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Improved Forecasting for Multivariate Time Series using GNAR models with General Inverse Distance Weights — arXiv:2610.19921

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.19921
License (as archived): CC0-1.0
Archived: 2026-10-15T14:24:39.672Z
SHA-256 of the archived text: f4dbc7131af0f28e151648abc0ea71b121898721b3dae165255639ba03e213fb
Stable URL of this page: https://metraipolis.com/documento/dc_be2cd4f3d253

How to cite

Improved Forecasting for Multivariate Time Series using GNAR models with General Inverse Distance Weights — arXiv:2610.19921 — arXiv (en), https://arxiv.org/abs/2610.19921 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_be2cd4f3d253 (Metraipolis archive dc_be2cd4f3d253, sha256 f4dbc7131af0f28e151648abc0ea71b121898721b3dae165255639ba03e213fb)

BibTeX

@misc{dcbe2cd4f3d253,
  title = {Improved Forecasting for Multivariate Time Series using GNAR models with General Inverse Distance Weights — arXiv:2610.19921},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.19921},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_be2cd4f3d253; sha256 f4dbc7131af0f28e151648abc0ea71b121898721b3dae165255639ba03e213fb},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.19921. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Many multivariate time series arise on networks where relationships between variables depend on physical or more general distances. Standard vector autoregressive models struggle in such settings due to their quadratic parameter growth, while generalised network autoregressive (GNAR) models offer a parsimonious alternative by explicitly incorporating network structures. Existing GNAR formulations assume fixed weights, typically uniform or reciprocal distances, which may not reflect the true influence of distance in real systems. We introduce a novel model with general inverse distance weights (GNARID) that extends GNAR by introducing a tunable exponent parameter that controls the strength of distance penalisation. We establish theoretical results on the consistency and asymptotic normality of new GNARID estimators, including an extension to the setting where the number of nodes grows. We analyse the effect of misspecifying the exponent on forecasting error, which helps assess how much GNAR models could be improved by our tunable weights. Simulation studies confirm the theoretical properties and show measurable benefits from correct weight specification. Using the Brumadinho ground displacement dataset, we show that proper tuning of the weight exponent improves predictive performance, highlighting the practical value of flexible distance-based weighting in network time series models.

Tema degli esploratori: statistica e scienza dei dati (elenco arXiv stat.ME, nuovi lavori del giorno).
Categorie arXiv: Methodology (stat.ME).
Pagina del lavoro: https://arxiv.org/abs/2610.19921 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-15T13:54:35.313Z dalla pagina https://arxiv.org/list/stat.ME/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).