{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:UCSS4BDOVRKECXCNCQJT2FEELW","short_pith_number":"pith:UCSS4BDO","schema_version":"1.0","canonical_sha256":"a0a52e046eac54415c4d14133d14845d9ae4b33071cfdeac02feb8c4e1cf55bb","source":{"kind":"arxiv","id":"1709.06115","version":1},"attestation_state":"computed","paper":{"title":"An approximate fractional Gaussian noise model with ${\\mathcal O}(n)$ computational cost","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Eirik Myrvoll-Nilsen, H{\\aa}vard Rue, Sigrunn H. S{\\o}rbye","submitted_at":"2017-09-18T18:27:15Z","abstract_excerpt":"Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a likelihood-based approach is ${\\mathcal O}(n^{2})$, exploiting the Toeplitz structure of the covariance matrix. In most realistic cases, we do not observe the fGn process directly but only through indirect Gaussian observations, so the Toeplitz structure is easily lost and the computational cost increases to ${\\mathcal O}(n^{3})$. This paper presents an approxima"},"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":"1709.06115","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-09-18T18:27:15Z","cross_cats_sorted":[],"title_canon_sha256":"edb5fdee19508aa95b97e3a33c207aca8372c778a24e523939b177c3de2b73c7","abstract_canon_sha256":"6f899e8c8ec428a8d723d2cf9a24007fafda87bbbc68e83cdd1dbaff427b88cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:54.384619Z","signature_b64":"EnZh9wspZYHDiFy2xr1OhMtgOb0a4VVr+1CbGjp9qHr+A7vnpFx2ArDqbFQvBpjzu3/tO+VO6UkhPc4vAijWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0a52e046eac54415c4d14133d14845d9ae4b33071cfdeac02feb8c4e1cf55bb","last_reissued_at":"2026-05-18T00:34:54.383846Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:54.383846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An approximate fractional Gaussian noise model with ${\\mathcal O}(n)$ computational cost","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Eirik Myrvoll-Nilsen, H{\\aa}vard Rue, Sigrunn H. S{\\o}rbye","submitted_at":"2017-09-18T18:27:15Z","abstract_excerpt":"Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a likelihood-based approach is ${\\mathcal O}(n^{2})$, exploiting the Toeplitz structure of the covariance matrix. In most realistic cases, we do not observe the fGn process directly but only through indirect Gaussian observations, so the Toeplitz structure is easily lost and the computational cost increases to ${\\mathcal O}(n^{3})$. This paper presents an approxima"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06115","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1709.06115","created_at":"2026-05-18T00:34:54.383982+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.06115v1","created_at":"2026-05-18T00:34:54.383982+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06115","created_at":"2026-05-18T00:34:54.383982+00:00"},{"alias_kind":"pith_short_12","alias_value":"UCSS4BDOVRKE","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"UCSS4BDOVRKECXCN","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"UCSS4BDO","created_at":"2026-05-18T12:31:46.661854+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/UCSS4BDOVRKECXCNCQJT2FEELW","json":"https://pith.science/pith/UCSS4BDOVRKECXCNCQJT2FEELW.json","graph_json":"https://pith.science/api/pith-number/UCSS4BDOVRKECXCNCQJT2FEELW/graph.json","events_json":"https://pith.science/api/pith-number/UCSS4BDOVRKECXCNCQJT2FEELW/events.json","paper":"https://pith.science/paper/UCSS4BDO"},"agent_actions":{"view_html":"https://pith.science/pith/UCSS4BDOVRKECXCNCQJT2FEELW","download_json":"https://pith.science/pith/UCSS4BDOVRKECXCNCQJT2FEELW.json","view_paper":"https://pith.science/paper/UCSS4BDO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.06115&json=true","fetch_graph":"https://pith.science/api/pith-number/UCSS4BDOVRKECXCNCQJT2FEELW/graph.json","fetch_events":"https://pith.science/api/pith-number/UCSS4BDOVRKECXCNCQJT2FEELW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UCSS4BDOVRKECXCNCQJT2FEELW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UCSS4BDOVRKECXCNCQJT2FEELW/action/storage_attestation","attest_author":"https://pith.science/pith/UCSS4BDOVRKECXCNCQJT2FEELW/action/author_attestation","sign_citation":"https://pith.science/pith/UCSS4BDOVRKECXCNCQJT2FEELW/action/citation_signature","submit_replication":"https://pith.science/pith/UCSS4BDOVRKECXCNCQJT2FEELW/action/replication_record"}},"created_at":"2026-05-18T00:34:54.383982+00:00","updated_at":"2026-05-18T00:34:54.383982+00:00"}