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

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.