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State equation

State equation. Observation equation. Y is q by 1 var ( w ) = Q var ( v ) = R. State. Summary of the past behavior of the system Markov Advantages of approach. parsimonious estimation smoothing, forecasting/prediction missing values random effects

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State equation

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  1. State equation Observation equation Y is q by 1 var(w) = Qvar(v) = R

  2. State. Summary of the past behavior of the system Markov Advantages of approach. parsimonious estimation smoothing, forecasting/prediction missing values random effects time varying measurement error multivariate fitting ARMA by mle aggregation/disaggregation structural breaks nonlinear variants control …

  3. r by 1 exogenous input u

  4. Example. Brillinger, Guckenheimer, Guttorp, Oster (1992) Density dependent birth and death rates Data, graphs of data

  5. Autoregressive. VAR(m) Var(W) =

  6. Biomedical example with missing values A t is either identity or all zeros in a row when variable is missing

  7. Global warming. drift

  8. Actually ARMA(1,1) !

  9. Example. Brillinger and Kaiser “NMR”

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