February 2024 Estimation of functional ARMA models
Thomas Kuenzer
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Bernoulli 30(1): 117-142 (February 2024). DOI: 10.3150/23-BEJ1591

Abstract

Functional auto-regressive moving average (FARMA or ARMAH) models allow for flexible and natural modelling of functional time series. While there are many results on pure autoregressive (FAR) models in Hilbert spaces, results on estimation and prediction of FARMA models are considerably more scarce. We devise a simple two-step method to estimate ARMA models in separable Hilbert spaces. Estimation is based on dimension-reduction using principal components analysis of the functional time series. We explore two different approaches to selecting principal component subspaces for regularization and establish consistency of the proposed estimators both under minimal assumptions and in a practical setting. The empirical performance of the estimation algorithm is evaluated in a simulation study, where it performs better than competing methods.

Acknowledgments

The author would like to thank two anonymous reviewers for their comments that greatly improved the quality of this article. The author is especially grateful to his PhD supervisor Siegfried Hörmann for numerous discussions and valuable comments that helped shape this paper.

Citation

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Thomas Kuenzer. "Estimation of functional ARMA models." Bernoulli 30 (1) 117 - 142, February 2024. https://doi.org/10.3150/23-BEJ1591

Information

Received: 1 October 2022; Published: February 2024
First available in Project Euclid: 8 November 2023

MathSciNet: MR4665572
zbMATH: 07788878
Digital Object Identifier: 10.3150/23-BEJ1591

Keywords: FARMA model , Functional data analysis , functional time series , model estimation , moving average

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Vol.30 • No. 1 • February 2024
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