{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T17:37:46Z","timestamp":1790617066418,"version":"4.1.0"},"reference-count":28,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2012,7,31]],"date-time":"2012-07-31T00:00:00Z","timestamp":1343692800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2013,4]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1017\/s0266466612000345","type":"journal-article","created":{"date-parts":[[2012,7,31]],"date-time":"2012-07-31T13:00:39Z","timestamp":1343739639000},"page":"267-288","source":"Crossref","is-referenced-by-count":95,"title":["A FUNCTIONAL VERSION OF THE ARCH 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