{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:BN5GZB7ZJA73WNJMOWUENZTXKQ","short_pith_number":"pith:BN5GZB7Z","canonical_record":{"source":{"id":"1102.2053","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-10T08:11:33Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"1b976316f9b42f00969d90eb79ffe0120b2c292627015558e021538ccb76a621","abstract_canon_sha256":"1f853aee7705c5c376e96c57e75cf30908cc8aee2e6850f9082d45af496c0d4f"},"schema_version":"1.0"},"canonical_sha256":"0b7a6c87f9483fbb352c75a846e677543b639664df9eed38ed101a8420eddd7f","source":{"kind":"arxiv","id":"1102.2053","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2053","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2053v1","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2053","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"pith_short_12","alias_value":"BN5GZB7ZJA73","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BN5GZB7ZJA73WNJM","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BN5GZB7Z","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:BN5GZB7ZJA73WNJMOWUENZTXKQ","target":"record","payload":{"canonical_record":{"source":{"id":"1102.2053","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-10T08:11:33Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"1b976316f9b42f00969d90eb79ffe0120b2c292627015558e021538ccb76a621","abstract_canon_sha256":"1f853aee7705c5c376e96c57e75cf30908cc8aee2e6850f9082d45af496c0d4f"},"schema_version":"1.0"},"canonical_sha256":"0b7a6c87f9483fbb352c75a846e677543b639664df9eed38ed101a8420eddd7f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:29:34.380088Z","signature_b64":"wkUXZlJKRWStwTSpqj0rLI9XszinLhiCt84eJDBJBpnPj6o4RVDyEHVFM/Y6wqjwWsgT3ztvMYJoYT/6FPz0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b7a6c87f9483fbb352c75a846e677543b639664df9eed38ed101a8420eddd7f","last_reissued_at":"2026-05-18T04:29:34.379651Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:29:34.379651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.2053","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":"2026-05-18T04:29:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x1qc+eqql4Izg4CVXLv93hdpawusNY0jEXJHAJhkiGXmCESuWGRiTi8tvzd7O+4wbTIk7Q/O52nH9DAeLvH6Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:05:11.938127Z"},"content_sha256":"53decd12c00e5ae9cb5d029a0cb50bb1aa7bd25770e1d74443b2edbe6c5a32cf","schema_version":"1.0","event_id":"sha256:53decd12c00e5ae9cb5d029a0cb50bb1aa7bd25770e1d74443b2edbe6c5a32cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:BN5GZB7ZJA73WNJMOWUENZTXKQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mixing properties of ARCH and time-varying ARCH processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Piotr Fryzlewicz, Suhasini Subba Rao","submitted_at":"2011-02-10T08:11:33Z","abstract_excerpt":"There exist very few results on mixing for non-stationary processes. However, mixing is often required in statistical inference for non-stationary processes such as time-varying ARCH (tvARCH) models. In this paper, bounds for the mixing rates of a stochastic process are derived in terms of the conditional densities of the process. These bounds are used to obtain the $\\alpha$, 2-mixing and $\\beta$-mixing rates of the non-stationary time-varying $\\operatorname {ARCH}(p)$ process and $\\operatorname {ARCH}(\\infty)$ process. It is shown that the mixing rate of the time-varying $\\operatorname {ARCH}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2053","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":"2026-05-18T04:29:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WJpogGp5n5rsl9KnlVaRKp0FJ8dqcOBlBl1vKJIlvV73v9xEUjXTzXJSsoJUwusbmibZZBUtD04/Qxeg2W31Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:05:11.938729Z"},"content_sha256":"d41db6bf23fe5d8046cb1ab0c47c45397a4209691986179da39fe737055d89a6","schema_version":"1.0","event_id":"sha256:d41db6bf23fe5d8046cb1ab0c47c45397a4209691986179da39fe737055d89a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BN5GZB7ZJA73WNJMOWUENZTXKQ/bundle.json","state_url":"https://pith.science