{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EZJYJKGEZWQK2KHCKC56YT3I2H","short_pith_number":"pith:EZJYJKGE","canonical_record":{"source":{"id":"1603.05416","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-17T10:27:45Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"ac393ce084178e8097e2016bb489da78bdd8a4ba8c0d5fb51b6722234a6c1481","abstract_canon_sha256":"aaeb8b350a85895bb98a5bb13b5c7bcd3016ccb399b77f39d372227938e61c10"},"schema_version":"1.0"},"canonical_sha256":"265384a8c4cda0ad28e250bbec4f68d1cd17f3d5895dafd12a19b70a77727934","source":{"kind":"arxiv","id":"1603.05416","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05416","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05416v1","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05416","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"EZJYJKGEZWQK","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"EZJYJKGEZWQK2KHC","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"EZJYJKGE","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EZJYJKGEZWQK2KHCKC56YT3I2H","target":"record","payload":{"canonical_record":{"source":{"id":"1603.05416","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-17T10:27:45Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"ac393ce084178e8097e2016bb489da78bdd8a4ba8c0d5fb51b6722234a6c1481","abstract_canon_sha256":"aaeb8b350a85895bb98a5bb13b5c7bcd3016ccb399b77f39d372227938e61c10"},"schema_version":"1.0"},"canonical_sha256":"265384a8c4cda0ad28e250bbec4f68d1cd17f3d5895dafd12a19b70a77727934","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:56.405088Z","signature_b64":"PsPGxoqyf6bP6usUGqsLkNYYV/8lBYCxcDs301EdmwDsx5J5uQq8oKCOo1x+gCvHV3e4fXmxrj+V+fskfAqjCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"265384a8c4cda0ad28e250bbec4f68d1cd17f3d5895dafd12a19b70a77727934","last_reissued_at":"2026-05-18T01:18:56.404638Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:56.404638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.05416","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":"2026-05-18T01:18:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1iorvI/u96llaLfqTvuARHoOglwnqD4I9AgjftSnDLCbJ6288UWfaZwhg0S4FOi1tGklCWrU0YlKAek84W7VBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T13:46:28.816927Z"},"content_sha256":"d0deb83c1cbfd6fecc038a6abf033aabacfe2209aba78413720a352f39193776","schema_version":"1.0","event_id":"sha256:d0deb83c1cbfd6fecc038a6abf033aabacfe2209aba78413720a352f39193776"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EZJYJKGEZWQK2KHCKC56YT3I2H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimation of inverse autocovariance matrices for long memory processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Ching-Kang Ing, Hai-Tang Chiou, Meihui Guo","submitted_at":"2016-03-17T10:27:45Z","abstract_excerpt":"This work aims at estimating inverse autocovariance matrices of long memory processes admitting a linear representation. A modified Cholesky decomposition is used in conjunction with an increasing order autoregressive model to achieve this goal. The spectral norm consistency of the proposed estimate is established. We then extend this result to linear regression models with long-memory time series errors. In particular, we show that when the objective is to consistently estimate the inverse autocovariance matrix of the error process, the same approach still works well if the estimated (by leas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05416","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":"2026-05-18T01:18:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CEN75ijOsl+/fsXbJBhHMkfVTy1GYgf6ZXIM1laqzjJpYwVIBkBJHt+NPV0N1AUabq6GehIFPLAFnOHvEdrRCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T13:46:28.817266Z"},"content_sha256":"2487dbfd8205718865a201e7ab6f5d949fe786e6ee75446dec581e4078e8009d","schema_version":"1.0","event_id":"sha256:2487dbfd8205718865a201e7ab6f5d949fe786e6ee75446dec581e4078e8009d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EZJYJKGEZWQK2KHCKC56YT3I2H/bundle.json","state_url":"https://pith.science/pith/EZJYJKGEZWQK2KHCKC56YT3I2H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EZJYJKGEZWQK2KHCKC56YT3I2H/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":"2026-06-30T13:46:28Z","links":{"resolver":"https://pith.science/pith/EZJYJKGEZWQK2KHCKC56YT3I2H","bundle":"https://pith.science/pith/EZJYJKGEZWQK2KHCKC56YT3I2H/bundle.json","state":"https://pith.science/pith/EZJYJKGEZWQK2KHCKC56YT3I2H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EZJYJKGEZWQK2KHCKC56YT3I2H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EZJYJKGEZWQK2KHCKC56YT3I2H","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":"aaeb8b350a85895bb98a5bb13b5c7bcd3016ccb399b77f39d372227938e61c10","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-17T10:27:45Z","title_canon_sha256":"ac393ce084178e8097e2016bb489da78bdd8a4ba8c0d5fb51b6722234a6c1481"},"schema_version":"1.0","source":{"id":"1603.05416","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05416","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05416v1","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05416","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"EZJYJKGEZWQK","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"EZJYJKGEZWQK2KHC","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"EZJYJKGE","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:2487dbfd8205718865a201e7ab6f5d949fe786e6ee75446dec581e4078e8009d","target":"graph","created_at":"2026-05-18T01:18:56Z","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":"This work aims at estimating inverse autocovariance matrices of long memory processes admitting a linear representation. A modified Cholesky decomposition is used in conjunction with an increasing order autoregressive model to achieve this goal. The spectral norm consistency of the proposed estimate is established. We then extend this result to linear regression models with long-memory time series errors. In particular, we show that when the objective is to consistently estimate the inverse autocovariance matrix of the error process, the same approach still works well if the estimated (by leas","authors_text":"Ching-Kang Ing, Hai-Tang Chiou, Meihui Guo","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-17T10:27:45Z","title":"Estimation of inverse autocovariance matrices for long memory processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05416","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:d0deb83c1cbfd6fecc038a6abf033aabacfe2209aba78413720a352f39193776","target":"record","created_at":"2026-05-18T01:18:56Z","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":"aaeb8b350a85895bb98a5bb13b5c7bcd3016ccb399b77f39d372227938e61c10","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-17T10:27:45Z","title_canon_sha256":"ac393ce084178e8097e2016bb489da78bdd8a4ba8c0d5fb51b6722234a6c1481"},"schema_version":"1.0","source":{"id":"1603.05416","kind":"arxiv","version":1}},"canonical_sha256":"265384a8c4cda0ad28e250bbec4f68d1cd17f3d5895dafd12a19b70a77727934","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"265384a8c4cda0ad28e250bbec4f68d1cd17f3d5895dafd12a19b70a77727934","first_computed_at":"2026-05-18T01:18:56.404638Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:56.404638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PsPGxoqyf6bP6usUGqsLkNYYV/8lBYCxcDs301EdmwDsx5J5uQq8oKCOo1x+gCvHV3e4fXmxrj+V+fskfAqjCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:56.405088Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05416","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0deb83c1cbfd6fecc038a6abf033aabacfe2209aba78413720a352f39193776","sha256:2487dbfd8205718865a201e7ab6f5d949fe786e6ee75446dec581e4078e8009d"],"state_sha256":"6090de0d5e8a639f0bb31a4e390f70258d9a0d44ced137e2b04915c28acc8992"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sEd0sFSu5dWou015a0Ee61v5Ff6glfZX3RRJgyqL7FVpgO+LfEyEHhwjTV9TseUicaMdX1oh7dOpJjCfEBk1Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T13:46:28.819165Z","bundle_sha256":"7a3b047287b327616742d45e85f5c66c7f08506900ec1c1a4dd7ddfb1aaef9ed"}}