sha256":"2a8157b01d292fcb1d979d6ab5df6007c6cd46ec033d213825fcb5ab4a831f8f"}}