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Conversely, coarse aggregation (Annual) eliminates recursive error propagation but reduces data available to estimators. We formalize this trade-off and benchmark 10 models - spanning na\\\"ive, statistical, machine learning, and deep learning architectures - across six granularities using a 13-year public procurement dataset. The empirical results reveal a non-monotonic threshold structure: recursive autoregressive and seasonal models degrade substantially under high-frequency forecasting (e.g., Holt-Winters reaches a Test R-squared of -151 and TPFE of 425.85% at the Daily grain), while the LSTM traces a U-shaped error curve, worsening from Monthly","title":"The Granularity Paradox: How Temporal Disaggregation Inflates In-Sample Fit and Compounds Out-of-Sample Error","url":"https://arxiv.org/abs/2607.05450","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.05450v1 Announce Type: cross \nAbstract: This paper explores the \"Granularity Paradox\" in time-series forecasting, wherein finer temporal disaggregation (e.g., Monthly to Weekly/Daily) improves in-sample diagnostics and dataset size (N), but degrades out-of-sample accuracy due to recursive error compounding over longer horizons (H). Conversely, coarse aggregation (Annual) eliminates recursive error propagation but reduces data available to estimators. We formalize this trade-off and benchmark 10 models - spanning na\\\"ive, statistical, machine learning, and deep learning architectures - across six granularities using a 13-year public procurement dataset. The empirical results reveal a non-monotonic threshold structure: recursive autoregressive and seasonal models degrade substantially under high-frequency forecasting (e.g., Holt-Winters reaches a Test R-squared of -151 and TPFE of 425.85% at the Daily grain), while the LSTM traces a U-shaped error curve, worsening from Monthly","title":"The Granularity Paradox: How Temporal Disaggregation Inflates In-Sample Fit and Compounds Out-of-Sample Error","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-08T04:43:57Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.05450"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:803f4d7a96c59d04c06e79fa727cf2bcadf8a95aa07fe7d4fe4dc676b8cb524e522f1d13b92a784247c41bac3a0b15aa13d52ae4df1b4b2c4c67c4c74f1c7104","signer":"crovia.substrate","subject":{"observed_at":"2026-07-08T04:43:57Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.05450"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"cbe491542ac30be44f8954051197ecfa52ea9f497373ec90038ef344d40e075c","leaf_index":292679,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"75716b6e2117b795cdb2afd3328b8c3d2a12a1498477471c857bd0b9d9be421c","side":"left"},{"sibling":"6f35f66a201e566bc42463eaacedb8fc79d00ac0472cab4451fd7554c6c7cb5a","side":"left"},{"sibling":"ce796026f79cdc8e53c288cd74fad2d134a2d86ab83b1750adad37167d2414bc","side":"left"},{"sibling":"baacc3514695ee05d12a75da33041bde6b972d7c156dde1e11a2b748e54f7009","side":"right"},{"sibling":"28bc827aa3a58873cb8e6186189f7f562c6abdb932069ce37644cb45cbd0aa4d","side":"right"},{"sibling":"72f7f4fe9923986ba7eb993a43289fff6a04211feec32380568db20ee9ddf0ac","side":"right"},{"sibling":"b0c3c5751a1b9461c133083b884a2c1fa5dbc65b069dd53ccc95339ef1af56c5","side":"left"},{"sibling":"7db888cb3645d8b5e3052bd5d092a85490e29ab732a691eb6a8b8560770aa0ff","side":"right"},{"sibling":"1515812edbf9903d3d787f20218b8577e2f1fef32592508ce01a3b3ebe75f507","side":"left"},{"sibling":"d4b475beae71e5b4d5ab7e66f7144e7b8e1356fcd32339e49df234b455659fef","side":"left"},{"sibling":"cead64e0790e8871aeea2334210146b5e35fe7e4bc10748acdf76da0c565be05","side":"left"},{"sibling":"d1231ac6e6bd7d6867a9109fbdadede0b1631e97866ddde70f7ac2d52c28e15f","side":"right"},{"sibling":"76855b4804c75c52bf97aa34358950d42d6103cdc1a86be5f0a2c8de4d65c106","side":"left"},{"sibling":"a75ab4319e241beeddb1b3f5705febe0422937926c3479923ccfb0b0082fa4e3","side":"left"},{"sibling":"bd04fa605f883bfb2b81510d045b1e85e555a03da3be083619f61384dfe40ff8","side":"left"},{"sibling":"9e75f2ab0ddf2dc9e92af7049244c21b909734ab57906a35dfad2853ca9966e2","side":"right"},{"sibling":"e6cd4cad39a4b6ca6647d1b0ad2db86e57e5fa6240f65966c10093e91140769b","side":"right"},{"sibling":"90a7efc6b94ec8913fbdf03f4927a821b9fb89921d526716f5ee28f015303779","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":292998,"merkle_root":"f533b7efebdfd8fb6ba3e7cc158ee55261fd53a7985f234cfea359170dad4d5a","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260708T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-08T05:38:17Z","sig_algorithm":"ed25519","signature":"07ebb10c732bbffb28b55a5db01d5525f6b8ab7ef36e1e0a68c35c96ded99f7040c277edba75eb6b15c77feda30bd5321e31ada6f572b674d06f4f8e24bd2f07","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_98bf0290f9be6b254cba35c16eb660802b8a1c6bbfa69f42131035b25ae0cf6e"}}