A FUNCTIONAL VERSION OF THE ARCH MODEL
Lajos Horvath and
Econometric Theory, 2013, vol. 29, issue 02, 267-288
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.
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