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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
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    Citations

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    Cited by:

    1. Xiaorong Yang & Jia Chen & Degui Li & Runze Li, 2023. "Functional-Coefficient Quantile Regression for Panel Data with Latent Group Structure," Papers 2303.13218, arXiv.org.
    2. 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.
    3. 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.
    4. 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).
    5. 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).
    6. Elías, Antonio & Jiménez, Raúl & Shang, Han Lin, 2022. "On projection methods for functional time series forecasting," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    7. Richard Hunt & Shelton Peiris & Neville Weber, 2022. "Estimation methods for stationary Gegenbauer processes," Statistical Papers, Springer, vol. 63(6), pages 1707-1741, December.
    8. 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.
    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. 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.
    11. 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.
    12. Rituparna Sen & Anandamayee Majumdar & Shubhangi Sikaria, 2021. "Bayesian Testing Of Granger Causality In Functional Time Series," Papers 2112.15315, arXiv.org.
    13. Morten {O}rregaard Nielsen & Won-Ki Seo & Dakyung Seong, 2023. "Inference on common trends in functional time series," Papers 2312.00590, arXiv.org, revised Dec 2023.
    14. Cees Diks & Bram Wouters, 2023. "Noise reduction for functional time series," Papers 2307.02154, arXiv.org.
    15. 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).
    16. 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.
    17. Han Lin Shang, 2024. "Bootstrapping Long-Run Covariance of Stationary Functional Time Series," Forecasting, MDPI, vol. 6(1), pages 1-14, February.

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