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A FUNCTIONAL VERSION OF THE ARCH MODEL

Published online by Cambridge University Press:  31 July 2012

Siegfried Hörmann ,
Lajos Horváth  and
Ron Reeder
Siegfried Hörmann*
Affiliation:
Université Libre de Bruxelles
Lajos Horváth
Affiliation:
University of Utah
Ron Reeder
Affiliation:
University of Utah
*
*Address correspondence to Siegfried Hörmann, Départment de Mathématique, Université Libre de Bruxelles, CP 215, Boulevard du Triomphe, B-1050 Bruxelles, Belgium; e-mail: shormann@ulb.ac.be.
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Abstract

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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.

Information

Type
Articles
Information
Econometric Theory , Volume 29 , Issue 2 , April 2013 , pp. 267 - 288
Copyright
Copyright © Cambridge University Press 2012 

Footnotes

Research by Siegfried Hörmann was partially supported by the Banque National de Belgique and Communauté française de Belgique - Actions de Recherche Concertées (2010–2015). Research by Lajos Horváth and Ron Reeder was partially supported by NSF grant DMS 0905400.

References

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