IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v115y2020i530p957-971.html
   My bibliography  Save this article

Long-Range Dependent Curve Time Series

Author

Listed:
  • Degui Li
  • Peter M. Robinson
  • Han Lin Shang

Abstract

We introduce methods and theory for functional or curve time series with long-range dependence. The temporal sum of the curve process is shown to be asymptotically normally distributed, the conditions for this covering a functional version of fractionally integrated autoregressive moving averages. We also construct an estimate of the long-run covariance function, which we use, via functional principal component analysis, in estimating the orthonormal functions spanning the dominant subspace of the curves. In a semiparametric context, we propose an estimate of the memory parameter and establish its consistency. A Monte Carlo study of finite-sample performance is included, along with two empirical applications. The first of these finds a degree of stability and persistence in intraday stock returns. The second finds similarity in the extent of long memory in incremental age-specific fertility rates across some developed nations. Supplementary materials for this article are available online.

Suggested Citation

  • Degui Li & Peter M. Robinson & Han Lin Shang, 2020. "Long-Range Dependent Curve Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(530), pages 957-971, April.
    • Handle: RePEc:taf:jnlasa:v:115:y:2020:i:530:p:957-971
    DOI: 10.1080/01621459.2019.1604362
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2019.1604362
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/01621459.2019.1604362?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xiaorong Yang & Jia Chen & Degui Li & Runze Li, 2024. "Functional-Coefficient Quantile Regression for Panel Data with Latent Group Structure," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(3), pages 1026-1040, July.
    2. Jin Seo Cho & Meng Huang & Halbert White, 2021. "Testing a Constant Mean Function Using Functional Regression," Working papers 2021rwp-190, Yonsei University, Yonsei Economics Research Institute.
    3. Rituparna Sen & Anandamayee Majumdar & Shubhangi Sikaria, 2022. "Bayesian Testing of Granger Causality in Functional Time Series," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 191-210, September.
    4. Degui Li & Peter M. Robinson & Han Lin Shang, 2021. "Local Whittle estimation of long‐range dependence for functional time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 685-695, September.
    5. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2023. "Functional Data Inference in a Parametric Quantile Model applied to Lifetime Income Curves," Working papers 2023rwp-211, Yonsei University, Yonsei Economics Research Institute.
    6. Chang, Jinyuan & Chen, Cheng & Qiao, Xinghao & Yao, Qiwei, 2023. "An autocovariance-based learning framework for high-dimensional functional time series," LSE Research Online Documents on Economics 117910, London School of Economics and Political Science, LSE Library.
    7. Han Lin Shang, 2024. "Bootstrapping Long-Run Covariance of Stationary Functional Time Series," Forecasting, MDPI, vol. 6(1), pages 1-14, February.
    8. Morten {O}rregaard Nielsen & Won-Ki Seo & Dakyung Seong, 2023. "Inference on common trends in functional time series," Papers 2312.00590, arXiv.org, revised May 2024.
    9. Rice, Gregory & Wirjanto, Tony & Zhao, Yuqian, 2023. "Exploring volatility of crude oil intraday return curves: A functional GARCH-X model," Journal of Commodity Markets, Elsevier, vol. 32(C).
    10. 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.
    11. Yang, Yang & Yang, Yanrong & Shang, Han Lin, 2022. "Feature extraction for functional time series: Theory and application to NIR spectroscopy data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    12. Sommerfeldt, Nelson & Pearce, Joshua M., 2023. "Can grid-tied solar photovoltaics lead to residential heating electrification? A techno-economic case study in the midwestern U.S," Applied Energy, Elsevier, vol. 336(C).
    13. Shang, Han Lin & Haberman, Steven & Xu, Ruofan, 2022. "Multi-population modelling and forecasting life-table death counts," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 239-253.
    14. Cees Diks & Bram Wouters, 2023. "Noise reduction for functional time series," Papers 2307.02154, arXiv.org.
    15. Elías, Antonio & Jiménez, Raúl & Shang, Han Lin, 2022. "On projection methods for functional time series forecasting," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    16. Meintanis, Simos G. & Hušková, Marie & Hlávka, Zdeněk, 2022. "Fourier-type tests of mutual independence between functional time series," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    17. Richard Hunt & Shelton Peiris & Neville Weber, 2022. "Estimation methods for stationary Gegenbauer processes," Statistical Papers, Springer, vol. 63(6), pages 1707-1741, December.

    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:taf:jnlasa:v:115:y:2020:i:530:p:957-971. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    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.