Strong consistency rate in functional single index expectile model for spatial data

Zouaoui Chikr Elmezouar; Fatimah Alshahrani; Ibrahim M. Almanjahie; Salim Bouzebda; Zoulikha Kaid; Ali Laksaci; Zouaoui Chikr Elmezouar; Fatimah Alshahrani; Ibrahim M. Almanjahie; Salim Bouzebda; Zoulikha Kaid; Ali Laksaci

doi:10.3934/math.2024269

AIMS Mathematics

2024, Volume 9, Issue 3: 5550-5581. doi: 10.3934/math.2024269

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Strong consistency rate in functional single index expectile model for spatial data

1.
Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia; zchikrelemezouar@kku.edu.sa, imalmanjahi@kku.edu.sa, zqayd@kku.edu.sa, alikfa@kku.edu.sa
2.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P. O. Box 84428, Riyadh 11671, Saudi Arabia; fmalshahrani@pnu.edu.sa
3.
Département Génie Informatique, LMAC (Laboratoire de Mathématiques Appliquées de Compiègne), Université de Technologie de Compiègne, Avenue de Landshut 57, France

Received: 12 December 2023 Revised: 17 January 2024 Accepted: 23 January 2024 Published: 29 January 2024
MSC : 62G05, 62G08, 62R20

Analyzing the real impact of spatial dependency in financial time series data is crucial to financial risk management. It has been a challenging issue in the last decade. This is because most financial transactions are performed via the internet and the spatial dependency between different international stock markets is not standard. The present paper investigates functional expectile regression as a spatial financial risk model. Specifically, we construct a nonparametric estimator of this functional model for the functional single index regression (FSIR) structure. The asymptotic properties of this estimator are elaborated over general spatial settings. More precisely, we establish Borel-Cantelli consistency (BCC) of the constructed estimator. The latter is obtained with the precision of the convergence rate. A simulation investigation is performed to show the easy applicability of the constructed estimator in practice. Finally, real data analysis about the financial data (Euro Stoxx-50 index data) is used to illustrate the effectiveness of our methodology.
- functional spatial data,
- complete convergence (a.co.),
- kernel estimator,
- expectile function,
- functional index,
- bandwidth parameter,
- financial risk management
Citation: Zouaoui Chikr Elmezouar, Fatimah Alshahrani, Ibrahim M. Almanjahie, Salim Bouzebda, Zoulikha Kaid, Ali Laksaci. Strong consistency rate in functional single index expectile model for spatial data[J]. AIMS Mathematics, 2024, 9(3): 5550-5581. doi: 10.3934/math.2024269

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Abstract

Analyzing the real impact of spatial dependency in financial time series data is crucial to financial risk management. It has been a challenging issue in the last decade. This is because most financial transactions are performed via the internet and the spatial dependency between different international stock markets is not standard. The present paper investigates functional expectile regression as a spatial financial risk model. Specifically, we construct a nonparametric estimator of this functional model for the functional single index regression (FSIR) structure. The asymptotic properties of this estimator are elaborated over general spatial settings. More precisely, we establish Borel-Cantelli consistency (BCC) of the constructed estimator. The latter is obtained with the precision of the convergence rate. A simulation investigation is performed to show the easy applicability of the constructed estimator in practice. Finally, real data analysis about the financial data (Euro Stoxx-50 index data) is used to illustrate the effectiveness of our methodology.

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