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Locally Stationary Functional Time Series

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  • van Delft, Anne
  • Eichler, Michael
Abstract
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Suggested Citation

  • van Delft, Anne & Eichler, Michael, 2017. "Locally Stationary Functional Time Series," LIDAM Discussion Papers ISBA 2017023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2017023
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    File URL: https://dial.uclouvain.be/pr/boreal/fr/object/boreal%3A187160/datastream/PDF_01/view
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    References listed on IDEAS

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    1. Aue, Alexander & Gabrys, Robertas & Horváth, Lajos & Kokoszka, Piotr, 2009. "Estimation of a change-point in the mean function of functional data," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2254-2269, November.
    2. Müller, Hans-Georg & Yao, Fang, 2008. "Functional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1534-1544.
    3. Denis Bosq, 2002. "Estimation of Mean and Covariance Operator of Autoregressive Processes in Banach Spaces," Statistical Inference for Stochastic Processes, Springer, vol. 5(3), pages 287-306, October.
    4. István Berkes & Robertas Gabrys & Lajos Horváth & Piotr Kokoszka, 2009. "Detecting changes in the mean of functional observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 927-946, November.
    5. Bowsher, Clive G. & Meeks, Roland, 2008. "The Dynamics of Economic Functions: Modeling and Forecasting the Yield Curve," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1419-1437.
    6. Hörmann, Siegfried & Horváth, Lajos & Reeder, Ron, 2013. "A Functional Version Of The Arch Model," Econometric Theory, Cambridge University Press, vol. 29(2), pages 267-288, April.
    7. Antoniadis, Anestis & Sapatinas, Theofanis, 2003. "Wavelet methods for continuous-time prediction using Hilbert-valued autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 133-158, October.
    8. 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.
    9. Philippe Besse & J. Ramsay, 1986. "Principal components analysis of sampled functions," Psychometrika, Springer;The Psychometric Society, vol. 51(2), pages 285-311, June.
    10. Horváth, Lajos & Husková, Marie & Kokoszka, Piotr, 2010. "Testing the stability of the functional autoregressive process," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 352-367, February.
    11. Anestis Antoniadis & Efstathios Paparoditis & Theofanis Sapatinas, 2006. "A functional wavelet–kernel approach for time series prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(5), pages 837-857, November.
    12. Siegfried Hörmann & Łukasz Kidziński & Marc Hallin, 2015. "Dynamic functional principal components," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 319-348, March.
    13. Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
    14. Herold Dehling & Olimjon Sharipov, 2005. "Estimation of Mean and Covariance Operator for Banach Space Valued Autoregressive Processes with Dependent Innovations," Statistical Inference for Stochastic Processes, Springer, vol. 8(2), pages 137-149, September.
    15. Hyndman, Rob J. & Booth, Heather, 2008. "Stochastic population forecasts using functional data models for mortality, fertility and migration," International Journal of Forecasting, Elsevier, vol. 24(3), pages 323-342.
    16. Aue, Alexander & Van Delft, Anne, 2017. "Testing for stationarity of functional time series in the frequency domain," LIDAM Discussion Papers ISBA 2017001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
    18. Rainer Dahlhaus, 1983. "Spectral Analysis With Tapered Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 163-175, May.
    19. Michael Vogt, 2012. "Nonparametric regression for locally stationary time series," CeMMAP working papers CWP22/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    20. 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.
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    Cited by:

    1. Cerovecki, Clément & Francq, Christian & Hörmann, Siegfried & Zakoïan, Jean-Michel, 2019. "Functional GARCH models: The quasi-likelihood approach and its applications," Journal of Econometrics, Elsevier, vol. 209(2), pages 353-375.

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