{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2RGRUURQHLXSHBU7DVU5K37DII","short_pith_number":"pith:2RGRUURQ","canonical_record":{"source":{"id":"1804.02254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-06T13:28:57Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"5e032630a2029eb10ee0e0ff7449cee7c0079fd032e4de610a9943145d429bca","abstract_canon_sha256":"e7d4c017e0f2186d61f7218cdd4baff0fed1ad4eea9f7ae5244da4a77bd503e1"},"schema_version":"1.0"},"canonical_sha256":"d44d1a52303aef23869f1d69d56fe3420a567865ef0f160d5434ba3f5a5555da","source":{"kind":"arxiv","id":"1804.02254","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.02254","created_at":"2026-05-18T00:19:05Z"},{"alias_kind":"arxiv_version","alias_value":"1804.02254v1","created_at":"2026-05-18T00:19:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.02254","created_at":"2026-05-18T00:19:05Z"},{"alias_kind":"pith_short_12","alias_value":"2RGRUURQHLXS","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2RGRUURQHLXSHBU7","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2RGRUURQ","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2RGRUURQHLXSHBU7DVU5K37DII","target":"record","payload":{"canonical_record":{"source":{"id":"1804.02254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-06T13:28:57Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"5e032630a2029eb10ee0e0ff7449cee7c0079fd032e4de610a9943145d429bca","abstract_canon_sha256":"e7d4c017e0f2186d61f7218cdd4baff0fed1ad4eea9f7ae5244da4a77bd503e1"},"schema_version":"1.0"},"canonical_sha256":"d44d1a52303aef23869f1d69d56fe3420a567865ef0f160d5434ba3f5a5555da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:05.408401Z","signature_b64":"vMXbFauYgV7TP7D/qLonEj2dUrzuTbIXuEZzUU89E4RLVONKpvGiQ5/KGSya0iZQkfNZHAYogfxNcU8J5U0EBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d44d1a52303aef23869f1d69d56fe3420a567865ef0f160d5434ba3f5a5555da","last_reissued_at":"2026-05-18T00:19:05.407887Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:05.407887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.02254","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":"2026-05-18T00:19:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3v0GcWgKh85sSNpoPsK+/PowMLec0t5R+6PBTg0Rcr5zaySYWeOb7tCqy6jhBP5VISB+FvaQpAovSoewRMRYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T03:45:48.045039Z"},"content_sha256":"a77087f9aca814aa34633b4b7c1643b0bdef0f13840e26f069cc721a396881f7","schema_version":"1.0","event_id":"sha256:a77087f9aca814aa34633b4b7c1643b0bdef0f13840e26f069cc721a396881f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2RGRUURQHLXSHBU7DVU5K37DII","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the sample autocovariance of a L\\'evy driven moving average process when sampled at a renewal sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Dirk-Philip Brandes, Imma Valentina Curato","submitted_at":"2018-04-06T13:28:57Z","abstract_excerpt":"We consider a L\\'evy driven continuous time moving average process $X$ sampled at random times which follow a renewal structure independent of $X$. Asymptotic normality of the sample mean, the sample autocovariance, and the sample autocorrelation is established under certain conditions on the kernel and the random times. We compare our results to a classical non-random equidistant sampling method and give an application to parameter estimation of the L\\'evy driven Ornstein-Uhlenbeck process."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02254","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":"2026-05-18T00:19:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YD+yiAWuvYCYt1t7XWAcS+uFvtzAzZTcV6tZwb+wyXAtjirhitpQ4xQfHPtyMCTkuTUNx8VpxPr4Pl53HQ7tBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T03:45:48.045425Z"},"content_sha256":"8014da51e28c31fc78a2d18083881d2c6d67cd97beaa93a5cc921165b3bbdf61","schema_version":"1.0","event_id":"sha256:8014da51e28c31fc78a2d18083881d2c6d67cd97beaa93a5cc921165b3bbdf61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2RGRUURQHLXSHBU7DVU5K37DII/bundle.json","state_url":"https://pith.science