{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:5FFJIONMB4GLWQYLI7VNUPY67C","short_pith_number":"pith:5FFJIONM","schema_version":"1.0","canonical_sha256":"e94a9439ac0f0cbb430b47eada3f1ef8a8da78a77228ade9fb9d5863af907cda","source":{"kind":"arxiv","id":"1303.3482","version":1},"attestation_state":"computed","paper":{"title":"Measuring stationarity in long-memory processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Holger Dette, Kemal Sen, Philip Preuss","submitted_at":"2013-03-14T15:45:15Z","abstract_excerpt":"In this paper we consider the problem of measuring stationarity in locally stationary long-memory processes. We introduce an $L_2$-distance between the spectral density of the locally stationary process and its best approximation under the assumption of stationarity. The distance is estimated by a numerical approximation of the integrated spectral periodogram and asymptotic normality of the resulting estimate is established. The results can be used to construct a simple test for the hypothesis of stationarity in locally stationary long-range dependent processes. We also propose a bootstrap pro"},"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":"1303.3482","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-03-14T15:45:15Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"d2a3f647acb9416e289c07a625749bd3da67e2362338a5b746235966db56c0dc","abstract_canon_sha256":"7f3bd897d15d78bc5b68b908e23d7d349b28add238e88af596d87f1bed9b861c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:54.479587Z","signature_b64":"1PJo2Qr7qXau7WfD/82Xq/gAe6O2nvBNlCOwNoyVuFQSXRvcU6pW/8bIdN3Z9GquzOxweAY175L9VEEOiFEfAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e94a9439ac0f0cbb430b47eada3f1ef8a8da78a77228ade9fb9d5863af907cda","last_reissued_at":"2026-05-18T03:30:54.478924Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:54.478924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Measuring stationarity in long-memory processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Holger Dette, Kemal Sen, Philip Preuss","submitted_at":"2013-03-14T15:45:15Z","abstract_excerpt":"In this paper we consider the problem of measuring stationarity in locally stationary long-memory processes. We introduce an $L_2$-distance between the spectral density of the locally stationary process and its best approximation under the assumption of stationarity. The distance is estimated by a numerical approximation of the integrated spectral periodogram and asymptotic normality of the resulting estimate is established. The results can be used to construct a simple test for the hypothesis of stationarity in locally stationary long-range dependent processes. We also propose a bootstrap pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3482","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":"1303.3482","created_at":"2026-05-18T03:30:54.479010+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.3482v1","created_at":"2026-05-18T03:30:54.479010+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3482","created_at":"2026-05-18T03:30:54.479010+00:00"},{"alias_kind":"pith_short_12","alias_value":"5FFJIONMB4GL","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"5FFJIONMB4GLWQYL","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"5FFJIONM","created_at":"2026-05-18T12:27:34.582898+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/5FFJIONMB4GLWQYLI7VNUPY67C","json":"https://pith.science/pith/5FFJIONMB4GLWQYLI7VNUPY67C.json","graph_json":"https://pith.science/api/pith-number/5FFJIONMB4GLWQYLI7VNUPY67C/graph.json","events_json":"https://pith.science/api/pith-number/5FFJIONMB4GLWQYLI7VNUPY67C/events.json","paper":"https://pith.science/paper/5FFJIONM"},"agent_actions":{"view_html":"https://pith.science/pith/5FFJIONMB4GLWQYLI7VNUPY67C","download_json":"https://pith.science/pith/5FFJIONMB4GLWQYLI7VNUPY67C.json","view_paper":"https://pith.science/paper/5FFJIONM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.3482&json=true","fetch_graph":"https://pith.science/api/pith-number/5FFJIONMB4GLWQYLI7VNUPY67C/graph.json","fetch_events":"https://pith.science/api/pith-number/5FFJIONMB4GLWQYLI7VNUPY67C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5FFJIONMB4GLWQYLI7VNUPY67C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5FFJIONMB4GLWQYLI7VNUPY67C/action/storage_attestation","attest_author":"https://pith.science/pith/5FFJIONMB4GLWQYLI7VNUPY67C/action/author_attestation","sign_citation":"https://pith.science/pith/5FFJIONMB4GLWQYLI7VNUPY67C/action/citation_signature","submit_replication":"https://pith.science/pith/5FFJIONMB4GLWQYLI7VNUPY67C/action/replication_record"}},"created_at":"2026-05-18T03:30:54.479010+00:00","updated_at":"2026-05-18T03:30:54.479010+00:00"}