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Functional Ergodic Time Series Analysis Using Expectile Regression

Author

Listed:
  • Fatimah Alshahrani

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia)

  • Ibrahim M. Almanjahie

    (Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia
    Statistical Research and Studies Support Unit, King Khalid University, Abha 62529, Saudi Arabia)

  • Zouaoui Chikr Elmezouar

    (Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia)

  • Zoulikha Kaid

    (Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia)

  • Ali Laksaci

    (Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia)

  • Mustapha Rachdi

    (Laboratory AGEIS, University of Grenoble Alpes (France), EA 7407, AGIM Team, UFR SHS, BP. 47, CEDEX 09, F38040 Grenoble, France)

Abstract

In this article, we study the problem of the recursive estimator of the expectile regression of a scalar variable Y given a random variable X that belongs in functional space. We construct a new estimator and study the asymptotic properties over a general functional time structure. Precisely, the strong consistency of this estimator is established, considering that the sampled observations are taken from an ergodic functional process. Next, a simulation experiment is conducted to highlight the great impact of the constructed estimator as well as the ergodic functional time series data. Finally, a real data analysis is used to demonstrate the superiority of the constructed estimator.

Suggested Citation

  • Fatimah Alshahrani & Ibrahim M. Almanjahie & Zouaoui Chikr Elmezouar & Zoulikha Kaid & Ali Laksaci & Mustapha Rachdi, 2022. "Functional Ergodic Time Series Analysis Using Expectile Regression," Mathematics, MDPI, vol. 10(20), pages 1-17, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3919-:d:950049
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    References listed on IDEAS

    as
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    10. Ali Laksaci & Salah Khardani & Sihem Semmar, 2022. "Semi-recursive kernel conditional density estimators under random censorship and dependent data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(7), pages 2116-2138, April.
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    Cited by:

    1. Tzung Hsuen Khoo & Dharini Pathmanathan & Sophie Dabo-Niang, 2023. "Spatial Autocorrelation of Global Stock Exchanges Using Functional Areal Spatial Principal Component Analysis," Mathematics, MDPI, vol. 11(3), pages 1-24, January.
    2. Litimein, Ouahiba & Laksaci, Ali & Ait-Hennani, Larbi & Mechab, Boubaker & Rachdi, Mustapha, 2024. "Asymptotic normality of the local linear estimator of the functional expectile regression," Journal of Multivariate Analysis, Elsevier, vol. 202(C).

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