First order autoregressive periodically correlated model in Banach spaces: Existence and central limit theorem.

We let B be a separable Banach space, and let { Z n } be a sequence of independent and identically distributed random elements in B . Then we prove that for a given strongly periodic sequence of bounded linear operators { ρ n } , the order one autoregressive system equations X n = ρ n X n − 1 + Z n , n in set on integers, possesses a unique almost sure strictly periodically correlated solution; under E [ log + ⁡ ‖ Z 0 ‖ ] < ∞ , which appears to be necessary as well. We proceed on to derive the limiting distribution of ∑ n = 1 N X n that appears to be a Gaussian distribution on B . We also provide interesting examples and observations. [ABSTRACT FROM AUTHOR]