IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v28y2019i4d10.1007_s10260-019-00457-x.html
   My bibliography  Save this article

Dynamic partially functional linear regression model

Author

Listed:
  • Jiang Du

    (Beijing University of Technology)

  • Hui Zhao

    (Beijing University of Technology)

  • Zhongzhan Zhang

    (Beijing University of Technology)

Abstract

In this paper, we develop a dynamic partially functional linear regression model in which the functional dependent variable is explained by the first order lagged functional observation and a finite number of real-valued variables. The bivariate slope function is estimated by bivariate tensor-product B-splines. Under some regularity conditions, the large sample properties of the proposed estimators are established. We investigate the finite sample performance of the proposed methods via Monte Carlo simulation studies, and illustrate its usefulness by the analysis of the electricity consumption data.

Suggested Citation

  • Jiang Du & Hui Zhao & Zhongzhan Zhang, 2019. "Dynamic partially functional linear regression model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 679-693, December.
    • Handle: RePEc:spr:stmapp:v:28:y:2019:i:4:d:10.1007_s10260-019-00457-x
    DOI: 10.1007/s10260-019-00457-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-019-00457-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10260-019-00457-x?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. Fan, Zhaohu & Reimherr, Matthew, 2017. "High-dimensional adaptive function-on-scalar regression," Econometrics and Statistics, Elsevier, vol. 1(C), pages 167-183.
    2. He, Xuming & Fung, Wing K. & Zhu, Zhongyi, 2005. "Robust Estimation in Generalized Partial Linear Models for Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1176-1184, December.
    3. 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.
    4. Aneiros-Pérez, Germán & Vieu, Philippe, 2008. "Nonparametric time series prediction: A semi-functional partial linear modeling," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 834-857, May.
    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. Han Lin Shang & Yang Yang, 2021. "Forecasting Australian subnational age-specific mortality rates," Journal of Population Research, Springer, vol. 38(1), pages 1-24, March.
    2. 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.
    3. Gao, Yuan & Shang, Han Lin & Yang, Yanrong, 2019. "High-dimensional functional time series forecasting: An application to age-specific mortality rates," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 232-243.
    4. Han Lin Shang & Yang Yang & Fearghal Kearney, 2019. "Intraday forecasts of a volatility index: functional time series methods with dynamic updating," Annals of Operations Research, Springer, vol. 282(1), pages 331-354, November.
    5. Xueying Zheng & Wing Fung & Zhongyi Zhu, 2013. "Robust estimation in joint mean–covariance regression model for longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 617-638, August.
    6. Horváth, Lajos & Rice, Gregory & Whipple, Stephen, 2016. "Adaptive bandwidth selection in the long run covariance estimator of functional time series," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 676-693.
    7. Zhang, Xianyang, 2016. "White noise testing and model diagnostic checking for functional time series," Journal of Econometrics, Elsevier, vol. 194(1), pages 76-95.
    8. 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.
    9. Kokoszka, Piotr & Oja, Hanny & Park, Byeong & Sangalli, Laura, 2017. "Special issue on functional data analysis," Econometrics and Statistics, Elsevier, vol. 1(C), pages 99-100.
    10. Nengxiang Ling & Rui Kan & Philippe Vieu & Shuyu Meng, 2019. "Semi-functional partially linear regression model with responses missing at random," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 39-70, January.
    11. Timmermans, Catherine & Delsol, Laurent & von Sachs, Rainer, 2013. "Using Bagidis in nonparametric functional data analysis: Predicting from curves with sharp local features," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 421-444.
    12. Allam, Abdelaziz & Mourid, Tahar, 2019. "Optimal rate for covariance operator estimators of functional autoregressive processes with random coefficients," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 130-137.
    13. 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.
    14. Peng, Cheng & Yang, Yihe & Zhou, Jie & Pan, Jianxin, 2022. "Latent Gaussian copula models for longitudinal binary data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    15. Boukhiar, Souad & Mourid, Tahar, 2022. "Resolvent estimators for functional autoregressive processes with random coefficients," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    16. Zhang, Yuexia & Qin, Guoyou & Zhu, Zhongyi & Zhang, Jiajia, 2018. "Robust estimation in linear regression models for longitudinal data with covariate measurement errors and outliers," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 261-275.
    17. Berkes, István & Horváth, Lajos & Rice, Gregory, 2016. "On the asymptotic normality of kernel estimators of the long run covariance of functional time series," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 150-175.
    18. Liu, Xialu & Xiao, Han & Chen, Rong, 2016. "Convolutional autoregressive models for functional time series," Journal of Econometrics, Elsevier, vol. 194(2), pages 263-282.
    19. Gheriballah, Abdelkader & Laksaci, Ali & Sekkal, Soumeya, 2013. "Nonparametric M-regression for functional ergodic data," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 902-908.
    20. Kangning Wang & Wen Shan, 2021. "Copula and composite quantile regression-based estimating equations for longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 441-455, 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:spr:stmapp:v:28:y:2019:i:4:d:10.1007_s10260-019-00457-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.