Autoregressive representation for the empirical covariance operator of an ARH(1)

Authors
Bosq, D
Citation
D. Bosq, Autoregressive representation for the empirical covariance operator of an ARH(1), CR AC S I, 329(6), 1999, pp. 531-534
Citations number
10
Categorie Soggetti
Mathematics
Journal title
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE
ISSN journal
07644442 → ACNP
Volume
329
Issue
6
Year of publication
1999
Pages
531 - 534
Database
ISI
SICI code
0764-4442(19990915)329:6<531:ARFTEC>2.0.ZU;2-Z
Abstract
Given ail order 1 autoregressive process with values in a separable Hilbert space we show that its empirical covariance operator say C-n, is the empir ical mean of an autoregressive process which takes its values in the space of Hilbert-Schmidt operators with a noise which is an Hilbertian martingale difference. This allows to obtain precise results concerning the asymptoti c behaviour of C-n and its eigenvalues. (C) 1999 Academie des Sciences/Edit ions scientifiques et medicales Elsevier SAS.