IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v77y2021i3p866-878.html
   My bibliography  Save this article

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

Author

Listed:
  • Israel Martínez‐Hernández
  • Marc G. Genton

Abstract

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.

Suggested Citation

  • Israel Martínez‐Hernández & Marc G. Genton, 2021. "Nonparametric trend estimation in functional time series with application to annual mortality rates," Biometrics, The International Biometric Society, vol. 77(3), pages 866-878, September.
    • Handle: RePEc:bla:biomet:v:77:y:2021:i:3:p:866-878
    DOI: 10.1111/biom.13353
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/biom.13353
    Download Restriction: no
    File URL: https://libkey.io/10.1111/biom.13353?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Horváth, Lajos & Kokoszka, Piotr & Rice, Gregory, 2014. "Testing stationarity of functional time series," Journal of Econometrics, Elsevier, vol. 179(1), pages 66-82.
    2. Wei Biao Wu & Zhibiao Zhao, 2007. "Inference of trends in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 391-410, June.
    3. Simon N. Wood, 2006. "Low-Rank Scale-Invariant Tensor Product Smooths for Generalized Additive Mixed Models," Biometrics, The International Biometric Society, vol. 62(4), pages 1025-1036, December.
    4. Simon N. Wood, 2003. "Thin plate regression splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 95-114, February.
    5. Laura Azzimonti & Laura M. Sangalli & Piercesare Secchi & Maurizio Domanin & Fabio Nobile, 2015. "Blood Flow Velocity Field Estimation Via Spatial Regression With PDE Penalization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1057-1071, September.
    6. Yingxing Li & David Ruppert, 2008. "On the asymptotics of penalized splines," Biometrika, Biometrika Trust, vol. 95(2), pages 415-436.
    7. Luo Xiao, 2019. "Asymptotics of bivariate penalised splines," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 31(2), pages 289-314, April.
    8. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
    9. Donatello Telesca & Lurdes Y.T. Inoue & Mauricio Neira & Ruth Etzioni & Martin Gleave & Colleen Nelson, 2009. "Differential Expression and Network Inferences through Functional Data Modeling," Biometrics, The International Biometric Society, vol. 65(3), pages 793-804, September.
    10. Lajos Horváth & Gregory Rice, 2015. "Testing Equality Of Means When The Observations Are From Functional Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(1), pages 84-108, January.
    11. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
    12. Krivobokova, Tatyana & Kauermann, Goran, 2007. "A Note on Penalized Spline Smoothing With Correlated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1328-1337, December.
    13. Alexander Aue & Diogo Dubart Norinho & Siegfried Hörmann, 2015. "On the Prediction of Stationary Functional Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 378-392, March.
    14. Brendan K. Beare & Juwon Seo & Won-Ki Seo, 2017. "Cointegrated Linear Processes in Hilbert Space," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 1010-1027, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lee, Wang-Sheng, 2014. "Big and Tall: Is there a Height Premium or Obesity Penalty in the Labor Market?," IZA Discussion Papers 8606, Institute of Labor Economics (IZA).
    2. Georgios Gioldasis & Antonio Musolesi & Michel Simioni, 2020. "Model uncertainty, nonlinearities and out-of-sample comparison: evidence from international technology diffusion," Working Papers hal-02790523, HAL.
    3. Gioldasis, Georgios & Musolesi, Antonio & Simioni, Michel, 2023. "Interactive R&D spillovers: An estimation strategy based on forecasting-driven model selection," International Journal of Forecasting, Elsevier, vol. 39(1), pages 144-169.
    4. Won-Ki Seo, 2020. "Functional Principal Component Analysis for Cointegrated Functional Time Series," Papers 2011.12781, arXiv.org, revised Apr 2023.
    5. Georgios Gioldasis & Antonio Musolesi & Michel Simioni, 2018. "Nonparametric estimation of international R&D spillovers," SEEDS Working Papers 0318, SEEDS, Sustainability Environmental Economics and Dynamics Studies, revised Mar 2018.
    6. Simon N. Wood & Zheyuan Li & Gavin Shaddick & Nicole H. Augustin, 2017. "Generalized Additive Models for Gigadata: Modeling the U.K. Black Smoke Network Daily Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1199-1210, July.
    7. Georgios Gioldasis & Antonio Musolesi & Michel Simioni, 2019. "Nonparametric estimation of R&D international spillovers," Post-Print hal-02789474, HAL.
    8. Antonio Musolesi & Michel Simioni & Georgios Gioldasis, 2018. "Nonparametric estimation of international R&D spillovers," Working Papers 2018037, University of Ferrara, Department of Economics.
    9. Georgios Gioldasis & Antonio Musolesi & Michel Simioni, 2020. "Model uncertainty, nonlinearities and out-of-sample comparison: evidence from international technology diffusion," SEEDS Working Papers 0120, SEEDS, Sustainability Environmental Economics and Dynamics Studies, revised Jan 2020.
    10. Georgios Gioldasis & Antonio Musolesi & Michel Simioni, 2021. "Interactive R&D Spillovers: An estimation strategy based on forecasting-driven model selection," SEEDS Working Papers 0621, SEEDS, Sustainability Environmental Economics and Dynamics Studies, revised Jun 2021.
    11. Georgios Gioldasis & Antonio Musolesi & Michel Simioni, 2021. "Interactive R&D Spillovers: an estimation strategy based on forecasting-driven model selection," Working Papers hal-03224910, HAL.
    12. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    13. Lee, Wang-Sheng, 2014. "Is the BMI a Relic of the Past?," IZA Discussion Papers 8637, Institute of Labor Economics (IZA).
    14. Haixu Wang & Jiguo Cao, 2023. "Nonlinear prediction of functional time series," Environmetrics, John Wiley & Sons, Ltd., vol. 34(5), August.
    15. Feng, Yuanhua & Härdle, Wolfgang Karl, 2020. "A data-driven P-spline smoother and the P-Spline-GARCH models," IRTG 1792 Discussion Papers 2020-016, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    16. Martínez-Hernández, Israel & Genton, Marc G. & González-Farías, Graciela, 2019. "Robust depth-based estimation of the functional autoregressive model," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 66-79.
    17. Han Lin Shang & Jiguo Cao & Peijun Sang, 2022. "Stopping time detection of wood panel compression: A functional time‐series approach," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1205-1224, November.
    18. Yuan Gao & Han Lin Shang, 2017. "Multivariate Functional Time Series Forecasting: Application to Age-Specific Mortality Rates," Risks, MDPI, vol. 5(2), pages 1-18, March.
    19. repec:wyi:journl:002174 is not listed on IDEAS
    20. Kauermann Goeran & Krivobokova Tatyana & Semmler Willi, 2011. "Filtering Time Series with Penalized Splines," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(2), pages 1-28, March.
    21. Daniel R. Kowal & David S. Matteson & David Ruppert, 2019. "Functional Autoregression for Sparsely Sampled Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(1), pages 97-109, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:biomet:v:77:y:2021:i:3:p:866-878. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0006-341X .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.