IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v150y2019icp114-120.html
   My bibliography  Save this article

Best linear predictor of a C[0,1]-valued functional autoregressive process

Author

Listed:
  • Kada Kloucha, Meryem
  • Mourid, Tahar

Abstract

We establish exponential bounds and the a.s. convergence of the best linear predictor BLP of a C[0,1]-valued autoregressive process. Simulation studies on real series illustrate the performance of the BLP and show competitive results.

Suggested Citation

  • Kada Kloucha, Meryem & Mourid, Tahar, 2019. "Best linear predictor of a C[0,1]-valued functional autoregressive process," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 114-120.
    • Handle: RePEc:eee:stapro:v:150:y:2019:i:c:p:114-120
    DOI: 10.1016/j.spl.2019.03.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715219300793
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2019.03.003?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fatiha Mokhtari & Tahar Mourid, 2003. "Prediction of Continuous Time Autoregressive Processes via the Reproducing Kernel Spaces," Statistical Inference for Stochastic Processes, Springer, vol. 6(3), pages 247-266, October.
    2. Berhoune, Kamila & Bensmain, Nawel, 2018. "Sieves estimator of functional autoregressive process," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 60-69.
    3. 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.
    4. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    5. Bosq, D., 2014. "Computing the best linear predictor in a Hilbert space. Applications to general ARMAH processes," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 436-450.
    6. Kargin, V. & Onatski, A., 2008. "Curve forecasting by functional autoregression," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2508-2526, November.
    7. Besnik Pumo, 1998. "Prediction of Continuous Time Processes by C[0,1]‐Valued Autoregressive Process," Statistical Inference for Stochastic Processes, Springer, vol. 1(3), pages 297-309, October.
    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. Xu, Meng & Li, Jialiang & Chen, Ying, 2017. "Varying coefficient functional autoregressive model with application to the U.S. treasuries," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 168-183.
    2. Álvarez-Liébana, Javier & Bosq, Denis & Ruiz-Medina, María D., 2016. "Consistency of the plug-in functional predictor of the Ornstein–Uhlenbeck process in Hilbert and Banach spaces," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 12-22.
    3. Klepsch, J. & Klüppelberg, C., 2017. "An innovations algorithm for the prediction of functional linear processes," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 252-271.
    4. Atefeh Zamani & Hossein Haghbin & Maryam Hashemi & Rob J. Hyndman, 2022. "Seasonal functional autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 197-218, March.
    5. Battey, Heather & Sancetta, Alessio, 2013. "Conditional estimation for dependent functional data," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 1-17.
    6. Álvarez-Liébana, J. & Bosq, D. & Ruiz-Medina, M.D., 2017. "Asymptotic properties of a component-wise ARH(1) plug-in predictor," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 12-34.
    7. Jiménez Recaredo, Raúl José & Elías Fernández, Antonio, 2017. "Prediction Bands for Functional Data Based on Depth Measures," DES - Working Papers. Statistics and Econometrics. WS 24606, Universidad Carlos III de Madrid. Departamento de Estadística.
    8. Ajroldi, Niccolò & Diquigiovanni, Jacopo & Fontana, Matteo & Vantini, Simone, 2023. "Conformal prediction bands for two-dimensional functional time series," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    9. 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.
    10. Horváth, Lajos & Hušková, Marie & Rice, Gregory, 2013. "Test of independence for functional data," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 100-119.
    11. Sven Otto & Nazarii Salish, 2022. "Approximate Factor Models for Functional Time Series," Papers 2201.02532, arXiv.org, revised Aug 2022.
    12. Klepsch, J. & Klüppelberg, C. & Wei, T., 2017. "Prediction of functional ARMA processes with an application to traffic data," Econometrics and Statistics, Elsevier, vol. 1(C), pages 128-149.
    13. Elías, Antonio & Jiménez, Raúl & Shang, Han Lin, 2022. "On projection methods for functional time series forecasting," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    14. 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.
    15. Horváth, Lajos & Kokoszka, Piotr & Rice, Gregory, 2014. "Testing stationarity of functional time series," Journal of Econometrics, Elsevier, vol. 179(1), pages 66-82.
    16. Ayse Yilmaz & Ufuk Yolcu, 2022. "Dendritic neuron model neural network trained by modified particle swarm optimization for time‐series forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(4), pages 793-809, July.
    17. Wang, Jingxing & Chung, Seokhyun & AlShelahi, Abdullah & Kontar, Raed & Byon, Eunshin & Saigal, Romesh, 2021. "Look-ahead decision making for renewable energy: A dynamic “predict and store” approach," Applied Energy, Elsevier, vol. 296(C).
    18. Zhang, Xianyang, 2016. "White noise testing and model diagnostic checking for functional time series," Journal of Econometrics, Elsevier, vol. 194(1), pages 76-95.
    19. Li, Pai-Ling & Chiou, Jeng-Min, 2011. "Identifying cluster number for subspace projected functional data clustering," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2090-2103, June.
    20. Guangxing Wang & Sisheng Liu & Fang Han & Chong‐Zhi Di, 2023. "Robust functional principal component analysis via a functional pairwise spatial sign operator," Biometrics, The International Biometric Society, vol. 79(2), pages 1239-1253, June.

    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:eee:stapro:v:150:y:2019:i:c:p:114-120. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.