A FUNCTIONAL VERSION OF THE ARCH MODEL
将流行的ARCH模型扩展到函数型数据框架，研究高频金融数据，给出严格平稳解的存在条件、弱相依性和矩条件，证明估计量的一致性，并用实证研究验证模型与真实数据的匹配。
Improvements in data acquisition and processing techniques have led to an almost continuous flow of information for financial data. High-resolution tick data are available and can be quite conveniently described by a continuous-time process. It is therefore natural to ask for possible extensions of financial time series models to a functional setup. In this paper we propose a functional version of the popular autoregressive conditional heteroskedasticity model. We will establish conditions for the existence of a strictly stationary solution, derive weak dependence and moment conditions, show consistency of the estimators, and perform a small empirical study demonstrating how our model matches with real data.