On the spectrum of correlation autoregressive sequences

In this paper some properties of the correlation autoregressive (CAR) sequences are studied. A representation for the correlation function of an arbitrary CAR sequence is obtained and the relationship between a CAR equation and the growth of the variance and location of spectral lines is revealed. It is also observed that bounded correlation autoregressive sequences coincide with almost periodically correlated sequences with the spectral measure supported on finitely many lines. As a consequence a characterization of the spectrum of a bounded CAR sequence is provided.