{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:FSBX5IMULBLGKD7BCTRA56ZMO3","short_pith_number":"pith:FSBX5IMU","canonical_record":{"source":{"id":"1209.0952","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-09-05T12:49:26Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"2f9c3cf5131bbf345ae9bd45803cad61ab4a770f2b675cb36eb89f292bf4d013","abstract_canon_sha256":"3544d3e51baf04f9385725f0463707c4df6938a3446cc92a7a9c79258b1f3382"},"schema_version":"1.0"},"canonical_sha256":"2c837ea1945856650fe114e20efb2c76e1596e05aa597afc42b2915ac3493af9","source":{"kind":"arxiv","id":"1209.0952","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0952","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0952v1","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0952","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"pith_short_12","alias_value":"FSBX5IMULBLG","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FSBX5IMULBLGKD7B","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FSBX5IMU","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:FSBX5IMULBLGKD7BCTRA56ZMO3","target":"record","payload":{"canonical_record":{"source":{"id":"1209.0952","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-09-05T12:49:26Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"2f9c3cf5131bbf345ae9bd45803cad61ab4a770f2b675cb36eb89f292bf4d013","abstract_canon_sha256":"3544d3e51baf04f9385725f0463707c4df6938a3446cc92a7a9c79258b1f3382"},"schema_version":"1.0"},"canonical_sha256":"2c837ea1945856650fe114e20efb2c76e1596e05aa597afc42b2915ac3493af9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:32.553916Z","signature_b64":"nEKOeZjvge/zF5AWpeDhSjJgWCkq/LtpWZI10Caj1SAjYOMIvMD8UQp4MaAlJaOd4+bAaK0+t+EO3ZMInQayDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c837ea1945856650fe114e20efb2c76e1596e05aa597afc42b2915ac3493af9","last_reissued_at":"2026-05-18T02:07:32.553384Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:32.553384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.0952","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":"2026-05-18T02:07:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5YpDrshwFm+hEsfKZLdsHNJInpLr1haz33rDpgWmCsztlRRGYQN8YAIzuGOzSo5Pj9tzHCOLfjhBSoiVdQTvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:28:36.170502Z"},"content_sha256":"1815a4a95ce6e0cad8bc30aa8ee6c4d29f89e163cd74a2bea3edcad3ea42d2f0","schema_version":"1.0","event_id":"sha256:1815a4a95ce6e0cad8bc30aa8ee6c4d29f89e163cd74a2bea3edcad3ea42d2f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:FSBX5IMULBLGKD7BCTRA56ZMO3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parametric estimation of the driving L\\'evy process of multivariate CARMA processes from discrete observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Eckhard Schlemm, Peter J. Brockwell","submitted_at":"2012-09-05T12:49:26Z","abstract_excerpt":"We consider the parametric estimation of the driving L\\'evy process of a multivariate continuous-time autoregressive moving average (MCARMA) process, which is observed on the discrete time grid $(0,h,2h,...)$. Beginning with a new state space representation, we develop a method to recover the driving L\\'evy process exactly from a continuous record of the observed MCARMA process. We use tools from numerical analysis and the theory of infinitely divisible distributions to extend this result to allow for the approximate recovery of unit increments of the driving L\\'evy process from discrete-time "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0952","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":"2026-05-18T02:07:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N1b738Q0Dz1+bwK601wfgngy5Dbrrth992z/QgnXGP+wmax5doSXS6MNSLe3ra+c2eW2I2jW4TbjmUyyk0raBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:28:36.170845Z"},"content_sha256":"dd005bd728c35c237b98208d501ed6f819eac10929e2dd29bd4bb8f1fb17b8f9","schema_version":"1.0","event_id":"sha256:dd005bd728c35c237b98208d501ed6f819eac10929e2dd29bd4bb8f1fb17b8f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FSBX5IMULBLGKD7BCTRA56ZMO3/bundle.json","state_url":"https://pith.science