/pith/BN5GZB7ZJA73WNJMOWUENZTXKQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BN5GZB7ZJA73WNJMOWUENZTXKQ/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":"2026-05-26T04:05:11Z","links":{"resolver":"https://pith.science/pith/BN5GZB7ZJA73WNJMOWUENZTXKQ","bundle":"https://pith.science/pith/BN5GZB7ZJA73WNJMOWUENZTXKQ/bundle.json","state":"https://pith.science/pith/BN5GZB7ZJA73WNJMOWUENZTXKQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BN5GZB7ZJA73WNJMOWUENZTXKQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BN5GZB7ZJA73WNJMOWUENZTXKQ","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":"1f853aee7705c5c376e96c57e75cf30908cc8aee2e6850f9082d45af496c0d4f","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-10T08:11:33Z","title_canon_sha256":"1b976316f9b42f00969d90eb79ffe0120b2c292627015558e021538ccb76a621"},"schema_version":"1.0","source":{"id":"1102.2053","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2053","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2053v1","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2053","created_at":"2026-05-18T04:29:34Z"},{"alias_kind":"pith_short_12","alias_value":"BN5GZB7ZJA73","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BN5GZB7ZJA73WNJM","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BN5GZB7Z","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:d41db6bf23fe5d8046cb1ab0c47c45397a4209691986179da39fe737055d89a6","target":"graph","created_at":"2026-05-18T04:29:34Z","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":"There exist very few results on mixing for non-stationary processes. However, mixing is often required in statistical inference for non-stationary processes such as time-varying ARCH (tvARCH) models. In this paper, bounds for the mixing rates of a stochastic process are derived in terms of the conditional densities of the process. These bounds are used to obtain the $\\alpha$, 2-mixing and $\\beta$-mixing rates of the non-stationary time-varying $\\operatorname {ARCH}(p)$ process and $\\operatorname {ARCH}(\\infty)$ process. It is shown that the mixing rate of the time-varying $\\operatorname {ARCH}","authors_text":"Piotr Fryzlewicz, Suhasini Subba Rao","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-10T08:11:33Z","title":"Mixing properties of ARCH and time-varying ARCH processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2053","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":"sha256:53decd12c00e5ae9cb5d029a0cb50bb1aa7bd25770e1d74443b2edbe6c5a32cf","target":"record","created_at":"2026-05-18T04:29:34Z","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":"1f853aee7705c5c376e96c57e75cf30908cc8aee2e6850f9082d45af496c0d4f","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-10T08:11:33Z","title_canon_sha256":"1b976316f9b42f00969d90eb79ffe0120b2c292627015558e021538ccb76a621"},"schema_version":"1.0","source":{"id":"1102.2053","kind":"arxiv","version":1}},"canonical_sha256":"0b7a6c87f9483fbb352c75a846e677543b639664df9eed38ed101a8420eddd7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b7a6c87f9483fbb352c75a846e677543b639664df9eed38ed101a8420eddd7f","first_computed_at":"2026-05-18T04:29:34.379651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:29:34.379651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wkUXZlJKRWStwTSpqj0rLI9XszinLhiCt84eJDBJBpnPj6o4RVDyEHVFM/Y6wqjwWsgT3ztvMYJoYT/6FPz0Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:29:34.380088Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.2053","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53decd12c00e5ae9cb5d029a0cb50bb1aa7bd25770e1d74443b2edbe6c5a32cf","sha256:d41db6bf23fe5d8046cb1ab0c47c45397a4209691986179da39fe737055d89a6"],"state_sha256":"3335cac815cca71a15b31f7eac5530d2acc5e78f0693021c21ca328c5885ef93"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hAU/Hko0foUxeKt0lSH7BLYQRn25aikmh6AStuyo7HkbTQkFLZVVKpqArYDR48V5OjIwoQz7ixhSKEFpwzOmCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T04:05:11.942141Z","bundle_sha256":"2d03ca0f567976458c33474db639bc2c425929bec625af9c00f790f69f62a8c0"}}