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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Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Nonparametric trend estimation in functional time series with application to annual mortality rates
AU - Martínez-Hernández, Israel
AU - Genton, Marc G.
N1 - 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.
PY - 2021/9/30
Y1 - 2021/9/30
N2 - 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.
AB - 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.
KW - annual mortality rate
KW - detrending functional time series
KW - nonparametric estimator
KW - nonstationary functional time series
KW - penalized tensor product surface
U2 - 10.1111/biom.13353
DO - 10.1111/biom.13353
M3 - Journal article
VL - 77
SP - 866
EP - 878
JO - Biometrics
JF - Biometrics
SN - 0006-341X
IS - 3
ER -