{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5FFJIONMB4GLWQYLI7VNUPY67C","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":"7f3bd897d15d78bc5b68b908e23d7d349b28add238e88af596d87f1bed9b861c","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-03-14T15:45:15Z","title_canon_sha256":"d2a3f647acb9416e289c07a625749bd3da67e2362338a5b746235966db56c0dc"},"schema_version":"1.0","source":{"id":"1303.3482","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3482","created_at":"2026-05-18T03:30:54Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3482v1","created_at":"2026-05-18T03:30:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3482","created_at":"2026-05-18T03:30:54Z"},{"alias_kind":"pith_short_12","alias_value":"5FFJIONMB4GL","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5FFJIONMB4GLWQYL","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5FFJIONM","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:110c80c8e319243a306d585d37919793a33fd509b4873e8681c46f104cca8935","target":"graph","created_at":"2026-05-18T03:30:54Z","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 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","authors_text":"Holger Dette, Kemal Sen, Philip Preuss","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-03-14T15:45:15Z","title":"Measuring stationarity in long-memory processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3482","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:d08f6b5f030b31478c86d7394dbe747fc392bb7bf71a65fdae5edc97cf5488ce","target":"record","created_at":"2026-05-18T03:30:54Z","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":"7f3bd897d15d78bc5b68b908e23d7d349b28add238e88af596d87f1bed9b861c","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-03-14T15:45:15Z","title_canon_sha256":"d2a3f647acb9416e289c07a625749bd3da67e2362338a5b746235966db56c0dc"},"schema_version":"1.0","source":{"id":"1303.3482","kind":"arxiv","version":1}},"canonical_sha256":"e94a9439ac0f0cbb430b47eada3f1ef8a8da78a77228ade9fb9d5863af907cda","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e94a9439ac0f0cbb430b47eada3f1ef8a8da78a77228ade9fb9d5863af907cda","first_computed_at":"2026-05-18T03:30:54.478924Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:54.478924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1PJo2Qr7qXau7WfD/82Xq/gAe6O2nvBNlCOwNoyVuFQSXRvcU6pW/8bIdN3Z9GquzOxweAY175L9VEEOiFEfAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:54.479587Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.3482","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d08f6b5f030b31478c86d7394dbe747fc392bb7bf71a65fdae5edc97cf5488ce","sha256:110c80c8e319243a306d585d37919793a33fd509b4873e8681c46f104cca8935"],"state_sha256":"4158eff6c28ac9abee259a3b225405ff80a43f11dca2a882bd0ae2f3cf03f83f"}