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Biometrika 1985 72(2):325-330; doi:10.1093/biomet/72.2.325
© 1985 by Biometrika Trust
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On the rate of convergence of the innovation representation of a moving average process

CRAIG F. ANSLEY and ROBERT KOHN

Graduate School of Business, University of Chicago Chicago, Illinois 60637, U.S.A.

A moving average process of order q can be written as a linear combination of the (q+1) most recent innovations. We show that if the moving average polynomial has roots on the unit circle, then the coefficients of the innovations tend to the true moving average coefficients, the difference between the two being O (1/t), where t is the number of observations we consider. The results are extended to mixed autoregressive moving average models and multivariate models.

Key Words: Cholesky factorization • Moving average • Time Series


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