{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EXBEDPHPDCSSQPXNJG3OM6YUZ5","short_pith_number":"pith:EXBEDPHP","canonical_record":{"source":{"id":"1812.03475","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2018-12-09T12:51:14Z","cross_cats_sorted":[],"title_canon_sha256":"81065f45651de7a015e7c77e73f993aded651d773727f64d1a518dac0824d1ec","abstract_canon_sha256":"517dc4439ac7d8419a11110e535b35ed64cd372a7e6bfd3ce6bf385f7594eeb0"},"schema_version":"1.0"},"canonical_sha256":"25c241bcef18a5283eed49b6e67b14cf55b20bdd674cd3f576a3e7ddf6f12dfa","source":{"kind":"arxiv","id":"1812.03475","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.03475","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"arxiv_version","alias_value":"1812.03475v1","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03475","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"pith_short_12","alias_value":"EXBEDPHPDCSS","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EXBEDPHPDCSSQPXN","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EXBEDPHP","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EXBEDPHPDCSSQPXNJG3OM6YUZ5","target":"record","payload":{"canonical_record":{"source":{"id":"1812.03475","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2018-12-09T12:51:14Z","cross_cats_sorted":[],"title_canon_sha256":"81065f45651de7a015e7c77e73f993aded651d773727f64d1a518dac0824d1ec","abstract_canon_sha256":"517dc4439ac7d8419a11110e535b35ed64cd372a7e6bfd3ce6bf385f7594eeb0"},"schema_version":"1.0"},"canonical_sha256":"25c241bcef18a5283eed49b6e67b14cf55b20bdd674cd3f576a3e7ddf6f12dfa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:46.181514Z","signature_b64":"vnixceqEUX6ytQ4Pir5r1xIanI1HcBTYk2mruKgt1DO7vT3L9D1qpI6+Poc07K5vaPKUHE5IUmmkpoBceHNSDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25c241bcef18a5283eed49b6e67b14cf55b20bdd674cd3f576a3e7ddf6f12dfa","last_reissued_at":"2026-05-17T23:58:46.181002Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:46.181002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.03475","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":"2026-05-17T23:58:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zSys+dq/gkbPpYgTXAiQDylMP1WFauCHMBn4ShNokTjQWf6YfC125rGLhwALEOGHTjWvCpg1ccub3HWxpKNUAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:33:37.729029Z"},"content_sha256":"5a873a55725e6e4908fbd662079d370555b7e553904ef8c06c034c073de6126b","schema_version":"1.0","event_id":"sha256:5a873a55725e6e4908fbd662079d370555b7e553904ef8c06c034c073de6126b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EXBEDPHPDCSSQPXNJG3OM6YUZ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A supreme test for periodic explosive GARCH","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"econ.EM","authors_text":"Stefan Richter, Wei Biao Wu, Weining Wang","submitted_at":"2018-12-09T12:51:14Z","abstract_excerpt":"We develop a uniform test for detecting and dating explosive behavior of a strictly stationary GARCH$(r,s)$ (generalized autoregressive conditional heteroskedasticity) process. Namely, we test the null hypothesis of a globally stable GARCH process with constant parameters against an alternative where there is an 'abnormal' period with changed parameter values. During this period, the change may lead to an explosive behavior of the volatility process. It is assumed that both the magnitude and the timing of the breaks are unknown. We develop a double supreme test for the existence of a break, an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03475","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":"2026-05-17T23:58:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GtfNeITiVMDP0aRKOs83+khG9fDfpU8nvOlswk4Ra/2tPsM19N8Eo7RmFvN9KjuHDtCdelPmVZpj8K5qXq+vAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:33:37.729702Z"},"content_sha256":"0cca056bc5f3281c724493dd6ad51a95c510cae4cde9694c3310bed6998378cc","schema_version":"1.0","event_id":"sha256:0cca056bc5f3281c724493dd6ad51a95c510cae4cde9694c3310bed6998378cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EXBEDPHPDCSSQPXNJG3OM6YUZ5/bundle.json","state_url":"https