Functional Ergodic Time Series Analysis Using Expectile Regression

Abstract

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.

Keywords

• functional ergodic data
• recursive estimator
• complete convergence (a.co.)
• expectile function
• kernel method
• bandwidth parameter