MOVING-AVERAGE REPRESENTATION OF AUTOREGRESSIVE APPROXIMATIONS

We study the properties of an MA(infinity)-representation of an autore gressive approximation for a stationary, real-valued process. In doing so we give an extension of Wiener's theorem in the deterministic appr oximation setup. When dealing with data, we can use this new key resul t to obtain insight into the structure of MA(infinity)-representations of fitted autoregressive models where the order increases with the sa mple size. In particular, we give a uniform bound for estimating the m oving-average coefficients via autoregressive approximation being unif orm over ail integers.