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Nonparametric estimation of expectile regression in functional dependent data

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  • Ibrahim M. Almanjahie
  • Salim Bouzebda
  • Zoulikha Kaid
  • Ali Laksaci

Abstract

In this paper, the problem of the nonparametric estimation of the expectile regression model for strong mixing functional time series data is investigated. To be more precise, we establish the almost complete consistency and the asymptotic normality of the kernel-type expectile regression estimator under some mild conditions. The usefulness of our theoretical results in the financial time series analysis is discussed. Further, we provide some practical algorithms to select the smoothing parameter or to construct the confidence intervals using the bootstrap techniques. In addition, a simulation study is carried out to verify the small sample behaviour of the proposed approach. Finally, we give an empirical example using the daily returns of the stock index SP500.

Suggested Citation

  • Ibrahim M. Almanjahie & Salim Bouzebda & Zoulikha Kaid & Ali Laksaci, 2022. "Nonparametric estimation of expectile regression in functional dependent data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 34(1), pages 250-281, January.
    • Handle: RePEc:taf:gnstxx:v:34:y:2022:i:1:p:250-281
    DOI: 10.1080/10485252.2022.2027412
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    Citations

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    Cited by:

    1. Litimein, Ouahiba & Laksaci, Ali & Mechab, Boubaker & Bouzebda, Salim, 2023. "Local linear estimate of the functional expectile regression," Statistics & Probability Letters, Elsevier, vol. 192(C).
    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).
    3. Sultana DIDI & Ahoud AL HARBY & Salim BOUZEBDA, 2022. "Wavelet Density and Regression Estimators for Functional Stationary and Ergodic Data: Discrete Time," Mathematics, MDPI, vol. 10(19), pages 1-33, September.
    4. Salim Bouzebda & Boutheina Nemouchi, 2023. "Weak-convergence of empirical conditional processes and conditional U-processes involving functional mixing data," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 33-88, April.

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