/pith/FSBX5IMULBLGKD7BCTRA56ZMO3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FSBX5IMULBLGKD7BCTRA56ZMO3/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":"2026-06-23T00:28:36Z","links":{"resolver":"https://pith.science/pith/FSBX5IMULBLGKD7BCTRA56ZMO3","bundle":"https://pith.science/pith/FSBX5IMULBLGKD7BCTRA56ZMO3/bundle.json","state":"https://pith.science/pith/FSBX5IMULBLGKD7BCTRA56ZMO3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FSBX5IMULBLGKD7BCTRA56ZMO3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FSBX5IMULBLGKD7BCTRA56ZMO3","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":"3544d3e51baf04f9385725f0463707c4df6938a3446cc92a7a9c79258b1f3382","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-09-05T12:49:26Z","title_canon_sha256":"2f9c3cf5131bbf345ae9bd45803cad61ab4a770f2b675cb36eb89f292bf4d013"},"schema_version":"1.0","source":{"id":"1209.0952","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0952","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0952v1","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0952","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"pith_short_12","alias_value":"FSBX5IMULBLG","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FSBX5IMULBLGKD7B","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FSBX5IMU","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:dd005bd728c35c237b98208d501ed6f819eac10929e2dd29bd4bb8f1fb17b8f9","target":"graph","created_at":"2026-05-18T02:07:32Z","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 the parametric estimation of the driving L\\'evy process of a multivariate continuous-time autoregressive moving average (MCARMA) process, which is observed on the discrete time grid $(0,h,2h,...)$. Beginning with a new state space representation, we develop a method to recover the driving L\\'evy process exactly from a continuous record of the observed MCARMA process. We use tools from numerical analysis and the theory of infinitely divisible distributions to extend this result to allow for the approximate recovery of unit increments of the driving L\\'evy process from discrete-time ","authors_text":"Eckhard Schlemm, Peter J. Brockwell","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-09-05T12:49:26Z","title":"Parametric estimation of the driving L\\'evy process of multivariate CARMA processes from discrete observations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0952","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":"sha256:1815a4a95ce6e0cad8bc30aa8ee6c4d29f89e163cd74a2bea3edcad3ea42d2f0","target":"record","created_at":"2026-05-18T02:07:32Z","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":"3544d3e51baf04f9385725f0463707c4df6938a3446cc92a7a9c79258b1f3382","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-09-05T12:49:26Z","title_canon_sha256":"2f9c3cf5131bbf345ae9bd45803cad61ab4a770f2b675cb36eb89f292bf4d013"},"schema_version":"1.0","source":{"id":"1209.0952","kind":"arxiv","version":1}},"canonical_sha256":"2c837ea1945856650fe114e20efb2c76e1596e05aa597afc42b2915ac3493af9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c837ea1945856650fe114e20efb2c76e1596e05aa597afc42b2915ac3493af9","first_computed_at":"2026-05-18T02:07:32.553384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:32.553384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nEKOeZjvge/zF5AWpeDhSjJgWCkq/LtpWZI10Caj1SAjYOMIvMD8UQp4MaAlJaOd4+bAaK0+t+EO3ZMInQayDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:32.553916Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.0952","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1815a4a95ce6e0cad8bc30aa8ee6c4d29f89e163cd74a2bea3edcad3ea42d2f0","sha256:dd005bd728c35c237b98208d501ed6f819eac10929e2dd29bd4bb8f1fb17b8f9"],"state_sha256":"f98921935ac40d279aec5cd1263c2f4f541044b80fc60e6d9b2f95c4397841b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k4riY2aKhbeXQ8v7EjpIz7y0u30FzUjadye5qxJs2C4MrovQXQSx9LvlfxSr7u79yN64dhE2GoFI1pSVnivDCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T00:28:36.172795Z","bundle_sha256":"a5cb4f01c13b051a07a2e6334869deb0876bfaabac4a7c7d0d69a585d40ee736"}}