{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NILZ3OYTTBEBPSXDOMDZMHLSQD","short_pith_number":"pith:NILZ3OYT","canonical_record":{"source":{"id":"1107.2802","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-07-14T12:38:04Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"9c96ae5aff291111dac86130eceb904213af0b0b39d66b97e26528e3db06543a","abstract_canon_sha256":"a02af605237f1dac8045c5636041da64fe983b983625ee8e79f43a3d298d9af6"},"schema_version":"1.0"},"canonical_sha256":"6a179dbb13984817cae37307961d7280eee8e7d2473e173d6d35d383057142af","source":{"kind":"arxiv","id":"1107.2802","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2802","created_at":"2026-05-18T04:18:15Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2802v1","created_at":"2026-05-18T04:18:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2802","created_at":"2026-05-18T04:18:15Z"},{"alias_kind":"pith_short_12","alias_value":"NILZ3OYTTBEB","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NILZ3OYTTBEBPSXD","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NILZ3OYT","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NILZ3OYTTBEBPSXDOMDZMHLSQD","target":"record","payload":{"canonical_record":{"source":{"id":"1107.2802","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-07-14T12:38:04Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"9c96ae5aff291111dac86130eceb904213af0b0b39d66b97e26528e3db06543a","abstract_canon_sha256":"a02af605237f1dac8045c5636041da64fe983b983625ee8e79f43a3d298d9af6"},"schema_version":"1.0"},"canonical_sha256":"6a179dbb13984817cae37307961d7280eee8e7d2473e173d6d35d383057142af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:15.665102Z","signature_b64":"ifa/vYOO4F0M70zj2JDrmzgP1z1oM+k7Ot7Wxnx735u0uBdZbdrhQYPW3hqAduuSFcaBfQL6PReb8/18/1pfBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a179dbb13984817cae37307961d7280eee8e7d2473e173d6d35d383057142af","last_reissued_at":"2026-05-18T04:18:15.664680Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:15.664680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.2802","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":"2026-05-18T04:18:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ET+NUe4fdNDMajBuw+B9RygteDZEb0RMTJj2h6NItWs1sSpD+xxNrxU5userfxNoUBKIUYoQVLEsMyPGSeQYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:44:14.221785Z"},"content_sha256":"431aa7579837c79b5201e90fb9e5696090e0de3f6a35570681a61e89fccaacc9","schema_version":"1.0","event_id":"sha256:431aa7579837c79b5201e90fb9e5696090e0de3f6a35570681a61e89fccaacc9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NILZ3OYTTBEBPSXDOMDZMHLSQD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On non-stationary threshold autoregressive models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Qi-Man Shao, Shiqing Ling, Weidong Liu","submitted_at":"2011-07-14T12:38:04Z","abstract_excerpt":"In this paper we study the limiting distributions of the least-squares estimators for the non-stationary first-order threshold autoregressive (TAR(1)) model. It is proved that the limiting behaviors of the TAR(1) process are very different from those of the classical unit root model and the explosive AR(1)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2802","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":"2026-05-18T04:18:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uv8Wy5xDUl55LcwgA4I4/ojW16E7VtVtXiMs0+X04TV1qyQ9D7Lr+pYNEhglyV40Q4UClUHag82u/wT3gAE2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:44:14.222496Z"},"content_sha256":"07778770823dac5632a8f4c6546c581053c33e2a20424c6c99a095ef0c6264b2","schema_version":"1.0","event_id":"sha256:07778770823dac5632a8f4c6546c581053c33e2a20424c6c99a095ef0c6264b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NILZ3OYTTBEBPSXDOMDZMHLSQD/bundle.json","state_url":"https://pith.science/pith/NILZ3OYTTBEBPSXDOMDZMHLSQD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NILZ3OYTTBEBPSXDOMDZMHLSQD/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":"2026-05-26T22:44:14Z","links":{"resolver":"https://pith.science/pith/NILZ3OYTTBEBPSXDOMDZMHLSQD","bundle":"https://pith.science/pith/NILZ3OYTTBEBPSXDOMDZMHLSQD/bundle.json","state":"https://pith.science/pith/NILZ3OYTTBEBPSXDOMDZMHLSQD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NILZ3OYTTBEBPSXDOMDZMHLSQD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NILZ3OYTTBEBPSXDOMDZMHLSQD","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":"a02af605237f1dac8045c5636041da64fe983b983625ee8e79f43a3d298d9af6","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-07-14T12:38:04Z","title_canon_sha256":"9c96ae5aff291111dac86130eceb904213af0b0b39d66b97e26528e3db06543a"},"schema_version":"1.0","source":{"id":"1107.2802","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2802","created_at":"2026-05-18T04:18:15Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2802v1","created_at":"2026-05-18T04:18:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2802","created_at":"2026-05-18T04:18:15Z"},{"alias_kind":"pith_short_12","alias_value":"NILZ3OYTTBEB","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NILZ3OYTTBEBPSXD","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NILZ3OYT","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:07778770823dac5632a8f4c6546c581053c33e2a20424c6c99a095ef0c6264b2","target":"graph","created_at":"2026-05-18T04:18:15Z","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 study the limiting distributions of the least-squares estimators for the non-stationary first-order threshold autoregressive (TAR(1)) model. It is proved that the limiting behaviors of the TAR(1) process are very different from those of the classical unit root model and the explosive AR(1).","authors_text":"Qi-Man Shao, Shiqing Ling, Weidong Liu","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-07-14T12:38:04Z","title":"On non-stationary threshold autoregressive models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2802","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":"sha256:431aa7579837c79b5201e90fb9e5696090e0de3f6a35570681a61e89fccaacc9","target":"record","created_at":"2026-05-18T04:18:15Z","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":"a02af605237f1dac8045c5636041da64fe983b983625ee8e79f43a3d298d9af6","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-07-14T12:38:04Z","title_canon_sha256":"9c96ae5aff291111dac86130eceb904213af0b0b39d66b97e26528e3db06543a"},"schema_version":"1.0","source":{"id":"1107.2802","kind":"arxiv","version":1}},"canonical_sha256":"6a179dbb13984817cae37307961d7280eee8e7d2473e173d6d35d383057142af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a179dbb13984817cae37307961d7280eee8e7d2473e173d6d35d383057142af","first_computed_at":"2026-05-18T04:18:15.664680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:15.664680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ifa/vYOO4F0M70zj2JDrmzgP1z1oM+k7Ot7Wxnx735u0uBdZbdrhQYPW3hqAduuSFcaBfQL6PReb8/18/1pfBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:15.665102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.2802","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:431aa7579837c79b5201e90fb9e5696090e0de3f6a35570681a61e89fccaacc9","sha256:07778770823dac5632a8f4c6546c581053c33e2a20424c6c99a095ef0c6264b2"],"state_sha256":"e6b020522ef257c80af3cae5f98e743270d3c6f391d2b92201d1fc6c825f71e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6mUnXeIfaNpLARXko0KzjC5V9GnBIoL2WfOK0XQoXj2qe/F9a8GCJ5aX11QdUdgN1inEjw7QQ2EKvaUnRtKRCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:44:14.226232Z","bundle_sha256":"9858188b3f57d51cc745fc8a5be03cf2058c678f086c41cc73159c4b1ef7d181"}}