On the invertibility conditions for moving average processes |
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Authors: | OD Anderson |
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Institution: | 1. Division of Statistics and Operational Research , Civil Service College , 11 Belgrave Road, London, SW1 V1RB, England;2. Department of Mathematics , University Park, Nottingham University , Nottingham, NG7 2RD, EnglandPresent address |
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Abstract: | Conditions for the general Moving Average process, of order q, to be invertible or borderline non-invertible are deduced. These are termed the acceptability conditions. It turns out that they depend on the magnitude of the final moving average parameter, θ q . If ‖θ q ‖ >1, the process is not acceptable. Should ‖θ q ‖ = 1, the conditions, for any particular q, follow simply - if use is made of the remainder theorem. When ‖θq‖< 1, an appeal is made to ROUCH* E'S theorem, to establish the conditions. Analogous stationarity results immediately follow for autoregressive processes. |
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Keywords: | Linear stationary process covariance estimate asymptotic distribution rate of convergence |
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