On the existence of Hilbert valued periodically correlated‎ autoregressive processes

نویسندگان

  • A. Parvardeh Department of Statistics‎, ‎Faculty of Sciences‎, ‎University of‎ ‎Isfahan‎, ‎Isfahan‎, ‎Iran.
  • N. Mohammadi Jouzdani Department of Mathematical‎ ‎Sciences‎, ‎Isfahan University of Technology‎, ‎Isfahan‎, ‎Iran‎.
  • S. Mahmoodi Department of Mathematical Sciences‎, ‎Isfahan‎ ‎University of Technology‎, ‎Isfahan‎, ‎Iran.
چکیده مقاله:

‎In this paper we provide sufficient condition for existence of a‎ ‎unique Hilbert valued ($mathbb{H}$-valued) periodically‎ ‎correlated solution to the first order autoregressive model‎ ‎$X_{n}=rho _{n}X_{n-1}+Z_{n}$‎, ‎for $nin mathbb{Z}$‎, ‎and‎ ‎formulate the existing solution and its autocovariance operator‎. ‎Also we specially investigate equivalent condition for the‎ ‎coordinate process $leftlangle X_{n},vrightrangle $‎, ‎for‎ ‎arbitrary element $v$ in $mathbb{H}$‎, ‎to satisfy in some‎ ‎autoregressive model‎. ‎Finally‎, ‎we extend our result to the‎ ‎autoregressive process with finite order‎.

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عنوان ژورنال

دوره 43  شماره 7

صفحات  2531- 2545

تاریخ انتشار 2017-12-30

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