arbiter
JournalsAccount

Estimating invertible processes in Hilbert spaces, with applications to functional ARMA processes

Sebastian Kühnert et al.

Bernoulli2026https://doi.org/10.3150/25-bej1918article
ABDC A
Weight
0.50

Abstract

Invertible processes are central to functional time series analysis, making the estimation of their defining operators a key problem. While asymptotic error bounds have been established for specific ARMA models on L2[0,1], a general theoretical framework has not yet been considered. This paper fills in this gap by deriving consistent estimators for the operators characterizing the invertible representation of a functional time series with white noise innovations in a general separable Hilbert space. Under mild conditions covering a broad class of functional time series, we establish explicit asymptotic error bounds, with rates determined by operator smoothness and eigenvalue decay. These results further provide consistency-rate estimates for operators in Hilbert space-valued causal linear processes, including functional MA, AR, and ARMA models of arbitrary order.

Open via your library →

Cite this paper

https://doi.org/https://doi.org/10.3150/25-bej1918

Or copy a formatted citation

@article{sebastian2026,
  title        = {{Estimating invertible processes in Hilbert spaces, with applications to functional ARMA processes}},
  author       = {Sebastian Kühnert et al.},
  journal      = {Bernoulli},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.3150/25-bej1918},
}

Paste directly into BibTeX, Zotero, or your reference manager.

Flag this paper

Estimating invertible processes in Hilbert spaces, with applications to functional ARMA processes

Flags are reviewed by the Arbiter methodology team within 5 business days.

Evidence weight

0.50

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

† Text relevance is estimated at 0.50 on the detail page — for your query’s actual relevance score, open this paper from a search result.