Applicability of Kalman filtering theory to identification of time series with non-stationary covariance structures

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Abstract
A need exists for the accurate identification of time series models having fast time–varying parameters. Recent work by Kitagawa and Gersch (1985) provides a comprehensive powerful algorithm for such non-stationary identification but leaves some of the theoretical foundations incomplete. The present paper clarifies some of the complicating factors concerning this algorithm to establish its optimality and stability. Among these are the non-linear and time-varying nature of the formulation. It is shown that this non-stationary identifier's estimate exists and is stable. Proofs are reviewed that show the identifier is optimal for gaussian noise inputs and is also optimal over a limited class of identifiers for non–gaussian noise inputs and for the mean squared error loss function.

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