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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.

The main aim of this paper is to consider a new risk metric that permits taking into account the spatial interactions of data. The considered risk metric explores the spatial tail-expectation of the data. Indeed, it is obtained by combining the ideas of expected shortfall regression with an expectile risk model. A spatio-functional Nadaraya–Watson estimator of the studied metric risk is constructed. The main asymptotic results of this work are the establishment of almost complete convergence under a mixed spatial structure. The claimed asymptotic result is obtained under standard assumptions covering the double functionality of the model as well as the data. The impact of the spatial interaction of the data in the proposed risk metric is evaluated using simulated data. A real experiment was conducted to measure the feasibility of the Spatio-Functional Expectile Shortfall Regression (SFESR) in practice.

This paper treats the problem of risk management through a new conditional expected shortfall function. The new risk metric is defined by the expectile as the shortfall threshold. A nonparametric estimator based on the Nadaraya–Watson approach is constructed. The asymptotic property of the constructed estimator is established using a functional time-series structure. We adopt some concentration inequalities to fit this complex structure and to precisely determine the convergence rate of the estimator. The easy implantation of the new risk metric is shown through real and simulated data. Specifically, we show the feasibility of the new model as a risk tool by examining its sensitivity to the fluctuation in financial time-series data. Finally, a comparative study between the new shortfall and the standard one is conducted using real data.

This paper deals with the problem of financial risk management using a new expected shortfall regression. The latter is based on the expectile model for financial risk-threshold. Unlike the VaR model, the expectile threshold is constructed by an asymmetric least square loss function. We construct an estimator of this new model using the k-nearest neighbors (kNN) smoothing approach. The mathematical properties of the constructed estimator are stated through the establishment of the pointwise complete convergence. Additionally, we prove that the constructed estimator is uniformly consistent over the nearest neighbors (UCNN). Such asymptotic results constitute a good mathematical support of the proposed financial risk process. Thus, we examine the easy implantation of this process through an artificial and real data. Our empirical analysis confirms the superiority of the kNN-approach over the kernel method as well as the superiority of the expectile over the quantile in financial risk analysis.

Analyzing the co-variability between the Hilbert regressor and the scalar output variable is crucial in functional statistics. In this contribution, the kernel smoothing of the Relative Error Regression (RE-regression) is used to resolve this problem. Precisely, we use the relative square error to establish an estimator of the Hilbertian regression. As asymptotic results, the Hilbertian observations are assumed to be quasi-associated, and we demonstrate the almost complete consistency of the constructed estimator. The feasibility of this Hilbertian model as a predictor in functional time series data is discussed. Moreover, we give some practical ideas for selecting the smoothing parameter based on the bootstrap procedure. Finally, an empirical investigation is performed to examine the behavior of the RE-regression estimation and its superiority in practice.

In this paper, we study the nonparametric estimation of the expected shortfall regression when the exogenous observation is functional. The constructed estimator is obtained by combining the double kernels estimator of both conditional value at risk and conditional density function. The asymptotic proprieties of this estimator are established under weak dependency condition. Precisely, we assume that the observations are generated from quasi-associated functional time series and we prove the almost complete convergence of the constructed estimator. This asymptotic result is obtained under a standard condition of functional time series analysis. The finite sample performance of this estimator is evaluated using artificial data.

In this article, we study the problem of the recursive estimator of the expectile regression of a scalar variable Y given a random variable X that belongs in functional space. We construct a new estimator and study the asymptotic properties over a general functional time structure. Precisely, the strong consistency of this estimator is established, considering that the sampled observations are taken from an ergodic functional process. Next, a simulation experiment is conducted to highlight the great impact of the constructed estimator as well as the ergodic functional time series data. Finally, a real data analysis is used to demonstrate the superiority of the constructed estimator.

Predicting the yearly curve of the temperature, based on meteorological data, is essential for understanding the impact of climate change on humans and the environment. The standard statistical models based on the big data discretization in the finite grid suffer from certain drawbacks such as dimensionality when the size of the data is large. We consider, in this paper, the predictive region problem in functional time series analysis. We study the prediction by the shortest conditional modal interval constructed by the local linear estimation of the cumulative function of $Y$Y given functional input variable $X$X . More precisely, we combine the $k$k -Nearest Neighbors procedure to the local linear algorithm to construct two estimators of the conditional distribution function. The main purpose of this paper is to compare, by a simulation study, the efficiency of the two estimators concerning the level of dependence. The feasibility of these estimators in the functional times series prediction is examined at the end of this paper. More precisely, we compare the shortest conditional modal interval predictive regions of both estimators using real meteorological data.

In this study, the problem of conditional density estimation of a scalar response variable, given a functional covariable, is considered. A new estimator is proposed by combining the k-nearest neighbors (k-N-N) procedure with the local linear approach. Then, the uniform consistency in the number of neighbors (UNN) of the proposed estimator is established. Such result is useful in the study of some data-driven rules. As a direct application and consequence of the conditional density estimation, we derive the UNN consistency of the conditional mode function estimator. Finally, to highlight the efficiency and superiority of the obtained results, we applied our new estimator to real data and compare it to its existing competitive estimator.