On the structure of moving average processes |
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Authors: | Craig F. Ansley W.Allen Spivey William J. Wrobleski |
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Affiliation: | The University of Michigan, Ann Arbor, MI 48109, U.S.A. |
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Abstract: | This paper uses Hilbert space methods to develop a rigorous proof that the sum of two uncorrelated moving average processes of order q1 and q2 is an MA process of order q ≦ max (q1, q2). The methods establish the existence of suitable random shocks for the summed process, they illuminate relationships between the coefficients of such processes and their random shocks, and they provide means for proving that the random shocks of the summed processes are normal when the shocks of the underlying processes are normal. The role of the Wold decomposition is examined in terms of multiple representations of an MA process. |
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