Pith Number

pith:UYC7RJBP

pith:2026:UYC7RJBPUVOAAGFCCBEYCCEDPK

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Edge-indexed network time series with graph Ornstein-Uhlenbeck dynamics

Almut E. D. Veraart, Jiaming Chen

Lévy-driven graph Ornstein-Uhlenbeck models extend continuous-time dynamics to edge-indexed network time series.

arxiv:2605.15907 v1 · 2026-05-15 · math.ST · stat.TH

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Claims

C1strongest claim

The results indicate that grOU models for edge-indexed network time series improve forecasting accuracy and reduce computational time relative to standard benchmarks while maintaining robustness through their network-based parametrization.

C2weakest assumption

That the adaptation of graph Ornstein-Uhlenbeck dynamics from node-indexed to edge-indexed processes preserves the key statistical properties (such as stationarity and estimability) needed for the maximum-likelihood framework and asymptotic results to apply, as stated in the abstract's description of the extension.

C3one line summary

Proposes Lévy-driven grOU models for edge-indexed network time series, extending GNAR processes to continuous time with MLE estimation, asymptotic results, simulations, and financial data application showing improved forecasting.

References

15 extracted · 15 resolved · 1 Pith anchors

[1] Barndorﬀ-Nielsen, O. E. & Shephard, N. (2001), ‘Non-Gaussian Or nstein–Uhlenbeck-based models and some of their uses in ﬁnancial economics’, Journal of the Royal Statistical Society: Series B (Statist 2001

[2] Christensen, K., Kinnebrock, S. & Podolskij, M. (2010), ‘Pre-aver aging estimators of the ex-post covariance matrix in noisy diﬀusion models with non-synchro nous data’, Journal of econometrics 159(1) 2010

[3] Courgeau, V. & Veraart, A. E. (2022 a), ‘High-frequency estimation of the L´ evy-driven graph Ornstein-Uhlenbeck process’, Electronic Journal of Statistics 16(2), 4863–4925 2022

[4] Courgeau, V. & Veraart, A. E. (2022 b), ‘Likelihood theory for the graph Ornstein-Uhlenbeck process’, Statistical Inference for Stochastic Processes 25(2), 227–260 2022

[5] Epps, T. W. (1979), ‘Comovements in stock prices in the very short run’, Journal of the American Statistical Association 74(366a), 291–298. iti Sato, K. & Yamazato, M. (1984), ‘Operator-selfdecomposab 1979

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Receipt and verification

First computed	2026-05-20T00:01:24.872551Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a605f8a42fa55c0018a210498108837a855e9f161f0121168cc9c8a2ba3ea2a3

Aliases

arxiv: 2605.15907 · arxiv_version: 2605.15907v1 · doi: 10.48550/arxiv.2605.15907 · pith_short_12: UYC7RJBPUVOA · pith_short_16: UYC7RJBPUVOAAGFC · pith_short_8: UYC7RJBP

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/UYC7RJBPUVOAAGFCCBEYCCEDPK \
  | 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: a605f8a42fa55c0018a210498108837a855e9f161f0121168cc9c8a2ba3ea2a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8b98e0781b0cba2a61cabcf1af90a9a1dbc28e3d14a72bdf91f17851ee2a0b4",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-05-15T12:45:15Z",
    "title_canon_sha256": "798512c731d750f0f4b73426a6cf411a4576968ef38c61c5badadf06be8ce71f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15907",
    "kind": "arxiv",
    "version": 1
  }
}