It is well known that no strongly harmonizable S S process assumes classical ARMA representation with respect to a SalphaS noise sequence with independent values. In this article we introduce certain strongly harmonizable ARMA SalphaS models, in which the noise sequences have orthogonal values in certain Hilbert spaces. Our study on strongly harmonizable ARMA SalphaS models involves parameter estimation, simulation, moving average representation, regularity and prediction. We generate the corresponding noise
series, that appear to be challenging and interesting.
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