2011/05/02 by Siegfried Hörmann, Siegfried Hormann, Hormann, Siegfried +5 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistics Theory (math.ST) #Stock Market Forecasting Methods #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1105.0343
arxiv created 2011/05/02 · openalex publication_date 2011/05/02 · arxiv updated 2011/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Improvements in data acquisition and processing techniques have lead 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 ARCH 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.