{"paper":{"title":"ARMA approximation of a Non-separable Spatio-Temporal Model with Fractional Smoothnesses in Space and Time","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Rational approximations in time turn a non-separable fractional spatio-temporal model into a convergent vector ARMA process.","cross_cats":["cs.NA","math.NA"],"primary_cat":"stat.ME","authors_text":"Espen R. Jakobsen, Geir-Arne Fuglstad, S. Knutsen Furset","submitted_at":"2026-04-29T11:04:56Z","abstract_excerpt":"The Mat\\'ern covariance model is ubiquitous in spatial modelling, but there is no default choice for spatio-temporal modelling. In this paper, we consider the recently proposed ``diffusion-based'' extension of the spatial Mat\\'ern covariance model to a spatio-temporal non-separable covariance model that allows fractional smoothnesses in space and in time. The model is described in terms of a space-time fractional stochastic partial differential equation, but currently proposed computational approaches have strong restrictions on the possible smoothnesses in time. We propose a discretization me"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We propose a discretization method based on rational approximations in time to handle arbitrary smoothnesses, which leads to a vector autoregressive moving average process (VARMA). We prove that the covariance function of the approximation converges pointwise, determine explicit convergence rates as a function of spatial and temporal resolutions and the accuracy of the rational approximation.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The rational approximation of the temporal fractional operator can be made arbitrarily accurate while preserving the non-separable structure and validity of the resulting spatio-temporal covariance without introducing uncontrolled bias.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Rational approximations in time convert a fractional space-time SPDE into a convergent VARMA model that handles arbitrary smoothness and improves forecasting when temporal smoothness is correctly specified.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Rational approximations in time turn a non-separable fractional spatio-temporal model into a convergent vector ARMA process.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"468b2e36b99c0bbeabd5e828b61227bd2db67e2fe5893aec7f16735b73bfa8f3"},"source":{"id":"2604.26535","kind":"arxiv","version":2},"verdict":{"id":"a274d130-bbf7-49b5-a1a5-2b32e62ba79b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T12:40:15.361792Z","strongest_claim":"We propose a discretization method based on rational approximations in time to handle arbitrary smoothnesses, which leads to a vector autoregressive moving average process (VARMA). We prove that the covariance function of the approximation converges pointwise, determine explicit convergence rates as a function of spatial and temporal resolutions and the accuracy of the rational approximation.","one_line_summary":"Rational approximations in time convert a fractional space-time SPDE into a convergent VARMA model that handles arbitrary smoothness and improves forecasting when temporal smoothness is correctly specified.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The rational approximation of the temporal fractional operator can be made arbitrarily accurate while preserving the non-separable structure and validity of the resulting spatio-temporal covariance without introducing uncontrolled bias.","pith_extraction_headline":"Rational approximations in time turn a non-separable fractional spatio-temporal model into a convergent vector ARMA process."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.26535/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T23:49:23.860292Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T20:02:56.779924Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"8082129dd18f9bc92b342714ff2623c0950a947b536420d17d30b1ee81646c94"},"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"}