Skip to main content
SpringerLink
Log in
Book cover

Functional Statistics and Related Fields pp 51–58Cite as

Estimating invertible functional time series

  • Conference paper
  • First Online:

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Abstract

This contribution discusses the estimation of an invertible functional time series through fitting of functional moving average processes. The method uses a functional version of the innovations algorithm and dimension reduction onto a number of principal directions. Several methods are suggested to automate the procedures. Empirical evidence is presented in the form of simulations and an application to traffic data.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aston, J.A.D., Kirch, C.: Detecting and estimating changes in dependent functional data. J. Mult. Anal. 109, 204–220 (2012)

    Google Scholar 

  2. Aston, J.A.D., Kirch, C.: Evaluating stationarity via change-point alternatives with applications to FMRI data. Ann. Appl. Statist. 6, 1906–1948 (2012)

    Google Scholar 

  3. Aue, A., Dubart Norinho, D., Hörmann, S.: On the prediction of stationary functional time series. J. Am. Stat. Assoc. 110, 378–392 (2015)

    Google Scholar 

  4. Aue, A., Horváth, L.: Structural breaks in time series. J. Time Ser. Anal. 34, 1–16 (2013)

    Google Scholar 

  5. Aue, A., Horváth, L., Pellatt, D.: Functional generalized autoregressive conditional heteroskedasticity. J. Time Ser. Anal. 38, 3–21 (2017)

    Google Scholar 

  6. Aue, A., Klepsch, J.: Estimating functional time series by moving average model fitting. ArXiv preprint (2017). Available online at https://arxiv.org/abs/1701.00770

  7. Aue, A., Rice, G., Sönmez, O.: Detecting and dating structural breaks in functional data without dimension reduction. ArXiv preprint (2017). Available online at https://arxiv.org/abs/1511.04020

  8. Aue, A., van Delft, A.: Testing for stationarity of functional time series in the frequency domain. ArXiv preprint (2017). Available online at https://arxiv.org/abs/1701.01741.

  9. Chakraborty, A., Panaretos, V.M.: Functional registration and local variations. ArXiv preprint (2017). Available online at https://arxiv.org/abs/1702.03556

  10. Hörmann, S., Kokoszka, P.: Weakly dependent functional data. Ann. Statist. 38, 1845–1884 (2010)

    Google Scholar 

  11. Hörmann, S., Horváth, L., Reeder, R.: A functional version of the ARCH model. Econometr. Th. 29, 267–288 (2013)

    Google Scholar 

  12. Hörmann, S., Kokoszka, P., Nisol, G.: Detection of periodicity in functional time series. ArXiv preprint (2016). Available online at https://arxiv.org/abs/1607.02017

  13. Horváth, L., Kokoszka, P., Rice, G.: Testing stationarity of functional time series. J. Econ. 179, 66–82 (2014)

    Google Scholar 

  14. Klepsch, J., Klüppelberg, C.: An innovations algorithm for the prediction of functional linear processes. J. Mult. Anal. 155, 252–271 (2017)

    Google Scholar 

  15. Klepsch, J., Klüppelberg, C.,Wei, T.: Prediction of functional ARMA processes with an application to traffic data. Econ. Statist. 1, 128–149 (2017)

    Google Scholar 

  16. Kowal, D.R, Matteson, D.S., Ruppert, D.: A Bayesian multivariate functional dynamic linear model. J. Am. Statist. Assoc. (2016) doi:10.1080/01621459.2016.1165104

    Google Scholar 

  17. Paparoditis, E.: Sieve bootstrap for functional time series. ArXiv preprint (2016). Available online at https://arxiv.org/abs/1609.06029

  18. Raña, P., Aneiros, G., Vilar, J.M.: Detection of outliers in functional time series. Environm. 26, 178–191 (2015)

    Google Scholar 

  19. Raña, P., Aneiros, G., Vilar, J.M., Vieu, P.: Bootstrap confidence intervals for nonparametric regression under dependence. Electr. J. Statist. 10, 1973–1999 (2016)

    Google Scholar 

  20. Van Delft, A., Eichler, M.: Locally stationary functional time series. ArXiv preprint (2016). Available online at https://arxiv.org/abs/1602.05125

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, University of California, One Shields Avenue, Davis, CA, 95616, USA

    Alexander Aue

  2. Center for Mathematical Sciences, Technische Universität München, 85748, Garching, Boltzmannstraße 3, Germany

    Johannes Klepsch

Authors
  1. Alexander Aue
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Johannes Klepsch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexander Aue .

Editor information

Editors and Affiliations

  1. Dept. of Mathematics, University of A Coruña, A Coruña, Spain

    Germán Aneiros

  2. Dept. of Studies in Econ.and Business, University of Eastern Piedmont "Amedeo Avogadro", Novara, Italy

    Enea G. Bongiorno

  3. Dept. of Mathematics, University of A Coruña, A Coruña, Spain

    Ricardo Cao

  4. Toulouse Mathematics Institute (IMT), Paul Sabatier University, Toulouse, France

    Philippe Vieu

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Aue, A., Klepsch, J. (2017). Estimating invertible functional time series. In: Aneiros, G., G. Bongiorno, E., Cao, R., Vieu, P. (eds) Functional Statistics and Related Fields. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-55846-2_8

Download citation

Publish with us

Policies and ethics

Search

Navigation