{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:PS6NF5R2YM2773U2JL3NJW5SM2","short_pith_number":"pith:PS6NF5R2","schema_version":"1.0","canonical_sha256":"7cbcd2f63ac335ffee9a4af6d4dbb26689f4d9d16d6c685125bf0cca7c4436c5","source":{"kind":"arxiv","id":"1511.00734","version":2},"attestation_state":"computed","paper":{"title":"Modeling of Stationary Periodic Time Series by ARMA Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Anders Lindquist, Giorgio Picci","submitted_at":"2015-11-02T22:43:43Z","abstract_excerpt":"This is a survey of some recent results on the rational circulant covariance extension problem: Given a partial sequence $(c_0,c_1,\\dots,c_n)$ of covariance lags $c_k=\\mathbb{E}\\{y(t+k)\\overline{y(t)}\\}$ emanating from a stationary periodic process $\\{y(t)\\}$ with period $2N>2n$, find all possible rational spectral functions of $\\{y(t)\\}$ of degree at most $2n$ or, equivalently, all bilateral and unilateral ARMA models of order at most $n$, having this partial covariance sequence. Each representation is obtained as the solution of a pair of dual convex optimization problems. This theory is the"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1511.00734","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-11-02T22:43:43Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"fb535a02669ed2dbf47ff10c47f309af731c03775659cec789eca3d85a0912ce","abstract_canon_sha256":"6300c6729c4af1d26148ed89c37a9e54561584f3a736397215f0ab3b2f35b096"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:10.419845Z","signature_b64":"B3ckI3iGYcc+W66JEqLkrKnnHC36/7mpsMkw8RJQwuI8XE/bgmtx1reeAEUdvzPA48wtdP6bMFzoVI3BpzxwAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cbcd2f63ac335ffee9a4af6d4dbb26689f4d9d16d6c685125bf0cca7c4436c5","last_reissued_at":"2026-05-18T01:24:10.419451Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:10.419451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modeling of Stationary Periodic Time Series by ARMA Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Anders Lindquist, Giorgio Picci","submitted_at":"2015-11-02T22:43:43Z","abstract_excerpt":"This is a survey of some recent results on the rational circulant covariance extension problem: Given a partial sequence $(c_0,c_1,\\dots,c_n)$ of covariance lags $c_k=\\mathbb{E}\\{y(t+k)\\overline{y(t)}\\}$ emanating from a stationary periodic process $\\{y(t)\\}$ with period $2N>2n$, find all possible rational spectral functions of $\\{y(t)\\}$ of degree at most $2n$ or, equivalently, all bilateral and unilateral ARMA models of order at most $n$, having this partial covariance sequence. Each representation is obtained as the solution of a pair of dual convex optimization problems. This theory is the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00734","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1511.00734","created_at":"2026-05-18T01:24:10.419509+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.00734v2","created_at":"2026-05-18T01:24:10.419509+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00734","created_at":"2026-05-18T01:24:10.419509+00:00"},{"alias_kind":"pith_short_12","alias_value":"PS6NF5R2YM27","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"PS6NF5R2YM2773U2","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"PS6NF5R2","created_at":"2026-05-18T12:29:37.295048+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PS6NF5R2YM2773U2JL3NJW5SM2","json":"https://pith.science/pith/PS6NF5R2YM2773U2JL3NJW5SM2.json","graph_json":"https://pith.science/api/pith-number/PS6NF5R2YM2773U2JL3NJW5SM2/graph.json","events_json":"https://pith.science/api/pith-number/PS6NF5R2YM2773U2JL3NJW5SM2/events.json","paper":"https://pith.science/paper/PS6NF5R2"},"agent_actions":{"view_html":"https://pith.science/pith/PS6NF5R2YM2773U2JL3NJW5SM2","download_json":"https://pith.science/pith/PS6NF5R2YM2773U2JL3NJW5SM2.json","view_paper":"https://pith.science/paper/PS6NF5R2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.00734&json=true","fetch_graph":"https://pith.science/api/pith-number/PS6NF5R2YM2773U2JL3NJW5SM2/graph.json","fetch_events":"https://pith.science/api/pith-number/PS6NF5R2YM2773U2JL3NJW5SM2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PS6NF5R2YM2773U2JL3NJW5SM2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PS6NF5R2YM2773U2JL3NJW5SM2/action/storage_attestation","attest_author":"https://pith.science/pith/PS6NF5R2YM2773U2JL3NJW5SM2/action/author_attestation","sign_citation":"https://pith.science/pith/PS6NF5R2YM2773U2JL3NJW5SM2/action/citation_signature","submit_replication":"https://pith.science/pith/PS6NF5R2YM2773U2JL3NJW5SM2/action/replication_record"}},"created_at":"2026-05-18T01:24:10.419509+00:00","updated_at":"2026-05-18T01:24:10.419509+00:00"}