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Abstract
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Autoregressive Hilbertian (ARH) processes are of great importance in
the analysis of functional time series data and estimation of the autocorrelation operators attracts the attention of various researchers.
In this paper, we study estimators of the autocorrelation operators of periodically correlated autoregressive Hilbertian processes of
order one (PCARH(1)), which is an extension of ARH(1) processes.
The estimation method is based on the spectral decomposition of
the covariance operator and considers two main cases: known and
unknown eigenvectors. We show the consistency in the mean integrated quadratic sense of the estimators of the autocorrelation operators and present upper bounds for the corresponding rates.
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