Pith Number

pith:3VVYQYWK

pith:2026:3VVYQYWKG5AANTV5KRAFHAXSFF

not attested not anchored not stored refs pending

ARMA approximation of a Non-separable Spatio-Temporal Model with Fractional Smoothnesses in Space and Time

Espen R. Jakobsen, Geir-Arne Fuglstad, S. Knutsen Furset

Rational approximations in time turn a non-separable fractional spatio-temporal model into a convergent vector ARMA process.

arxiv:2604.26535 v2 · 2026-04-29 · stat.ME · cs.NA · math.NA

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\usepackage{pith}
\pithnumber{3VVYQYWKG5AANTV5KRAFHAXSFF}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest 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.

C2weakest 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.

C3one 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.

Receipt and verification

First computed	2026-06-08T01:04:05.893239Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd6b8862ca374006cebd54405382f229723bc34057a3fd5e3ccd004dc3ab64a5

Aliases

arxiv: 2604.26535 · arxiv_version: 2604.26535v2 · doi: 10.48550/arxiv.2604.26535 · pith_short_12: 3VVYQYWKG5AA · pith_short_16: 3VVYQYWKG5AANTV5 · pith_short_8: 3VVYQYWK

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3VVYQYWKG5AANTV5KRAFHAXSFF \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: dd6b8862ca374006cebd54405382f229723bc34057a3fd5e3ccd004dc3ab64a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de936f92aeb1afd573e4b73a2e400109e9f7d9652bec4a50e92090a822626295",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-04-29T11:04:56Z",
    "title_canon_sha256": "ac076e0ac6e5fcb8a68fe05223313d235ebc28dad6b6a1850e13b82182e446b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.26535",
    "kind": "arxiv",
    "version": 2
  }
}