*(English)*Zbl 1032.62086

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.

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:

62M10 | Time series, auto-correlation, regression, etc. (statistics) |

62M20 | Prediction; filtering (statistics) |

62F10 | Point estimation |