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Abstract
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This paper is devoted to a study on the structure of tensorial products of periodically
correlated autoregressive (PCAR) processes with values in separable Hilbert spaces. It will
be demonstrated that the resulting processes are PCAR with values in the space of Hilbert
Schmidt operators. These processes are applied while studying the convergence rate, limiting
behavior and asymptotic distribution of the empirical estimators of the covariance operators of
PCAR processes.
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