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

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.