Inference on the asymptotic behavior of covariance operator of first-order periodically correlated autoregressive Hilbertian processes |
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Authors: | Hossein Haghbin Zohreh Shishebor |
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Institution: | 1. Department of Statistics, Faculty of Science, Persian Gulf University, Bushehr, Bushehr, Iran;2. Department of Statistics, Faculty of Science, Shiraz University, Shiraz, Fars, Iran |
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Abstract: | 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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Keywords: | Autoregressive Hilbertian processes Periodically correlated covariance operator |
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