On AR(1) models with periodic and almost periodic coefficients

This paper is concerned with the existence of bounded solutions to the system of equations X_n=a_nX_n−1+ξ_n, nZ, where ξ_n are uncorrelated constant variance zero mean random variables. We give necessary and sufficient conditions for boundedness in the general case and then specifically for periodic and almost periodic (a_n). This provides the first step in extending the periodic autoregressive models, for which boundedness is equivalent to the stationarity of the blocked vector sequence

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to the almost periodic case.