On the existence of Hilbert valued periodically correlated autoregressive processes
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Abstract:
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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Journal title
volume 43 issue 7
pages 2531- 2545
publication date 2017-12-30
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