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G. Gardner, A. C. Harvey, G. D. A. Phillips, Algorithm AS 154: An Algorithm for Exact Maximum Likelihood Estimation of Autoregressive-Moving Average Models by Means of Kalman Filtering, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 29, No. 3 (1980), pp. 311-322
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Gardner et al. (1980) studied this question.
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