://pith.science/pith/EXBEDPHPDCSSQPXNJG3OM6YUZ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EXBEDPHPDCSSQPXNJG3OM6YUZ5/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":"2026-05-26T21:33:37Z","links":{"resolver":"https://pith.science/pith/EXBEDPHPDCSSQPXNJG3OM6YUZ5","bundle":"https://pith.science/pith/EXBEDPHPDCSSQPXNJG3OM6YUZ5/bundle.json","state":"https://pith.science/pith/EXBEDPHPDCSSQPXNJG3OM6YUZ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EXBEDPHPDCSSQPXNJG3OM6YUZ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EXBEDPHPDCSSQPXNJG3OM6YUZ5","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":"517dc4439ac7d8419a11110e535b35ed64cd372a7e6bfd3ce6bf385f7594eeb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2018-12-09T12:51:14Z","title_canon_sha256":"81065f45651de7a015e7c77e73f993aded651d773727f64d1a518dac0824d1ec"},"schema_version":"1.0","source":{"id":"1812.03475","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.03475","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"arxiv_version","alias_value":"1812.03475v1","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03475","created_at":"2026-05-17T23:58:46Z"},{"alias_kind":"pith_short_12","alias_value":"EXBEDPHPDCSS","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EXBEDPHPDCSSQPXN","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EXBEDPHP","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:0cca056bc5f3281c724493dd6ad51a95c510cae4cde9694c3310bed6998378cc","target":"graph","created_at":"2026-05-17T23:58:46Z","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":"We develop a uniform test for detecting and dating explosive behavior of a strictly stationary GARCH$(r,s)$ (generalized autoregressive conditional heteroskedasticity) process. Namely, we test the null hypothesis of a globally stable GARCH process with constant parameters against an alternative where there is an 'abnormal' period with changed parameter values. During this period, the change may lead to an explosive behavior of the volatility process. It is assumed that both the magnitude and the timing of the breaks are unknown. We develop a double supreme test for the existence of a break, an","authors_text":"Stefan Richter, Wei Biao Wu, Weining Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2018-12-09T12:51:14Z","title":"A supreme test for periodic explosive GARCH"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03475","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":"sha256:5a873a55725e6e4908fbd662079d370555b7e553904ef8c06c034c073de6126b","target":"record","created_at":"2026-05-17T23:58:46Z","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":"517dc4439ac7d8419a11110e535b35ed64cd372a7e6bfd3ce6bf385f7594eeb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2018-12-09T12:51:14Z","title_canon_sha256":"81065f45651de7a015e7c77e73f993aded651d773727f64d1a518dac0824d1ec"},"schema_version":"1.0","source":{"id":"1812.03475","kind":"arxiv","version":1}},"canonical_sha256":"25c241bcef18a5283eed49b6e67b14cf55b20bdd674cd3f576a3e7ddf6f12dfa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25c241bcef18a5283eed49b6e67b14cf55b20bdd674cd3f576a3e7ddf6f12dfa","first_computed_at":"2026-05-17T23:58:46.181002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:46.181002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vnixceqEUX6ytQ4Pir5r1xIanI1HcBTYk2mruKgt1DO7vT3L9D1qpI6+Poc07K5vaPKUHE5IUmmkpoBceHNSDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:46.181514Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.03475","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a873a55725e6e4908fbd662079d370555b7e553904ef8c06c034c073de6126b","sha256:0cca056bc5f3281c724493dd6ad51a95c510cae4cde9694c3310bed6998378cc"],"state_sha256":"c4c03ba99226a9a7f80130bb66a2df7019a838e4c3d2b7045468a7f117e0b190"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DEifYQHEwuT2t+uW/IVZ6EuJDdil/JoPE6XQz5LdFDnNlZf83ZXHZlUyjRRJfHA7UETZK7NS2WBiSqMahAgiDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:33:37.733613Z","bundle_sha256":"aa5540b48143b8d98489aadf4d0c7d099be95bbcc9e933bd1750b76e94dde277"}}