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    Rights statement: This is the peer reviewed version of the following article: Martínez-Hernández, I, Genton, MG. Nonparametric trend estimation in functional time series with application to annual mortality rates. Biometrics. 2021; 77: 866– 878. https://doi.org/10.1111/biom.13353 which has been published in final form at https://onlinelibrary.wiley.com/doi/10.1111/biom.13353 This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.

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    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

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Nonparametric trend estimation in functional time series with application to annual mortality rates

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>30/09/2021
<mark>Journal</mark>Biometrics
Issue number3
Volume77
Number of pages13
Pages (from-to)866-878
Publication StatusPublished
Early online date27/08/20
<mark>Original language</mark>English

Abstract

Here, we address the problem of trend estimation for functional time series. Existing contributions either deal with detecting a functional trend or assuming a simple model. They consider neither the estimation of a general functional trend nor the analysis of functional time series with a functional trend component. Similarly to univariate time series, we propose an alternative methodology to analyze functional time series, taking into account a functional trend component. We propose to estimate the functional trend by using a tensor product surface that is easy to implement, to interpret, and allows to control the smoothness properties of the estimator. Through a Monte Carlo study, we simulate different scenarios of functional processes to show that our estimator accurately identifies the functional trend component. We also show that the dependency structure of the estimated stationary time series component is not significantly affected by the error approximation of the functional trend component. We apply our methodology to annual mortality rates in France.

Bibliographic note

This is the peer reviewed version of the following article: Martínez-Hernández, I, Genton, MG. Nonparametric trend estimation in functional time series with application to annual mortality rates. Biometrics. 2021; 77: 866– 878. https://doi.org/10.1111/biom.13353 which has been published in final form at https://onlinelibrary.wiley.com/doi/10.1111/biom.13353 This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.