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

Martínez-Hernández, Israel and Genton, Marc G. (2021) Nonparametric trend estimation in functional time series with application to annual mortality rates. Biometrics, 77 (3). pp. 866-878. ISSN 0006-341X

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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.

Item Type:
Journal Article
Journal or Publication Title:
Biometrics
Additional Information:
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.
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2700
Subjects:
ID Code:
160898
Deposited By:
Deposited On:
13 Oct 2021 08:30
Refereed?:
Yes
Published?:
Published
Last Modified:
22 Oct 2021 05:26