/pith/2RGRUURQHLXSHBU7DVU5K37DII/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2RGRUURQHLXSHBU7DVU5K37DII/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":"2026-06-01T03:45:48Z","links":{"resolver":"https://pith.science/pith/2RGRUURQHLXSHBU7DVU5K37DII","bundle":"https://pith.science/pith/2RGRUURQHLXSHBU7DVU5K37DII/bundle.json","state":"https://pith.science/pith/2RGRUURQHLXSHBU7DVU5K37DII/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2RGRUURQHLXSHBU7DVU5K37DII/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2RGRUURQHLXSHBU7DVU5K37DII","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":"e7d4c017e0f2186d61f7218cdd4baff0fed1ad4eea9f7ae5244da4a77bd503e1","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-06T13:28:57Z","title_canon_sha256":"5e032630a2029eb10ee0e0ff7449cee7c0079fd032e4de610a9943145d429bca"},"schema_version":"1.0","source":{"id":"1804.02254","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.02254","created_at":"2026-05-18T00:19:05Z"},{"alias_kind":"arxiv_version","alias_value":"1804.02254v1","created_at":"2026-05-18T00:19:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.02254","created_at":"2026-05-18T00:19:05Z"},{"alias_kind":"pith_short_12","alias_value":"2RGRUURQHLXS","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2RGRUURQHLXSHBU7","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2RGRUURQ","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:8014da51e28c31fc78a2d18083881d2c6d67cd97beaa93a5cc921165b3bbdf61","target":"graph","created_at":"2026-05-18T00:19:05Z","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":"We consider a L\\'evy driven continuous time moving average process $X$ sampled at random times which follow a renewal structure independent of $X$. Asymptotic normality of the sample mean, the sample autocovariance, and the sample autocorrelation is established under certain conditions on the kernel and the random times. We compare our results to a classical non-random equidistant sampling method and give an application to parameter estimation of the L\\'evy driven Ornstein-Uhlenbeck process.","authors_text":"Dirk-Philip Brandes, Imma Valentina Curato","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-06T13:28:57Z","title":"On the sample autocovariance of a L\\'evy driven moving average process when sampled at a renewal sequence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02254","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:a77087f9aca814aa34633b4b7c1643b0bdef0f13840e26f069cc721a396881f7","target":"record","created_at":"2026-05-18T00:19:05Z","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":"e7d4c017e0f2186d61f7218cdd4baff0fed1ad4eea9f7ae5244da4a77bd503e1","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-06T13:28:57Z","title_canon_sha256":"5e032630a2029eb10ee0e0ff7449cee7c0079fd032e4de610a9943145d429bca"},"schema_version":"1.0","source":{"id":"1804.02254","kind":"arxiv","version":1}},"canonical_sha256":"d44d1a52303aef23869f1d69d56fe3420a567865ef0f160d5434ba3f5a5555da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d44d1a52303aef23869f1d69d56fe3420a567865ef0f160d5434ba3f5a5555da","first_computed_at":"2026-05-18T00:19:05.407887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:05.407887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vMXbFauYgV7TP7D/qLonEj2dUrzuTbIXuEZzUU89E4RLVONKpvGiQ5/KGSya0iZQkfNZHAYogfxNcU8J5U0EBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:05.408401Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.02254","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a77087f9aca814aa34633b4b7c1643b0bdef0f13840e26f069cc721a396881f7","sha256:8014da51e28c31fc78a2d18083881d2c6d67cd97beaa93a5cc921165b3bbdf61"],"state_sha256":"9d91c025a405afc70e05966fe097dc89f57be3a2b7be3caa588380812316a1ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gooxIC3EG3EBAjdpFBgOmN9s7OHwxyxdGCm0o05oJ7mVWLt1dncay14xC8DTybJUaTLq0V//UbZXqtZguLKOAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T03:45:48.047500Z","bundle_sha256":"844c36fb81cf5da0405df56e14fee411abe3f17ddcf65c7626713ca273c0fdd7"}}