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Zbl 1032.62086
Shumway, Robert H.
Dynamic mixed models for irregularly observed time series. (English)
[J] Resen. Inst. Mat. Estat. Univ. São Paulo 4, No.4, 433-456 (2000). ISSN 0104-3854

Summary: We review the conventional dynamic linear model in state-space form and give a useful generalzation that admits fixed covariates to the measurement equation while treating the state vectors as time-varying random effects. What results is a time series analogue of the classical mixed model. The approach allows vector responses that can be incomplete and provides interpolated values for the missing components of the time sequenced vectors as well as maximum likelihood estimators for the model parameters.\par Estimators for the fixed covariate parameters and for the measurement matrix are derived. The Kalman filters and smoothers are applied to this model and produce best linear unbiased predictors for the time correlated random components, leading to a solution to the signal extraction problem. The results are illustrated for several environmental series involving stream-flows and pesticide concentrations.

MSC 2000:: *62M10 Time series, etc. (statistics)
62M20 Prediction, etc. (statistics)
62F10 Point estimation

Keywords: state-space model; EM algorithm; signal extraction; Kalman filter; smoother; missing data; benchmarks; stream-flows; pesticide levels

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Zentralblatt MATH Berlin [Germany]