Nonparametric multifunctional GARCH time series data analysis: Application to dynamic forecasting in financial data

Ali Laksaci; Fatimah Alshahrani; Ibrahim M. Almanjahie; Zoulikha Kaid; Ali Laksaci; Fatimah Alshahrani; Ibrahim M. Almanjahie; Zoulikha Kaid

doi:10.3934/math.20251163

AIMS Mathematics

2025, Volume 10, Issue 11: 26459-26483. doi: 10.3934/math.20251163

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Nonparametric multifunctional GARCH time series data analysis: Application to dynamic forecasting in financial data

1.
Department of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi Arabia
2.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

Received: 28 August 2025 Revised: 01 November 2025 Accepted: 04 November 2025 Published: 17 November 2025
MSC : 62G05, 62G08, 62R20

Financial risk management using the generalized autoregressive conditional heteroskedasticity model is a primordial topic in financial data analysis. It helps to improve risk assessment accuracy by taking into account the time-varying volatility. In this paper, we improved this feature by analyzing the functional nature of the high-frequency financial data. Specifically, we investigated the nonparametric estimation method of the multifunctional expectile function based on a kernel technique, developed the estimator, and established its stochastic consistency. The obtained asymptotic result provided a good mathematical foundation allowing us to enhance the expectile applicability in financial risk analysis. We assessed the algorithm's efficiency through empirical testing, and illustrated the practical value of expectile estimation in multi-asset risk management by applying it to real-world financial data with diverse scenarios.
- asymmetric error,
- expectile regression,
- value at risk,
- functional data,
- coherent measures,
- expected shortfall,
- risk mangement,
- prediction markets,
- big data analysis
Citation: Ali Laksaci, Fatimah Alshahrani, Ibrahim M. Almanjahie, Zoulikha Kaid. Nonparametric multifunctional GARCH time series data analysis: Application to dynamic forecasting in financial data[J]. AIMS Mathematics, 2025, 10(11): 26459-26483. doi: 10.3934/math.20251163

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Abstract

Financial risk management using the generalized autoregressive conditional heteroskedasticity model is a primordial topic in financial data analysis. It helps to improve risk assessment accuracy by taking into account the time-varying volatility. In this paper, we improved this feature by analyzing the functional nature of the high-frequency financial data. Specifically, we investigated the nonparametric estimation method of the multifunctional expectile function based on a kernel technique, developed the estimator, and established its stochastic consistency. The obtained asymptotic result provided a good mathematical foundation allowing us to enhance the expectile applicability in financial risk analysis. We assessed the algorithm's efficiency through empirical testing, and illustrated the practical value of expectile estimation in multi-asset risk management by applying it to real-world financial data with diverse scenarios.

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