On the estimation of ARIMA Models with Missing Values
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The problem of defining a likelihood for a nonstationary ARIMA process is discussed, and several alternative approaches are shown to be equivalent. A new algorithm based on a modification of the Kalman filter is developed to compute the likelihood recursively under any pattern of missing data, including missing starting values. A new state space representation is developed which exploits the covariance structure more efficiently than other representations that have been proposed in the literature.
KeywordsARIMA processes maximum likelihood estimation missing values Kalman filter
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